<table><caption>Table 59: Bissection of problem 3D with problem: 8, type: MinFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>44.11e-6</td><td>20472</td><td>20472</td><td>05:41:12</td><td>229302217</td><td>89.28e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>382.8</td><td>946.9</td><td>1329</td><td>22:09</td><td>4457773</td><td>212.4e-6</td><td>infeasible</td><td>4.625</td><td>6.495</td><td>1.944</td></tr><tr><td>MinVariance</td><td>420.7</td><td>938.0</td><td>1358</td><td>22:38</td><td>4457773</td><td>210.4e-6</td><td>infeasible</td><td>4.582</td><td>6.637</td><td>1.944</td></tr><tr><td>BSplines</td><td>389.7</td><td>940.2</td><td>1329</td><td>22:09</td><td>4457773</td><td>210.9e-6</td><td>infeasible</td><td>4.592</td><td>6.496</td><td>1.944</td></tr><tr><td>MinNorm</td><td>413.5</td><td>933.1</td><td>1346</td><td>22:26</td><td>4457773</td><td>209.3e-6</td><td>infeasible</td><td>4.558</td><td>6.578</td><td>1.944</td></tr><tr><td>MinVolume</td><td>408.4</td><td>931.2</td><td>1339</td><td>22:19</td><td>4457773</td><td>208.9e-6</td><td>infeasible</td><td>4.549</td><td>6.544</td><td>1.944</td></tr><tr><td>ApproxMinVolume</td><td>401.3</td><td>923.6</td><td>1324</td><td>22:04</td><td>4457773</td><td>207.2e-6</td><td>infeasible</td><td>4.511</td><td>6.471</td><td>1.944</td></tr><tr><td rowspan="4">0.01</td><td>Recursive</td><td>386.9</td><td>929.1</td><td>1316</td><td>21:56</td><td>4457773</td><td>208.4e-6</td><td>infeasible</td><td>4.538</td><td>6.428</td><td>1.944</td></tr><tr><td>Recursive2</td><td>386.7</td><td>937.2</td><td>1323</td><td>22:03</td><td>4457773</td><td>210.2e-6</td><td>infeasible</td><td>4.578</td><td>6.467</td><td>1.944</td></tr><tr><td>Interval</td><td>34.09e-6</td><td>20489</td><td>20489</td><td>05:41:29</td><td>229302217</td><td>89.36e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>389.5</td><td>929.9</td><td>1319</td><td>21:59</td><td>4457773</td><td>208.6e-6</td><td>infeasible</td><td>4.538</td><td>6.439</td><td>1.944</td></tr><tr><td>MinVariance</td><td>426.9</td><td>939.2</td><td>1366</td><td>22:46</td><td>4457773</td><td>210.7e-6</td><td>infeasible</td><td>4.584</td><td>6.667</td><td>1.944</td></tr><tr><td>BSplines</td><td>395.9</td><td>934.2</td><td>1330</td><td>22:10</td><td>4457773</td><td>209.6e-6</td><td>infeasible</td><td>4.559</td><td>6.492</td><td>1.944</td></tr><tr><td>MinNorm</td><td>418.2</td><td>918.9</td><td>1337</td><td>22:17</td><td>4457773</td><td>206.1e-6</td><td>infeasible</td><td>4.485</td><td>6.526</td><td>1.944</td></tr><tr><td>MinVolume</td><td>416.1</td><td>922.2</td><td>1338</td><td>22:18</td><td>4457773</td><td>206.9e-6</td><td>infeasible</td><td>4.501</td><td>6.532</td><td>1.944</td></tr><tr><td>ApproxMinVolume</td><td>404.4</td><td>935.8</td><td>1340</td><td>22:20</td><td>4457773</td><td>209.9e-6</td><td>infeasible</td><td>4.567</td><td>6.541</td><td>1.944</td></tr><tr><td>Recursive</td><td>386.9</td><td>938.8</td><td>1325</td><td>22:05</td><td>4457773</td><td>210.6e-6</td><td>infeasible</td><td>4.582</td><td>6.470</td><td>1.944</td></tr><tr><td>Recursive2</td><td>388.3</td><td>937.0</td><td>1325</td><td>22:05</td><td>4457773</td><td>210.2e-6</td><td>infeasible</td><td>4.573</td><td>6.468</td><td>1.944</td></tr></tbody></table>

<table><caption>Table 60: Bissection of problem 3D with problem: 11, type: MinFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>30.04e-6</td><td>2707</td><td>2707</td><td>45:07</td><td>45914699</td><td>58.98e-6</td><td>386.24</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.74</td><td>1134</td><td>1230</td><td>20:30</td><td>9843397</td><td>115.3e-6</td><td>385.26</td><td>41.91</td><td>45.45</td><td>21.44</td></tr><tr><td>MinVariance</td><td>168.3</td><td>1481</td><td>1649</td><td>27:29</td><td>11424189</td><td>129.7e-6</td><td>385.34</td><td>54.70</td><td>60.91</td><td>24.88</td></tr><tr><td>BSplines</td><td>101.4</td><td>5195</td><td>5297</td><td>01:28:17</td><td>49085549</td><td>105.9e-6</td><td>386.51</td><td>191.9</td><td>195.6</td><td>106.9</td></tr><tr><td>MinNorm</td><td>160.8</td><td>1350</td><td>1511</td><td>25:11</td><td>10714959</td><td>126.1e-6</td><td>385.30</td><td>49.89</td><td>55.83</td><td>23.34</td></tr><tr><td>MinVolume</td><td>158.2</td><td>1621</td><td>1780</td><td>29:40</td><td>13020547</td><td>124.6e-6</td><td>385.41</td><td>59.89</td><td>65.73</td><td>28.36</td></tr><tr><td>ApproxMinVolume</td><td>155.3</td><td>1614</td><td>1769</td><td>29:29</td><td>13067405</td><td>123.5e-6</td><td>385.41</td><td>59.61</td><td>65.34</td><td>28.46</td></tr><tr><td>Recursive</td><td>111.0</td><td>1151</td><td>1262</td><td>21:02</td><td>9867833</td><td>116.7e-6</td><td>385.26</td><td>42.52</td><td>46.62</td><td>21.49</td></tr><tr><td>Recursive2</td><td>127.0</td><td>1183</td><td>1310</td><td>21:50</td><td>9894687</td><td>119.6e-6</td><td>385.26</td><td>43.69</td><td>48.38</td><td>21.55</td></tr><tr><td rowspan="7">0.01</td><td>Interval</td><td>38.15e-6</td><td>57.04</td><td>57.04</td><td>57:041</td><td>904577</td><td>63.06e-6</td><td>414.99</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>96.51</td><td>26.38</td><td>122.9</td><td>02:02</td><td>206623</td><td>127.7e-6</td><td>404.04</td><td>46.25</td><td>215.4</td><td>22.84</td></tr><tr><td>MinVariance</td><td>167.6</td><td>30.91</td><td>198.5</td><td>03:18</td><td>225459</td><td>137.1e-6</td><td>405.30</td><td>54.18</td><td>348.0</td><td>24.92</td></tr><tr><td>BSplines</td><td>101.7</td><td>62.87</td><td>164.5</td><td>02:44</td><td>482219</td><td>130.4e-6</td><td>425.62</td><td>110.2</td><td>288.5</td><td>53.31</td></tr><tr><td>MinNorm</td><td>160.2</td><td>30.28</td><td>190.5</td><td>03:10</td><td>216861</td><td>139.6e-6</td><td>404.71</td><td>53.09</td><td>334.0</td><td>23.97</td></tr><tr><td>MinVolume</td><td>157.8</td><td>34.23</td><td>192.1</td><td>03:12</td><td>249181</td><td>137.4e-6</td><td>406.55</td><td>60.02</td><td>336.7</td><td>27.55</td></tr><tr><td>ApproxMinVolume</td><td>155.3</td><td>34.20</td><td>189.5</td><td>03:09</td><td>250067</td><td>136.8e-6</td><td>406.58</td><td>59.95</td><td>332.2</td><td>27.64</td></tr><tr><td>Recursive</td><td>111.0</td><td>27.43</td><td>138.4</td><td>02:18</td><td>212409</td><td>129.1e-6</td><td>404.04</td><td>48.08</td><td>242.6</td><td>23.48</td></tr><tr><td>Recursive2</td><td>127.1</td><td>28.06</td><td>155.1</td><td>02:35</td><td>212551</td><td>132.0e-6</td><td>404.04</td><td>49.18</td><td>271.9</td><td>23.50</td></tr></tbody></table>

<table><caption>Table 61: Bissection of problem 3D with problem: 12, type: MinFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>37.19e-6</td><td>1.540</td><td>1.540</td><td>1.540</td><td>24393</td><td>63.12e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.87</td><td>194.0e-3</td><td>96.06</td><td>01:36</td><td>4157</td><td>46.67e-6</td><td>infeasible</td><td>12.60</td><td>6239.1</td><td>17.04</td></tr><tr><td>MinVariance</td><td>165.1</td><td>726.8e-3</td><td>165.9</td><td>02:45</td><td>4157</td><td>174.8e-6</td><td>infeasible</td><td>47.21</td><td>10773.4</td><td>17.04</td></tr><tr><td>BSplines</td><td>101.7</td><td>203.3e-3</td><td>101.9</td><td>01:41</td><td>4157</td><td>48.90e-6</td><td>infeasible</td><td>13.20</td><td>6618.2</td><td>17.04</td></tr><tr><td>MinNorm</td><td>158.6</td><td>176.1e-3</td><td>158.8</td><td>02:38</td><td>4157</td><td>42.36e-6</td><td>infeasible</td><td>11.44</td><td>10312.5</td><td>17.04</td></tr><tr><td>MinVolume</td><td>156.9</td><td>220.1e-3</td><td>157.1</td><td>02:37</td><td>4157</td><td>52.94e-6</td><td>infeasible</td><td>14.29</td><td>10204.0</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>154.2</td><td>193.7e-3</td><td>154.4</td><td>02:34</td><td>4157</td><td>46.59e-6</td><td>infeasible</td><td>12.58</td><td>10030.7</td><td>17.04</td></tr><tr><td>Recursive</td><td>111.2</td><td>225.8e-3</td><td>111.4</td><td>01:51</td><td>4157</td><td>54.32e-6</td><td>infeasible</td><td>14.67</td><td>7234.2</td><td>17.04</td></tr><tr><td>Recursive2</td><td>127.1</td><td>191.5e-3</td><td>127.3</td><td>02:07</td><td>4157</td><td>46.06e-6</td><td>infeasible</td><td>12.44</td><td>8269.5</td><td>17.04</td></tr><tr><td rowspan="7">0.01</td><td>Interval</td><td>31.95e-6</td><td>1.542</td><td>1.542</td><td>1.542</td><td>24393</td><td>63.20e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.76</td><td>194.4e-3</td><td>95.95</td><td>01:35</td><td>4157</td><td>46.77e-6</td><td>infeasible</td><td>12.61</td><td>6224.1</td><td>17.04</td></tr><tr><td>MinVariance</td><td>168.1</td><td>179.8e-3</td><td>168.3</td><td>02:48</td><td>4157</td><td>43.24e-6</td><td>infeasible</td><td>11.66</td><td>10918.0</td><td>17.04</td></tr><tr><td>BSplines</td><td>101.6</td><td>237.9e-3</td><td>101.8</td><td>01:41</td><td>4157</td><td>57.24e-6</td><td>infeasible</td><td>15.43</td><td>6603.2</td><td>17.04</td></tr><tr><td>MinNorm</td><td>161.2</td><td>181.0e-3</td><td>161.4</td><td>02:41</td><td>4157</td><td>43.54e-6</td><td>infeasible</td><td>11.74</td><td>10468.7</td><td>17.04</td></tr><tr><td>MinVolume</td><td>159.0</td><td>195.0e-3</td><td>159.2</td><td>02:39</td><td>4157</td><td>46.90e-6</td><td>infeasible</td><td>12.65</td><td>10323.8</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>156.6</td><td>197.7e-3</td><td>156.8</td><td>02:36</td><td>4157</td><td>47.55e-6</td><td>infeasible</td><td>12.82</td><td>10171.4</td><td>17.04</td></tr><tr><td>Recursive</td><td>111.1</td><td>190.6e-3</td><td>111.2</td><td>01:51</td><td>4157</td><td>45.85e-6</td><td>infeasible</td><td>12.36</td><td>7216.4</td><td>17.04</td></tr><tr><td>Recursive2</td><td>127.3</td><td>193.1e-3</td><td>127.5</td><td>02:07</td><td>4157</td><td>46.46e-6</td><td>infeasible</td><td>12.53</td><td>8271.8</td><td>17.04</td></tr></tbody></table>

<table><caption>Table 62: Bissection of problem 3D with problem: 13, type: MinFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>48.88e-6</td><td>2639</td><td>2639</td><td>43:59</td><td>45913293</td><td>57.50e-6</td><td>386.24</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.83</td><td>1133</td><td>1229</td><td>20:29</td><td>9843061</td><td>115.2e-6</td><td>385.26</td><td>42.94</td><td>46.57</td><td>21.44</td></tr><tr><td>MinVariance</td><td>168.4</td><td>1480</td><td>1649</td><td>27:29</td><td>11423655</td><td>129.6e-6</td><td>385.34</td><td>56.09</td><td>62.47</td><td>24.88</td></tr><tr><td>BSplines</td><td>101.6</td><td>5213</td><td>5315</td><td>01:28:35</td><td>49081787</td><td>106.2e-6</td><td>386.51</td><td>197.5</td><td>201.3</td><td>106.9</td></tr><tr><td>MinNorm</td><td>160.3</td><td>1357</td><td>1517</td><td>25:17</td><td>10714497</td><td>126.7e-6</td><td>385.30</td><td>51.43</td><td>57.50</td><td>23.34</td></tr><tr><td>MinVolume</td><td>158.1</td><td>1607</td><td>1765</td><td>29:25</td><td>13019791</td><td>123.5e-6</td><td>385.41</td><td>60.89</td><td>66.88</td><td>28.36</td></tr><tr><td>ApproxMinVolume</td><td>155.2</td><td>1604</td><td>1760</td><td>29:20</td><td>13066645</td><td>122.8e-6</td><td>385.41</td><td>60.80</td><td>66.68</td><td>28.46</td></tr><tr><td>Recursive</td><td>110.8</td><td>1154</td><td>1264</td><td>21:04</td><td>9867101</td><td>117.0e-6</td><td>385.26</td><td>43.71</td><td>47.91</td><td>21.49</td></tr><tr><td>Recursive2</td><td>127.3</td><td>1186</td><td>1313</td><td>21:53</td><td>9893863</td><td>119.9e-6</td><td>385.26</td><td>44.94</td><td>49.76</td><td>21.55</td></tr><tr><td rowspan="7">0.01</td><td>Interval</td><td>38.86e-6</td><td>56.72</td><td>56.72</td><td>56:716</td><td>902467</td><td>62.85e-6</td><td>414.99</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.55</td><td>26.57</td><td>122.1</td><td>02:02</td><td>205055</td><td>129.6e-6</td><td>404.04</td><td>46.84</td><td>215.3</td><td>22.72</td></tr><tr><td>MinVariance</td><td>167.4</td><td>30.63</td><td>198.0</td><td>03:18</td><td>223755</td><td>136.9e-6</td><td>405.30</td><td>54.00</td><td>349.2</td><td>24.79</td></tr><tr><td>BSplines</td><td>101.6</td><td>62.13</td><td>163.7</td><td>02:43</td><td>475861</td><td>130.6e-6</td><td>425.62</td><td>109.6</td><td>288.7</td><td>52.73</td></tr><tr><td>MinNorm</td><td>160.6</td><td>29.83</td><td>190.4</td><td>03:10</td><td>215179</td><td>138.6e-6</td><td>404.71</td><td>52.59</td><td>335.7</td><td>23.84</td></tr><tr><td>MinVolume</td><td>157.8</td><td>33.92</td><td>191.7</td><td>03:11</td><td>247349</td><td>137.2e-6</td><td>406.55</td><td>59.82</td><td>338.1</td><td>27.41</td></tr><tr><td>ApproxMinVolume</td><td>155.9</td><td>34.20</td><td>190.1</td><td>03:10</td><td>248235</td><td>137.8e-6</td><td>406.58</td><td>60.30</td><td>335.1</td><td>27.51</td></tr><tr><td>Recursive</td><td>110.8</td><td>27.28</td><td>138.1</td><td>02:18</td><td>210455</td><td>129.6e-6</td><td>404.04</td><td>48.11</td><td>243.5</td><td>23.32</td></tr><tr><td>Recursive2</td><td>127.0</td><td>27.85</td><td>154.9</td><td>02:34</td><td>210501</td><td>132.3e-6</td><td>404.04</td><td>49.10</td><td>273.1</td><td>23.33</td></tr></tbody></table>
<table><caption>Table 63: Bissection of problem 3D with problem: 14, type: MinFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep_time</th><th>comput_time</th><th>total_time</th><th>(D-H:M:S.ms)</th><th>nb_iter</th><th>time_per_iter</th><th>criteria</th><th>comput_time (%)</th><th>total_time (%)</th><th>nb_iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>32.90e-6</td><td>974.3e-3</td><td>974.3e-3</td><td>0.974</td><td>15151</td><td>64.30e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.81</td><td>206.5e-3</td><td>96.02</td><td>01:36</td><td>2207</td><td>93.56e-6</td><td>infeasible</td><td>21.19</td><td>9854.8</td><td>14.57</td></tr><tr><td>MinVariance</td><td>165.0</td><td>192.6e-3</td><td>165.2</td><td>02:45</td><td>2207</td><td>87.26e-6</td><td>infeasible</td><td>19.77</td><td>16953.6</td><td>14.57</td></tr><tr><td>BSplines</td><td>101.7</td><td>244.6e-3</td><td>101.9</td><td>01:41</td><td>2637</td><td>92.76e-6</td><td>infeasible</td><td>25.11</td><td>10462.9</td><td>17.40</td></tr><tr><td>MinNorm</td><td>159.1</td><td>195.2e-3</td><td>159.3</td><td>02:39</td><td>2205</td><td>88.52e-6</td><td>infeasible</td><td>20.03</td><td>16345.5</td><td>14.55</td></tr><tr><td>MinVolume</td><td>156.8</td><td>204.9e-3</td><td>157.0</td><td>02:36</td><td>2257</td><td>90.78e-6</td><td>infeasible</td><td>21.03</td><td>16111.2</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>154.6</td><td>211.2e-3</td><td>154.8</td><td>02:34</td><td>2257</td><td>93.58e-6</td><td>infeasible</td><td>21.68</td><td>15890.1</td><td>14.90</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>111.4</td><td>213.3e-3</td><td>111.6</td><td>01:51</td><td>2285</td><td>93.35e-6</td><td>infeasible</td><td>21.89</td><td>11453.0</td><td>15.08</td></tr><tr><td>Recursive2</td><td>127.0</td><td>215.6e-3</td><td>127.2</td><td>02:07</td><td>2309</td><td>93.38e-6</td><td>infeasible</td><td>22.13</td><td>13057.4</td><td>15.24</td></tr><tr><td>Interval</td><td>37.19e-6</td><td>898.6e-3</td><td>898.6e-3</td><td>0.899</td><td>15151</td><td>59.31e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.74</td><td>205.7e-3</td><td>95.94</td><td>01:35</td><td>2207</td><td>93.18e-6</td><td>infeasible</td><td>22.89</td><td>10676.9</td><td>14.57</td></tr><tr><td>MinVariance</td><td>168.1</td><td>199.1e-3</td><td>168.3</td><td>02:48</td><td>2207</td><td>90.23e-6</td><td>infeasible</td><td>22.16</td><td>18726.3</td><td>14.57</td></tr><tr><td>BSplines</td><td>101.7</td><td>244.8e-3</td><td>101.9</td><td>01:41</td><td>2637</td><td>92.83e-6</td><td>infeasible</td><td>27.24</td><td>11344.3</td><td>17.40</td></tr><tr><td>MinNorm</td><td>161.7</td><td>203.3e-3</td><td>161.9</td><td>02:41</td><td>2205</td><td>92.21e-6</td><td>infeasible</td><td>22.63</td><td>18015.7</td><td>14.55</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>159.1</td><td>212.3e-3</td><td>159.3</td><td>02:39</td><td>2257</td><td>94.08e-6</td><td>infeasible</td><td>23.63</td><td>17726.8</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>156.0</td><td>218.1e-3</td><td>156.2</td><td>02:36</td><td>2257</td><td>96.64e-6</td><td>infeasible</td><td>24.27</td><td>17386.0</td><td>14.90</td></tr><tr><td>Recursive</td><td>110.7</td><td>214.1e-3</td><td>110.9</td><td>01:50</td><td>2285</td><td>93.70e-6</td><td>infeasible</td><td>23.83</td><td>12343.3</td><td>15.08</td></tr><tr><td>Recursive2</td><td>127.3</td><td>217.6e-3</td><td>127.6</td><td>02:07</td><td>2309</td><td>94.26e-6</td><td>infeasible</td><td>24.22</td><td>14195.0</td><td>15.24</td></tr></tbody></table>

<table><caption>Table 64: Bissection of problem 3D with problem: 1, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep_time</th><th>comput_time</th><th>total_time</th><th>(D-H:M:S.ms)</th><th>nb_iter</th><th>time_per_iter</th><th>criteria</th><th>comput_time (%)</th><th>total_time (%)</th><th>nb_iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>32.90e-6</td><td>83.36</td><td>83.36</td><td>01:23</td><td>1316157</td><td>63.34e-6</td><td>2.6120</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>88.95</td><td>7.566</td><td>96.51</td><td>01:36</td><td>385193</td><td>19.64e-6</td><td>2.6084</td><td>9.077</td><td>115.8</td><td>29.27</td></tr><tr><td>MinVariance</td><td>163.1</td><td>7.736</td><td>170.9</td><td>02:50</td><td>427167</td><td>18.11e-6</td><td>2.6086</td><td>9.280</td><td>205.0</td><td>32.46</td></tr><tr><td>BSplines</td><td>96.59</td><td>18.74</td><td>115.3</td><td>01:55</td><td>1112923</td><td>16.84e-6</td><td>2.6100</td><td>22.48</td><td>138.3</td><td>84.56</td></tr><tr><td>MinNorm</td><td>158.1</td><td>7.797</td><td>165.9</td><td>02:45</td><td>407805</td><td>19.12e-6</td><td>2.6085</td><td>9.353</td><td>199.1</td><td>30.98</td></tr><tr><td>MinVolume</td><td>151.4</td><td>9.076</td><td>160.5</td><td>02:40</td><td>471811</td><td>19.24e-6</td><td>2.6087</td><td>10.89</td><td>192.5</td><td>35.85</td></tr><tr><td>ApproxMinVolume</td><td>148.4</td><td>9.325</td><td>157.7</td><td>02:37</td><td>472951</td><td>19.72e-6</td><td>2.6087</td><td>11.19</td><td>189.2</td><td>35.93</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>105.7</td><td>7.580</td><td>113.2</td><td>01:53</td><td>385813</td><td>19.65e-6</td><td>2.6084</td><td>9.093</td><td>135.8</td><td>29.31</td></tr><tr><td>Recursive2</td><td>121.0</td><td>7.656</td><td>128.6</td><td>02:08</td><td>386967</td><td>19.79e-6</td><td>2.6084</td><td>9.184</td><td>154.3</td><td>29.40</td></tr><tr><td>Interval</td><td>40.05e-6</td><td>9.641</td><td>9.641</td><td>9.641</td><td>154829</td><td>62.27e-6</td><td>2.7144</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>89.73</td><td>1.042</td><td>90.77</td><td>01:30</td><td>37321</td><td>27.91e-6</td><td>2.6766</td><td>10.80</td><td>941.5</td><td>24.10</td></tr><tr><td>MinVariance</td><td>158.9</td><td>1.079</td><td>159.9</td><td>02:39</td><td>39779</td><td>27.12e-6</td><td>2.6783</td><td>11.19</td><td>1659.0</td><td>25.69</td></tr><tr><td>BSplines</td><td>95.82</td><td>1.864</td><td>97.69</td><td>01:37</td><td>68765</td><td>27.11e-6</td><td>2.6975</td><td>19.33</td><td>1013.3</td><td>44.41</td></tr><tr><td>MinNorm</td><td>153.8</td><td>1.050</td><td>154.8</td><td>02:34</td><td>38621</td><td>27.18e-6</td><td>2.6775</td><td>10.89</td><td>1605.8</td><td>24.94</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>148.3</td><td>1.140</td><td>149.4</td><td>02:29</td><td>42283</td><td>26.96e-6</td><td>2.6799</td><td>11.82</td><td>1549.6</td><td>27.31</td></tr><tr><td>ApproxMinVolume</td><td>145.8</td><td>1.200</td><td>147.0</td><td>02:26</td><td>42337</td><td>28.34e-6</td><td>2.6799</td><td>12.45</td><td>1524.4</td><td>27.34</td></tr><tr><td>Recursive</td><td>104.8</td><td>1.065</td><td>105.9</td><td>01:45</td><td>37933</td><td>28.07e-6</td><td>2.6766</td><td>11.04</td><td>1098.5</td><td>24.50</td></tr><tr><td>Recursive2</td><td>119.5</td><td>1.102</td><td>120.6</td><td>02:00</td><td>38543</td><td>28.59e-6</td><td>2.6766</td><td>11.43</td><td>1251.2</td><td>24.89</td></tr></tbody></table>

<table><caption>Table 65: Bissection of problem 3D with problem: 2, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep_time</th><th>comput_time</th><th>total_time</th><th>(D-H:M:S.ms)</th><th>nb_iter</th><th>time_per_iter</th><th>criteria</th><th>comput_time (%)</th><th>total_time (%)</th><th>nb_iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>50.07e-6</td><td>1.566</td><td>1.566</td><td>1.566</td><td>24393</td><td>64.20e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>89.68</td><td>191.4e-3</td><td>89.87</td><td>01:29</td><td>4157</td><td>46.03e-6</td><td>infeasible</td><td>12.22</td><td>5738.2</td><td>17.04</td></tr><tr><td>MinVariance</td><td>162.6</td><td>181.7e-3</td><td>162.8</td><td>02:42</td><td>4157</td><td>43.72e-6</td><td>infeasible</td><td>11.60</td><td>10395.7</td><td>17.04</td></tr><tr><td>BSplines</td><td>95.47</td><td>200.5e-3</td><td>95.67</td><td>01:35</td><td>4157</td><td>48.24e-6</td><td>infeasible</td><td>12.81</td><td>6108.6</td><td>17.04</td></tr><tr><td>MinNorm</td><td>154.5</td><td>182.3e-3</td><td>154.7</td><td>02:34</td><td>4157</td><td>43.85e-6</td><td>infeasible</td><td>11.64</td><td>9878.3</td><td>17.04</td></tr><tr><td>MinVolume</td><td>148.7</td><td>186.8e-3</td><td>148.8</td><td>02:28</td><td>4157</td><td>44.93e-6</td><td>infeasible</td><td>11.93</td><td>9504.4</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>146.0</td><td>196.3e-3</td><td>146.2</td><td>02:26</td><td>4157</td><td>47.23e-6</td><td>infeasible</td><td>12.54</td><td>9336.1</td><td>17.04</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>105.2</td><td>189.2e-3</td><td>105.4</td><td>01:45</td><td>4157</td><td>45.52e-6</td><td>infeasible</td><td>12.08</td><td>6730.9</td><td>17.04</td></tr><tr><td>Recursive2</td><td>119.4</td><td>188.7e-3</td><td>119.6</td><td>01:59</td><td>4157</td><td>45.39e-6</td><td>infeasible</td><td>12.05</td><td>7634.1</td><td>17.04</td></tr><tr><td>Interval</td><td>27.89e-6</td><td>1.520</td><td>1.521</td><td>1.521</td><td>24393</td><td>62.33e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>89.70</td><td>191.9e-3</td><td>89.89</td><td>01:29</td><td>4157</td><td>46.17e-6</td><td>infeasible</td><td>12.62</td><td>5911.6</td><td>17.04</td></tr><tr><td>MinVariance</td><td>164.2</td><td>198.6e-3</td><td>164.4</td><td>02:44</td><td>4157</td><td>47.78e-6</td><td>infeasible</td><td>13.06</td><td>10815.0</td><td>17.04</td></tr><tr><td>BSplines</td><td>95.28</td><td>197.9e-3</td><td>95.48</td><td>01:35</td><td>4157</td><td>47.61e-6</td><td>infeasible</td><td>13.02</td><td>6279.4</td><td>17.04</td></tr><tr><td>MinNorm</td><td>158.9</td><td>195.1e-3</td><td>159.1</td><td>02:39</td><td>4157</td><td>46.94e-6</td><td>infeasible</td><td>12.83</td><td>10460.8</td><td>17.04</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>151.0</td><td>196.3e-3</td><td>151.2</td><td>02:31</td><td>4157</td><td>47.22e-6</td><td>infeasible</td><td>12.91</td><td>9943.9</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>148.0</td><td>194.5e-3</td><td>148.2</td><td>02:28</td><td>4157</td><td>46.79e-6</td><td>infeasible</td><td>12.79</td><td>9745.0</td><td>17.04</td></tr><tr><td>Recursive</td><td>104.8</td><td>188.0e-3</td><td>105.0</td><td>01:44</td><td>4157</td><td>45.23e-6</td><td>infeasible</td><td>12.37</td><td>6902.6</td><td>17.04</td></tr><tr><td>Recursive2</td><td>119.9</td><td>188.3e-3</td><td>120.1</td><td>02:00</td><td>4157</td><td>45.30e-6</td><td>infeasible</td><td>12.39</td><td>7898.2</td><td>17.04</td></tr></tbody></table>

<table><caption>Table 66: Bissection of problem 3D with problem: 3, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep_time</th><th>comput_time</th><th>total_time</th><th>(D-H:M:S.ms)</th><th>nb_iter</th><th>time_per_iter</th><th>criteria</th><th>comput_time (%)</th><th>total_time (%)</th><th>nb_iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>39.10e-6</td><td>114.9</td><td>114.9</td><td>01:54</td><td>1858809</td><td>61.81e-6</td><td>2.6120</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>66.59</td><td>12.65</td><td>79.24</td><td>01:19</td><td>442385</td><td>28.60e-6</td><td>2.6084</td><td>11.01</td><td>68.97</td><td>23.80</td></tr><tr><td>MinVariance</td><td>126.5</td><td>15.14</td><td>141.7</td><td>02:21</td><td>493407</td><td>30.69e-6</td><td>2.6086</td><td>13.18</td><td>123.3</td><td>26.54</td></tr><tr><td>BSplines</td><td>72.20</td><td>33.80</td><td>106.0</td><td>01:46</td><td>1317809</td><td>25.65e-6</td><td>2.6100</td><td>29.42</td><td>92.26</td><td>70.90</td></tr><tr><td>MinNorm</td><td>112.9</td><td>14.06</td><td>127.0</td><td>02:06</td><td>469353</td><td>29.95e-6</td><td>2.6085</td><td>12.23</td><td>110.5</td><td>25.25</td></tr><tr><td>MinVolume</td><td>115.0</td><td>15.95</td><td>130.9</td><td>02:10</td><td>545359</td><td>29.26e-6</td><td>2.6087</td><td>13.89</td><td>113.9</td><td>29.34</td></tr><tr><td>ApproxMinVolume</td><td>108.2</td><td>15.99</td><td>124.2</td><td>02:04</td><td>546659</td><td>29.26e-6</td><td>2.6087</td><td>13.92</td><td>108.1</td><td>29.41</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>77.84</td><td>12.87</td><td>90.71</td><td>01:30</td><td>443105</td><td>29.04e-6</td><td>2.6084</td><td>11.20</td><td>78.94</td><td>23.84</td></tr><tr><td>Recursive2</td><td>92.83</td><td>12.90</td><td>105.7</td><td>01:45</td><td>444233</td><td>29.03e-6</td><td>2.6084</td><td>11.23</td><td>92.02</td><td>23.90</td></tr><tr><td>Interval</td><td>36.00e-6</td><td>10.15</td><td>10.15</td><td>10.154</td><td>159279</td><td>63.75e-6</td><td>2.7144</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>89.18</td><td>1.503</td><td>90.68</td><td>01:30</td><td>38673</td><td>38.87e-6</td><td>2.6766</td><td>14.80</td><td>893.1</td><td>24.28</td></tr><tr><td>MinVariance</td><td>161.7</td><td>1.551</td><td>163.3</td><td>02:43</td><td>41101</td><td>37.74e-6</td><td>2.6783</td><td>15.27</td><td>1608.0</td><td>25.80</td></tr><tr><td>BSplines</td><td>96.06</td><td>2.680</td><td>98.74</td><td>01:38</td><td>68621</td><td>39.05e-6</td><td>2.6975</td><td>26.39</td><td>972.4</td><td>43.08</td></tr><tr><td>MinNorm</td><td>157.3</td><td>1.554</td><td>158.9</td><td>02:38</td><td>39963</td><td>38.89e-6</td><td>2.6775</td><td>15.31</td><td>1564.4</td><td>25.09</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>150.5</td><td>1.713</td><td>152.2</td><td>02:32</td><td>43655</td><td>39.23e-6</td><td>2.6799</td><td>16.87</td><td>1498.7</td><td>27.41</td></tr><tr><td>ApproxMinVolume</td><td>147.5</td><td>1.783</td><td>149.3</td><td>02:29</td><td>43715</td><td>40.78e-6</td><td>2.6799</td><td>17.56</td><td>1470.4</td><td>27.45</td></tr><tr><td>Recursive</td><td>105.1</td><td>1.563</td><td>106.7</td><td>01:46</td><td>39353</td><td>39.72e-6</td><td>2.6766</td><td>15.39</td><td>1050.8</td><td>24.71</td></tr><tr><td>Recursive2</td><td>120.3</td><td>1.577</td><td>121.9</td><td>02:01</td><td>39897</td><td>39.53e-6</td><td>2.6766</td><td>15.53</td><td>1200.4</td><td>25.05</td></tr></tbody></table>
<table><caption>Table 67: Bissection of problem 3D with problem: 4, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>38.15e-6</td><td>939.6e-3</td><td>939.7e-3</td><td>0.940</td><td>15151</td><td>62.02e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>67.27</td><td>201.0e-3</td><td>67.47</td><td>01:07</td><td>2207</td><td>91.07e-6</td><td>infeasible</td><td>21.39</td><td>7179.9</td><td>14.57</td></tr><tr><td>MinVariance</td><td>136.9</td><td>215.2e-3</td><td>137.1</td><td>02:17</td><td>2207</td><td>97.51e-6</td><td>infeasible</td><td>22.90</td><td>14593.1</td><td>14.57</td></tr><tr><td>BSplines</td><td>73.01</td><td>243.2e-3</td><td>73.25</td><td>01:13</td><td>2637</td><td>92.21e-6</td><td>infeasible</td><td>25.88</td><td>7795.3</td><td>17.40</td></tr><tr><td>MinNorm</td><td>132.0</td><td>213.7e-3</td><td>132.2</td><td>02:12</td><td>2205</td><td>96.93e-6</td><td>infeasible</td><td>22.75</td><td>14066.5</td><td>14.55</td></tr><tr><td>MinVolume</td><td>115.1</td><td>186.5e-3</td><td>115.3</td><td>01:55</td><td>2257</td><td>82.63e-6</td><td>infeasible</td><td>19.85</td><td>12271.7</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>117.1</td><td>195.8e-3</td><td>117.2</td><td>01:57</td><td>2257</td><td>86.77e-6</td><td>infeasible</td><td>20.84</td><td>12477.9</td><td>14.90</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>91.08</td><td>198.5e-3</td><td>91.28</td><td>01:31</td><td>2285</td><td>86.87e-6</td><td>infeasible</td><td>21.12</td><td>9713.7</td><td>15.08</td></tr><tr><td>Recursive2</td><td>98.25</td><td>186.6e-3</td><td>98.43</td><td>01:38</td><td>2309</td><td>80.80e-6</td><td>infeasible</td><td>19.86</td><td>10475.4</td><td>15.24</td></tr><tr><td>Interval</td><td>35.05e-6</td><td>945.4e-3</td><td>945.4e-3</td><td>0.945</td><td>15151</td><td>62.40e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>89.32</td><td>201.1e-3</td><td>89.52</td><td>01:29</td><td>2207</td><td>91.11e-6</td><td>infeasible</td><td>21.27</td><td>9469.3</td><td>14.57</td></tr><tr><td>MinVariance</td><td>160.4</td><td>197.8e-3</td><td>160.6</td><td>02:40</td><td>2207</td><td>89.60e-6</td><td>infeasible</td><td>20.92</td><td>16990.1</td><td>14.57</td></tr><tr><td>BSplines</td><td>96.68</td><td>243.6e-3</td><td>96.92</td><td>01:36</td><td>2637</td><td>92.37e-6</td><td>infeasible</td><td>25.77</td><td>10251.9</td><td>17.40</td></tr><tr><td>MinNorm</td><td>156.2</td><td>212.1e-3</td><td>156.4</td><td>02:36</td><td>2205</td><td>96.18e-6</td><td>infeasible</td><td>22.43</td><td>16539.6</td><td>14.55</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>150.5</td><td>215.2e-3</td><td>150.7</td><td>02:30</td><td>2257</td><td>95.35e-6</td><td>infeasible</td><td>22.76</td><td>15939.3</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>148.0</td><td>217.0e-3</td><td>148.3</td><td>02:28</td><td>2257</td><td>96.13e-6</td><td>infeasible</td><td>22.95</td><td>15681.9</td><td>14.90</td></tr><tr><td>Recursive</td><td>105.2</td><td>212.4e-3</td><td>105.5</td><td>01:45</td><td>2285</td><td>92.96e-6</td><td>infeasible</td><td>22.47</td><td>11155.0</td><td>15.08</td></tr><tr><td>Recursive2</td><td>119.8</td><td>213.1e-3</td><td>120.1</td><td>02:00</td><td>2309</td><td>92.28e-6</td><td>infeasible</td><td>22.54</td><td>12698.8</td><td>15.24</td></tr></tbody></table>

<table><caption>Table 68: Bissection of problem 3D with problem: 5, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>44.00e-6</td><td>1961390</td><td>1961390</td><td>22-16:49:50</td><td>21725405270</td><td>90.28e-6</td><td>2.3241</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>369.5</td><td>341713</td><td>342083</td><td>3-23:01:23</td><td>5158711215</td><td>66.24e-6</td><td>2.3211</td><td>17.42</td><td>17.44</td><td>23.75</td></tr><tr><td>MinVariance</td><td>405.6</td><td>373862</td><td>374268</td><td>4-07:57:48</td><td>5603984063</td><td>66.71e-6</td><td>2.3213</td><td>19.06</td><td>19.08</td><td>25.79</td></tr><tr><td>BSplines</td><td>377.9</td><td>785881</td><td>785882</td><td>9-02:18:02</td><td>13501926220</td><td>58.21e-6</td><td>2.3228</td><td>40.07</td><td>40.07</td><td>62.15</td></tr><tr><td>MinNorm</td><td>415.6</td><td>355407</td><td>355823</td><td>4-02:50:23</td><td>5396965307</td><td>65.85e-6</td><td>2.3212</td><td>18.12</td><td>18.14</td><td>24.84</td></tr><tr><td>MinVolume</td><td>413.9</td><td>390702</td><td>391116</td><td>4-12:38:36</td><td>6054653853</td><td>64.53e-6</td><td>2.3214</td><td>19.92</td><td>19.94</td><td>27.87</td></tr><tr><td>ApproxMinVolume</td><td>399.8</td><td>395183</td><td>395583</td><td>4-13:53:03</td><td>6066574285</td><td>65.14e-6</td><td>2.3214</td><td>20.15</td><td>20.17</td><td>27.92</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>389.5</td><td>336452</td><td>336841</td><td>3-21:34:01</td><td>5158943727</td><td>65.22e-6</td><td>2.3211</td><td>17.15</td><td>17.17</td><td>23.75</td></tr><tr><td>Recursive2</td><td>391.2</td><td>344116</td><td>344507</td><td>3-23:41:47</td><td>5166944403</td><td>66.60e-6</td><td>2.3211</td><td>17.54</td><td>17.56</td><td>23.78</td></tr><tr><td>Interval</td><td>35.05e-6</td><td>69746</td><td>69746</td><td>19-22:26</td><td>772563369</td><td>90.28e-6</td><td>2.4334</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>393.2</td><td>13012</td><td>13405</td><td>03:43:25</td><td>174381971</td><td>74.62e-6</td><td>2.4050</td><td>18.66</td><td>19.22</td><td>22.57</td></tr><tr><td>MinVariance</td><td>433.4</td><td>14401</td><td>14834</td><td>04:07:14</td><td>1884045815</td><td>76.44e-6</td><td>2.4067</td><td>20.65</td><td>21.27</td><td>24.39</td></tr><tr><td>BSplines</td><td>400.2</td><td>29734</td><td>30134</td><td>08:22:14</td><td>415697327</td><td>71.53e-6</td><td>2.4265</td><td>42.63</td><td>43.21</td><td>53.81</td></tr><tr><td>MinNorm</td><td>421.5</td><td>13586</td><td>14007</td><td>03:53:27</td><td>181903655</td><td>74.69e-6</td><td>2.4059</td><td>19.48</td><td>20.08</td><td>23.55</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>423.7</td><td>14931</td><td>15355</td><td>04:15:55</td><td>202463931</td><td>73.75e-6</td><td>2.4083</td><td>21.41</td><td>22.02</td><td>26.21</td></tr><tr><td>ApproxMinVolume</td><td>411.5</td><td>14974</td><td>15385</td><td>04:16:25</td><td>202832813</td><td>73.82e-6</td><td>2.4083</td><td>21.47</td><td>22.06</td><td>26.25</td></tr><tr><td>Recursive</td><td>279.0</td><td>13127</td><td>13406</td><td>03:43:26</td><td>174617583</td><td>75.18e-6</td><td>2.4050</td><td>18.82</td><td>19.22</td><td>22.60</td></tr><tr><td>Recursive2</td><td>277.9</td><td>13427</td><td>13705</td><td>03:48:25</td><td>176765395</td><td>75.96e-6</td><td>2.4050</td><td>19.25</td><td>19.65</td><td>22.88</td></tr></tbody></table>

<table><caption>Table 69: Bissection of problem 3D with problem: 6, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>39.10e-6</td><td>39416</td><td>39416</td><td>10:56:56</td><td>445969679</td><td>88.38e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>377.5</td><td>895.0</td><td>1272</td><td>21:12</td><td>8525007</td><td>105.0e-6</td><td>infeasible</td><td>2.271</td><td>3.228</td><td>1.912</td></tr><tr><td>MinVariance</td><td>392.4</td><td>886.4</td><td>1278</td><td>21:18</td><td>8525007</td><td>104.0e-6</td><td>infeasible</td><td>2.249</td><td>3.244</td><td>1.912</td></tr><tr><td>BSplines</td><td>359.2</td><td>882.2</td><td>1241</td><td>20:41</td><td>8525007</td><td>103.5e-6</td><td>infeasible</td><td>2.238</td><td>3.149</td><td>1.912</td></tr><tr><td>MinNorm</td><td>408.6</td><td>882.3</td><td>1290</td><td>21:30</td><td>8525007</td><td>103.5e-6</td><td>infeasible</td><td>2.238</td><td>3.275</td><td>1.912</td></tr><tr><td>MinVolume</td><td>400.8</td><td>886.9</td><td>1287</td><td>21:27</td><td>8525007</td><td>104.0e-6</td><td>infeasible</td><td>2.250</td><td>3.267</td><td>1.912</td></tr><tr><td>ApproxMinVolume</td><td>375.4</td><td>896.4</td><td>1271</td><td>21:11</td><td>8525007</td><td>105.2e-6</td><td>infeasible</td><td>2.274</td><td>3.227</td><td>1.912</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>377.3</td><td>890.4</td><td>1267</td><td>21:07</td><td>8525007</td><td>104.5e-6</td><td>infeasible</td><td>2.259</td><td>3.216</td><td>1.912</td></tr><tr><td>Recursive2</td><td>376.2</td><td>878.4</td><td>1254</td><td>20:54</td><td>8525007</td><td>103.0e-6</td><td>infeasible</td><td>2.228</td><td>3.183</td><td>1.912</td></tr><tr><td>Interval</td><td>26.94e-6</td><td>41124</td><td>41124</td><td>11:25:24</td><td>445969679</td><td>92.21e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>274.5</td><td>887.1</td><td>1161</td><td>19:21</td><td>8525007</td><td>104.1e-6</td><td>infeasible</td><td>2.157</td><td>2.824</td><td>1.912</td></tr><tr><td>MinVariance</td><td>302.5</td><td>880.7</td><td>1183</td><td>19:43</td><td>8525007</td><td>103.3e-6</td><td>infeasible</td><td>2.142</td><td>2.877</td><td>1.912</td></tr><tr><td>BSplines</td><td>346.0</td><td>899.6</td><td>1245</td><td>20:45</td><td>8525007</td><td>105.5e-6</td><td>infeasible</td><td>2.188</td><td>3.029</td><td>1.912</td></tr><tr><td>MinNorm</td><td>366.2</td><td>881.1</td><td>1247</td><td>20:47</td><td>8525007</td><td>103.4e-6</td><td>infeasible</td><td>2.143</td><td>3.033</td><td>1.912</td></tr><tr><td rowspan="7">0.01</td><td>MinVolume</td><td>297.4</td><td>876.2</td><td>1173</td><td>19:33</td><td>8525007</td><td>102.8e-6</td><td>infeasible</td><td>2.131</td><td>2.854</td><td>1.912</td></tr><tr><td>ApproxMinVolume</td><td>294.0</td><td>903.1</td><td>1197</td><td>19:57</td><td>8525007</td><td>105.9e-6</td><td>infeasible</td><td>2.196</td><td>2.911</td><td>1.912</td></tr><tr><td>Recursive</td><td>279.2</td><td>891.4</td><td>1170</td><td>19:30</td><td>8525007</td><td>104.6e-6</td><td>infeasible</td><td>2.168</td><td>2.847</td><td>1.912</td></tr><tr><td>Recursive2</td><td>275.8</td><td>888.6</td><td>1164</td><td>19:24</td><td>8525007</td><td>104.2e-6</td><td>infeasible</td><td>2.161</td><td>2.832</td><td>1.912</td></tr></tbody></table>

<table><caption>Table 70: Bissection of problem 3D with problem: 7, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>31.00e-6</td><td>2070930</td><td>2070930</td><td>23-23:15:30</td><td>23210368008</td><td>89.22e-6</td><td>2.3241</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>371.2</td><td>410597</td><td>410968</td><td>4-18:09:28</td><td>5394044627</td><td>76.12e-6</td><td>2.3211</td><td>19.83</td><td>19.84</td><td>23.24</td></tr><tr><td>MinVariance</td><td>420.9</td><td>445090</td><td>445510</td><td>5-03:45:10</td><td>5850239297</td><td>76.08e-6</td><td>2.3213</td><td>21.49</td><td>21.51</td><td>25.21</td></tr><tr><td>BSplines</td><td>353.8</td><td>910582</td><td>910582</td><td>10-12:56:22</td><td>13881904718</td><td>65.59e-6</td><td>2.3228</td><td>43.97</td><td>43.97</td><td>59.81</td></tr><tr><td>MinNorm</td><td>402.7</td><td>422038</td><td>422440</td><td>4-21:20:40</td><td>5638302317</td><td>74.85e-6</td><td>2.3212</td><td>20.38</td><td>20.40</td><td>24.29</td></tr><tr><td>MinVolume</td><td>409.4</td><td>465253</td><td>465663</td><td>5-09:21:03</td><td>6311789809</td><td>73.71e-6</td><td>2.3214</td><td>22.47</td><td>22.49</td><td>27.19</td></tr><tr><td>ApproxMinVolume</td><td>369.9</td><td>463804</td><td>464174</td><td>5-08:56:14</td><td>6323990517</td><td>73.34e-6</td><td>2.3214</td><td>22.40</td><td>22.41</td><td>27.25</td></tr><tr><td rowspan="7">0.01</td><td>Recursive</td><td>355.0</td><td>399527</td><td>399882</td><td>4-15:04:42</td><td>5394276879</td><td>74.07e-6</td><td>2.3211</td><td>19.29</td><td>19.31</td><td>23.24</td></tr><tr><td>Recursive2</td><td>382.3</td><td>407990</td><td>408372</td><td>4-17:26:12</td><td>5402414799</td><td>75.52e-6</td><td>2.3211</td><td>19.70</td><td>19.72</td><td>23.28</td></tr><tr><td>Interval</td><td>32.90e-6</td><td>127800</td><td>127800</td><td>1-11:30:00</td><td>1422543689</td><td>89.84e-6</td><td>2.4334</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>273.2</td><td>45618</td><td>45891</td><td>12:44:51</td><td>318506213</td><td>143.2e-6</td><td>2.4050</td><td>35.69</td><td>35.91</td><td>22.39</td></tr><tr><td>MinVariance</td><td>313.5</td><td>48763</td><td>49076</td><td>13:37:56</td><td>332585337</td><td>146.6e-6</td><td>2.4067</td><td>38.16</td><td>38.40</td><td>23.38</td></tr><tr><td>BSplines</td><td>289.3</td><td>67921</td><td>68211</td><td>18:56:51</td><td>554047171</td><td>122.6e-6</td><td>2.4265</td><td>53.15</td><td>53.37</td><td>38.95</td></tr><tr><td>MinNorm</td><td>298.0</td><td>47855</td><td>48153</td><td>13:22:33</td><td>326068257</td><td>146.8e-6</td><td>2.4059</td><td>37.45</td><td>37.68</td><td>22.92</td></tr><tr><td>MinVolume</td><td>302.6</td><td>49665</td><td>49968</td><td>13:52:48</td><td>346653905</td><td>143.3e-6</td><td>2.4083</td><td>38.86</td><td>39.10</td><td>24.37</td></tr><tr><td rowspan="7">0.01</td><td>ApproxMinVolume</td><td>291.0</td><td>49713</td><td>50004</td><td>13:53:24</td><td>347021943</td><td>143.3e-6</td><td>2.4083</td><td>38.90</td><td>39.13</td><td>24.39</td></tr><tr><td>Recursive</td><td>280.0</td><td>46999</td><td>47279</td><td>13:07:59</td><td>318741327</td><td>147.5e-6</td><td>2.4050</td><td>36.78</td><td>36.99</td><td>22.41</td></tr><tr><td>Recursive2</td><td>287.3</td><td>47109</td><td>47396</td><td>13:09:56</td><td>320924305</td><td>146.8e-6</td><td>2.4050</td><td>36.86</td><td>37.09</td><td>22.56</td></tr></tbody></table>
<table><caption>Table 71: Bissection of problem 3D with problem: 8, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>43.87e-6</td><td>20654</td><td>20654</td><td>05:44:14</td><td>229302217</td><td>90.08e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>370.0</td><td>931.2</td><td>1301</td><td>21:41</td><td>4457773</td><td>208.9e-6</td><td>infeasible</td><td>4.509</td><td>6.300</td><td>1.944</td></tr><tr><td>MinVariance</td><td>404.8</td><td>950.4</td><td>1355</td><td>22:35</td><td>4457773</td><td>213.2e-6</td><td>infeasible</td><td>4.601</td><td>6.561</td><td>1.944</td></tr><tr><td>BSplines</td><td>378.2</td><td>940.0</td><td>1318</td><td>21:58</td><td>4457773</td><td>210.9e-6</td><td>infeasible</td><td>4.551</td><td>6.382</td><td>1.944</td></tr><tr><td>MinNorm</td><td>397.4</td><td>934.3</td><td>1331</td><td>22:11</td><td>4457773</td><td>209.6e-6</td><td>infeasible</td><td>4.524</td><td>6.448</td><td>1.944</td></tr><tr><td>MinVolume</td><td>308.0</td><td>937.2</td><td>1245</td><td>20:45</td><td>4457773</td><td>210.2e-6</td><td>infeasible</td><td>4.537</td><td>6.029</td><td>1.944</td></tr><tr><td>ApproxMinVolume</td><td>302.5</td><td>922.0</td><td>1224</td><td>20:24</td><td>4457773</td><td>206.8e-6</td><td>infeasible</td><td>4.464</td><td>5.928</td><td>1.944</td></tr><tr><td rowspan="5">0.01</td><td>Recursive</td><td>315.9</td><td>921.4</td><td>1237</td><td>20:37</td><td>4457773</td><td>206.7e-6</td><td>infeasible</td><td>4.461</td><td>5.991</td><td>1.944</td></tr><tr><td>Recursive2</td><td>333.5</td><td>925.1</td><td>1258</td><td>20:58</td><td>4457773</td><td>207.5e-6</td><td>infeasible</td><td>4.479</td><td>6.093</td><td>1.944</td></tr><tr><td>Interval</td><td>29.09e-6</td><td>20779</td><td>20779</td><td>05:46:19</td><td>229302217</td><td>90.62e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>275.3</td><td>936.4</td><td>1211</td><td>20:11</td><td>4457773</td><td>210.1e-6</td><td>infeasible</td><td>4.506</td><td>5.831</td><td>1.944</td></tr><tr><td>MinVariance</td><td>315.0</td><td>950.2</td><td>1265</td><td>21:05</td><td>4457773</td><td>213.2e-6</td><td>infeasible</td><td>4.573</td><td>6.089</td><td>1.944</td></tr><tr><td rowspan="7">0.01</td><td>BSplines</td><td>287.2</td><td>933.6</td><td>1220</td><td>20:20</td><td>4457773</td><td>209.4e-6</td><td>infeasible</td><td>4.493</td><td>5.875</td><td>1.944</td></tr><tr><td>MinNorm</td><td>343.0</td><td>920.8</td><td>1263</td><td>21:03</td><td>4457773</td><td>206.6e-6</td><td>infeasible</td><td>4.431</td><td>6.082</td><td>1.944</td></tr><tr><td>MinVolume</td><td>312.2</td><td>930.7</td><td>1242</td><td>20:42</td><td>4457773</td><td>208.8e-6</td><td>infeasible</td><td>4.479</td><td>5.981</td><td>1.944</td></tr><tr><td>ApproxMinVolume</td><td>369.8</td><td>952.2</td><td>1322</td><td>22:02</td><td>4457773</td><td>213.6e-6</td><td>infeasible</td><td>4.583</td><td>6.362</td><td>1.944</td></tr><tr><td>Recursive</td><td>332.2</td><td>939.8</td><td>1271</td><td>21:11</td><td>4457773</td><td>210.8e-6</td><td>infeasible</td><td>4.523</td><td>6.121</td><td>1.944</td></tr><tr><td>Recursive2</td><td>283.1</td><td>926.5</td><td>1209</td><td>20:09</td><td>4457773</td><td>207.8e-6</td><td>infeasible</td><td>4.459</td><td>5.821</td><td>1.944</td></tr></tbody></table>

<table><caption>Table 72: Bissection of problem 3D with problem: 11, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>40.05e-6</td><td>1998</td><td>1998</td><td>33:18</td><td>36483067</td><td>54.78e-6</td><td>386.24</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>96.19</td><td>747.1</td><td>843.3</td><td>14:03</td><td>6347179</td><td>117.7e-6</td><td>385.26</td><td>37.38</td><td>42.19</td><td>17.40</td></tr><tr><td>MinVariance</td><td>168.0</td><td>947.0</td><td>1114</td><td>18:34</td><td>7229953</td><td>131.0e-6</td><td>385.34</td><td>47.38</td><td>55.78</td><td>19.82</td></tr><tr><td>BSplines</td><td>101.6</td><td>4231</td><td>4333</td><td>01:12:13</td><td>40300001</td><td>105.0e-6</td><td>386.51</td><td>211.7</td><td>216.8</td><td>110.5</td></tr><tr><td>MinNorm</td><td>160.1</td><td>880.5</td><td>1040</td><td>17:20</td><td>6826491</td><td>129.0e-6</td><td>385.30</td><td>44.05</td><td>52.06</td><td>18.71</td></tr><tr><td>MinVolume</td><td>158.2</td><td>1043</td><td>1201</td><td>20:01</td><td>8309215</td><td>125.6e-6</td><td>385.41</td><td>52.21</td><td>60.12</td><td>22.78</td></tr><tr><td>ApproxMinVolume</td><td>155.1</td><td>1054</td><td>1209</td><td>20:09</td><td>8349359</td><td>126.3e-6</td><td>385.41</td><td>52.74</td><td>60.50</td><td>22.89</td></tr><tr><td rowspan="5">0.01</td><td>Recursive</td><td>110.5</td><td>768.4</td><td>878.9</td><td>14:38</td><td>6389281</td><td>120.3e-6</td><td>385.26</td><td>38.45</td><td>43.97</td><td>17.51</td></tr><tr><td>Recursive2</td><td>127.0</td><td>777.8</td><td>904.7</td><td>15:04</td><td>6365803</td><td>122.2e-6</td><td>385.26</td><td>38.91</td><td>45.27</td><td>17.45</td></tr><tr><td>Interval</td><td>36.00e-6</td><td>56.05</td><td>56.05</td><td>56:049</td><td>1019361</td><td>61.57e-6</td><td>414.99</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.58</td><td>25.91</td><td>121.5</td><td>02:01</td><td>202943</td><td>127.7e-6</td><td>404.04</td><td>46.23</td><td>216.8</td><td>22.29</td></tr><tr><td>MinVariance</td><td>167.5</td><td>29.96</td><td>197.5</td><td>03:17</td><td>221987</td><td>134.9e-6</td><td>405.30</td><td>53.44</td><td>352.3</td><td>24.38</td></tr><tr><td rowspan="7">0.01</td><td>BSplines</td><td>101.0</td><td>61.35</td><td>162.3</td><td>02:42</td><td>475893</td><td>128.9e-6</td><td>425.62</td><td>109.4</td><td>289.6</td><td>52.28</td></tr><tr><td>MinNorm</td><td>159.4</td><td>29.43</td><td>188.8</td><td>03:08</td><td>213119</td><td>138.1e-6</td><td>404.71</td><td>52.51</td><td>336.9</td><td>23.41</td></tr><tr><td>MinVolume</td><td>157.4</td><td>33.40</td><td>190.8</td><td>03:10</td><td>245427</td><td>136.1e-6</td><td>406.55</td><td>59.59</td><td>340.4</td><td>26.96</td></tr><tr><td>ApproxMinVolume</td><td>155.4</td><td>33.96</td><td>189.4</td><td>03:09</td><td>246173</td><td>137.9e-6</td><td>406.58</td><td>60.59</td><td>337.9</td><td>27.04</td></tr><tr><td>Recursive</td><td>111.2</td><td>27.46</td><td>138.6</td><td>02:18</td><td>208803</td><td>131.5e-6</td><td>404.04</td><td>48.98</td><td>247.4</td><td>22.94</td></tr><tr><td>Recursive2</td><td>126.7</td><td>27.39</td><td>154.1</td><td>02:34</td><td>208691</td><td>131.3e-6</td><td>404.04</td><td>48.88</td><td>274.9</td><td>22.92</td></tr></tbody></table>

<table><caption>Table 73: Bissection of problem 3D with problem: 12, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>36.95e-6</td><td>1.532</td><td>1.532</td><td>1.532</td><td>24393</td><td>62.79e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>96.12</td><td>195.6e-3</td><td>96.31</td><td>01:36</td><td>4157</td><td>47.05e-6</td><td>infeasible</td><td>12.77</td><td>6288.6</td><td>17.04</td></tr><tr><td>MinVariance</td><td>166.2</td><td>175.3e-3</td><td>166.4</td><td>02:46</td><td>4157</td><td>42.18e-6</td><td>infeasible</td><td>11.45</td><td>10866.2</td><td>17.04</td></tr><tr><td>BSplines</td><td>102.4</td><td>201.3e-3</td><td>102.6</td><td>01:42</td><td>4157</td><td>48.43e-6</td><td>infeasible</td><td>13.14</td><td>6698.4</td><td>17.04</td></tr><tr><td>MinNorm</td><td>159.9</td><td>176.0e-3</td><td>160.0</td><td>02:40</td><td>4157</td><td>42.33e-6</td><td>infeasible</td><td>11.49</td><td>10448.8</td><td>17.04</td></tr><tr><td>MinVolume</td><td>158.0</td><td>187.5e-3</td><td>158.2</td><td>02:38</td><td>4157</td><td>45.10e-6</td><td>infeasible</td><td>12.24</td><td>10328.2</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>155.2</td><td>194.9e-3</td><td>155.4</td><td>02:35</td><td>4157</td><td>46.89e-6</td><td>infeasible</td><td>12.73</td><td>10147.4</td><td>17.04</td></tr><tr><td rowspan="5">0.01</td><td>Recursive</td><td>111.9</td><td>190.8e-3</td><td>112.1</td><td>01:52</td><td>4157</td><td>45.90e-6</td><td>infeasible</td><td>12.46</td><td>7319.8</td><td>17.04</td></tr><tr><td>Recursive2</td><td>127.9</td><td>192.5e-3</td><td>128.1</td><td>02:08</td><td>4157</td><td>46.31e-6</td><td>infeasible</td><td>12.57</td><td>8361.0</td><td>17.04</td></tr><tr><td>Interval</td><td>32.90e-6</td><td>1.512</td><td>1.512</td><td>1.512</td><td>24393</td><td>61.99e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.99</td><td>193.1e-3</td><td>96.19</td><td>01:36</td><td>4157</td><td>46.46e-6</td><td>infeasible</td><td>12.77</td><td>6361.4</td><td>17.04</td></tr><tr><td>MinVariance</td><td>165.6</td><td>175.3e-3</td><td>165.8</td><td>02:45</td><td>4157</td><td>42.18e-6</td><td>infeasible</td><td>11.60</td><td>10964.1</td><td>17.04</td></tr><tr><td>BSplines</td><td>102.4</td><td>201.8e-3</td><td>102.6</td><td>01:42</td><td>4157</td><td>48.55e-6</td><td>infeasible</td><td>13.35</td><td>6785.3</td><td>17.04</td></tr><tr><td>MinNorm</td><td>159.1</td><td>177.8e-3</td><td>159.3</td><td>02:39</td><td>4157</td><td>42.76e-6</td><td>infeasible</td><td>11.76</td><td>10534.5</td><td>17.04</td></tr><tr><td>MinVolume</td><td>157.8</td><td>189.9e-3</td><td>158.0</td><td>02:38</td><td>4157</td><td>45.68e-6</td><td>infeasible</td><td>12.56</td><td>10451.3</td><td>17.04</td></tr><tr><td>ApproxMinVolume</td><td>154.5</td><td>191.2e-3</td><td>154.7</td><td>02:34</td><td>4157</td><td>46.00e-6</td><td>infeasible</td><td>12.65</td><td>10232.4</td><td>17.04</td></tr><tr><td>Recursive</td><td>111.2</td><td>191.4e-3</td><td>111.4</td><td>01:51</td><td>4157</td><td>46.04e-6</td><td>infeasible</td><td>12.66</td><td>7369.6</td><td>17.04</td></tr><tr><td>Recursive2</td><td>127.2</td><td>191.5e-3</td><td>127.4</td><td>02:07</td><td>4157</td><td>46.08e-6</td><td>infeasible</td><td>12.67</td><td>8424.1</td><td>17.04</td></tr></tbody></table>

<table><caption>Table 74: Bissection of problem 3D with problem: 13, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="7">0.001</td><td>Interval</td><td>35.05e-6</td><td>2173</td><td>2173</td><td>36:13</td><td>36386983</td><td>59.72e-6</td><td>386.24</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>69.88</td><td>751.6</td><td>821.5</td><td>13:41</td><td>6324949</td><td>118.8e-6</td><td>385.26</td><td>34.59</td><td>37.80</td><td>17.38</td></tr><tr><td>MinVariance</td><td>131.3</td><td>939.4</td><td>1070</td><td>17:50</td><td>7206457</td><td>130.4e-6</td><td>385.34</td><td>43.23</td><td>49.27</td><td>19.81</td></tr><tr><td>BSplines</td><td>75.13</td><td>4610</td><td>4685</td><td>01:18:05</td><td>40254141</td><td>114.5e-6</td><td>386.51</td><td>212.1</td><td>215.6</td><td>110.6</td></tr><tr><td>MinNorm</td><td>116.0</td><td>863.9</td><td>979.9</td><td>16:19</td><td>6803387</td><td>127.0e-6</td><td>385.30</td><td>39.75</td><td>45.09</td><td>18.70</td></tr><tr><td>MinVolume</td><td>122.0</td><td>1051</td><td>1173</td><td>19:33</td><td>8284391</td><td>127.0e-6</td><td>385.41</td><td>48.40</td><td>54.01</td><td>22.77</td></tr><tr><td>ApproxMinVolume</td><td>113.7</td><td>1041</td><td>1155</td><td>19:15</td><td>8324463</td><td>125.1e-6</td><td>385.41</td><td>47.92</td><td>53.16</td><td>22.88</td></tr><tr><td rowspan="5">0.01</td><td>Recursive</td><td>81.51</td><td>768.0</td><td>849.5</td><td>14:09</td><td>6366677</td><td>120.6e-6</td><td>385.26</td><td>35.34</td><td>39.09</td><td>17.50</td></tr><tr><td>Recursive2</td><td>94.84</td><td>789.5</td><td>884.3</td><td>14:44</td><td>6343087</td><td>124.5e-6</td><td>385.26</td><td>36.33</td><td>40.69</td><td>17.43</td></tr><tr><td>Interval</td><td>30.99e-6</td><td>56.81</td><td>56.81</td><td>56:814</td><td>908209</td><td>62.56e-6</td><td>414.99</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>96.23</td><td>25.90</td><td>122.1</td><td>02:02</td><td>201961</td><td>128.3e-6</td><td>404.04</td><td>45.59</td><td>215.0</td><td>22.24</td></tr><tr><td>MinVariance</td><td>167.2</td><td>30.31</td><td>197.5</td><td>03:17</td><td>220827</td><td>137.3e-6</td><td>405.30</td><td>53.36</td><td>347.6</td><td>24.31</td></tr><tr><td>BSplines</td><td>101.7</td><td>60.92</td><td>162.7</td><td>02:42</td><td>469759</td><td>129.7e-6</td><td>425.62</td><td>107.2</td><td>286.3</td><td>51.72</td></tr><tr><td>MinNorm</td><td>161.0</td><td>29.29</td><td>190.3</td><td>03:10</td><td>212063</td><td>138.1e-6</td><td>404.71</td><td>51.56</td><td>334.9</td><td>23.35</td></tr><tr><td>MinVolume</td><td>158.1</td><td>33.04</td><td>191.1</td><td>03:11</td><td>244065</td><td>135.4e-6</td><td>406.55</td><td>58.15</td><td>336.4</td><td>26.87</td></tr><tr><td>ApproxMinVolume</td><td>155.0</td><td>33.35</td><td>188.4</td><td>03:08</td><td>244805</td><td>136.2e-6</td><td>406.58</td><td>58.70</td><td>331.5</td><td>26.95</td></tr><tr><td>Recursive</td><td>110.9</td><td>26.70</td><td>137.6</td><td>02:17</td><td>207469</td><td>128.7e-6</td><td>404.04</td><td>47.00</td><td>242.3</td><td>22.84</td></tr><tr><td>Recursive2</td><td>127.1</td><td>27.15</td><td>154.2</td><td>02:34</td><td>207231</td><td>131.0e-6</td><td>404.04</td><td>47.79</td><td>271.4</td><td>22.82</td></tr></tbody></table>
<table><caption>Table 75: Bissection of problem 3D with problem: 14, type: MaxFirst</caption><thead><tr><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>criteria</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="8">0.001</td><td>Interval</td><td>36.00e-6</td><td>952.0e-3</td><td>952.0e-3</td><td>0.952</td><td>15151</td><td>62.83e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>70.20</td><td>204.0e-3</td><td>70.40</td><td>01:10</td><td>2207</td><td>92.44e-6</td><td>infeasible</td><td>21.43</td><td>7395.1</td><td>14.57</td></tr><tr><td>MinVariance</td><td>133.3</td><td>213.7e-3</td><td>133.5</td><td>02:13</td><td>2207</td><td>96.84e-6</td><td>infeasible</td><td>22.45</td><td>14023.1</td><td>14.57</td></tr><tr><td>BSplines</td><td>75.89</td><td>239.2e-3</td><td>76.13</td><td>01:16</td><td>2637</td><td>90.72e-6</td><td>infeasible</td><td>25.13</td><td>7996.8</td><td>17.40</td></tr><tr><td>MinNorm</td><td>147.6</td><td>214.4e-3</td><td>147.9</td><td>02:27</td><td>2205</td><td>97.25e-6</td><td>infeasible</td><td>22.53</td><td>15530.8</td><td>14.55</td></tr><tr><td>MinVolume</td><td>145.2</td><td>218.6e-3</td><td>145.4</td><td>02:25</td><td>2257</td><td>96.84e-6</td><td>infeasible</td><td>22.96</td><td>15275.6</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>141.3</td><td>218.1e-3</td><td>141.5</td><td>02:21</td><td>2257</td><td>96.64e-6</td><td>infeasible</td><td>22.91</td><td>14867.8</td><td>14.90</td></tr><tr><td>Recursive</td><td>92.43</td><td>187.8e-3</td><td>92.61</td><td>01:32</td><td>2285</td><td>82.20e-6</td><td>infeasible</td><td>19.73</td><td>9728.4</td><td>15.08</td></tr><tr><td>Recursive2</td><td>104.1</td><td>191.9e-3</td><td>104.3</td><td>01:44</td><td>2309</td><td>83.10e-6</td><td>infeasible</td><td>20.16</td><td>10952.7</td><td>15.24</td></tr><tr><td rowspan="8">0.01</td><td>Interval</td><td>56.98e-6</td><td>943.5e-3</td><td>943.6e-3</td><td>0.944</td><td>15151</td><td>62.27e-6</td><td>infeasible</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>95.47</td><td>205.0e-3</td><td>95.68</td><td>01:35</td><td>2207</td><td>92.89e-6</td><td>infeasible</td><td>21.73</td><td>10139.9</td><td>14.57</td></tr><tr><td>MinVariance</td><td>165.5</td><td>192.0e-3</td><td>165.7</td><td>02:45</td><td>2207</td><td>87.01e-6</td><td>infeasible</td><td>20.35</td><td>17564.0</td><td>14.57</td></tr><tr><td>BSplines</td><td>102.1</td><td>245.6e-3</td><td>102.4</td><td>01:42</td><td>2637</td><td>93.12e-6</td><td>infeasible</td><td>26.03</td><td>10848.4</td><td>17.40</td></tr><tr><td>MinNorm</td><td>159.0</td><td>195.4e-3</td><td>159.2</td><td>02:39</td><td>2205</td><td>88.62e-6</td><td>infeasible</td><td>20.71</td><td>16875.9</td><td>14.55</td></tr><tr><td>MinVolume</td><td>157.1</td><td>204.6e-3</td><td>157.3</td><td>02:37</td><td>2257</td><td>90.67e-6</td><td>infeasible</td><td>21.69</td><td>16667.5</td><td>14.90</td></tr><tr><td>ApproxMinVolume</td><td>154.7</td><td>211.3e-3</td><td>154.9</td><td>02:34</td><td>2257</td><td>93.62e-6</td><td>infeasible</td><td>22.40</td><td>16413.2</td><td>14.90</td></tr><tr><td>Recursive</td><td>110.9</td><td>213.3e-3</td><td>111.1</td><td>01:51</td><td>2285</td><td>93.34e-6</td><td>infeasible</td><td>22.61</td><td>11778.3</td><td>15.08</td></tr><tr><td>Recursive2</td><td>127.1</td><td>215.7e-3</td><td>127.3</td><td>02:07</td><td>2309</td><td>93.42e-6</td><td>infeasible</td><td>22.86</td><td>13494.4</td><td>15.24</td></tr></tbody></table>

<table><caption>Table 76: Average of Bissection for 3D problems</caption><thead><tr><th>robot</th><th>precision</th><th>solver</th><th>prep.time</th><th>comput.time</th><th>total.time</th><th>(D-H:M:S.ms)</th><th>nb.iter</th><th>time_per_iter</th><th>comput.time (%)</th><th>total.time (%)</th><th>nb.iter (%)</th></tr></thead><tbody><tr><td rowspan="12">../../model/kuka_lwr.xml</td><td rowspan="8">0.001</td><td>Interval</td><td>39.00e-6</td><td>598958</td><td>598958</td><td>6-22:22:38</td><td>6676040964</td><td>89.00e-6</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>378.3</td><td>643161</td><td>643444</td><td>7-10:44:04</td><td>10807857179</td><td>111.0e-6</td><td>6.361</td><td>7.065</td><td>6.837</td></tr><tr><td>MinVariance</td><td>414.4</td><td>733199</td><td>733508</td><td>8-11:45:08</td><td>12258260822</td><td>112.0e-6</td><td>6.781</td><td>7.546</td><td>7.339</td></tr><tr><td>BSplines</td><td>375.8</td><td>283355</td><td>283609</td><td>3-06:46:49</td><td>4568299416</td><td>126.0e-6</td><td>16.28</td><td>17.22</td><td>21.61</td></tr><tr><td>MinNorm</td><td>410.4</td><td>694917</td><td>695224</td><td>8-01:07:04</td><td>11577934452</td><td>110.0e-6</td><td>6.504</td><td>7.263</td><td>7.106</td></tr><tr><td>MinVolume</td><td>396.9</td><td>794907</td><td>795201</td><td>9-04:53:21</td><td>13774006396</td><td>110.0e-6</td><td>6.993</td><td>7.691</td><td>7.847</td></tr><tr><td>ApproxMinVolume</td><td>382.0</td><td>805262</td><td>805544</td><td>9-07:45:44</td><td>13813523254</td><td>110.0e-6</td><td>7.004</td><td>7.683</td><td>7.860</td></tr><tr><td>Recursive</td><td>373.3</td><td>641137</td><td>641414</td><td>7-10:10:14</td><td>10821224833</td><td>110.0e-6</td><td>6.239</td><td>6.913</td><td>6.837</td></tr><tr><td>Recursive2</td><td>377.2</td><td>648204</td><td>648486</td><td>7-12:08:06</td><td>10813911461</td><td>110.0e-6</td><td>6.341</td><td>7.025</td><td>6.846</td></tr><tr><td>Interval</td><td>32.00e-6</td><td>332676</td><td>332676</td><td>3-20:24:36</td><td>3624925264</td><td>91.00e-6</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>346.8</td><td>22166</td><td>22513</td><td>06:15:13</td><td>242652648</td><td>126.0e-6</td><td>9.706</td><td>10.42</td><td>7.982</td></tr><tr><td>MinVariance</td><td>384.1</td><td>24294</td><td>24678</td><td>06:51:18</td><td>264227566</td><td>127.0e-6</td><td>10.41</td><td>11.21</td><td>8.475</td></tr><tr><td>BSplines</td><td>363.4</td><td>49644</td><td>49908</td><td>13:51:48</td><td>619888324</td><td>122.0e-6</td><td>16.82</td><td>17.57</td><td>16.45</td></tr><tr><td>MinNorm</td><td>388.0</td><td>23320</td><td>23708</td><td>06:35:08</td><td>254207507</td><td>126.0e-6</td><td>10.08</td><td>10.90</td><td>8.246</td></tr><tr><td>MinVolume</td><td>375.2</td><td>25425</td><td>25800</td><td>07:10:00</td><td>285991552</td><td>125.0e-6</td><td>10.65</td><td>11.43</td><td>8.969</td></tr><tr><td>ApproxMinVolume</td><td>373.8</td><td>25545</td><td>25919</td><td>07:11:59</td><td>286566441</td><td>126.0e-6</td><td>10.70</td><td>11.50</td><td>8.982</td></tr><tr><td>Recursive</td><td>341.3</td><td>22390</td><td>22732</td><td>06:18:52</td><td>244304039</td><td>126.0e-6</td><td>9.869</td><td>10.60</td><td>8.001</td></tr><tr><td>Recursive2</td><td>336.6</td><td>22535</td><td>22871</td><td>06:21:11</td><td>244106457</td><td>126.0e-6</td><td>9.935</td><td>10.64</td><td>8.049</td></tr><tr><td rowspan="12">../../model/kuka_lwr.4dof.xml</td><td rowspan="8">0.001</td><td>Interval</td><td>38.00e-6</td><td>642.5</td><td>642.5</td><td>10:42</td><td>11047784</td><td>62.00e-6</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>38.50</td><td>212.5</td><td>297.6</td><td>04:57</td><td>2079581</td><td>61.00e-6</td><td>18.94</td><td>2995.8</td><td>20.74</td></tr><tr><td>MinVariance</td><td>68.98</td><td>268.7</td><td>422.2</td><td>07:02</td><td>2379840</td><td>68.00e-6</td><td>22.55</td><td>5349.6</td><td>22.32</td></tr><tr><td>BSplines</td><td>41.17</td><td>1075</td><td>1167</td><td>19:27</td><td>10671601</td><td>60.00e-6</td><td>60.90</td><td>3238.0</td><td>57.08</td></tr><tr><td>MinNorm</td><td>66.53</td><td>250.1</td><td>400.1</td><td>06:40</td><td>2243746</td><td>64.00e-6</td><td>20.62</td><td>5262.3</td><td>21.59</td></tr><tr><td>MinVolume</td><td>64.72</td><td>297.5</td><td>443.0</td><td>07:23</td><td>2703713</td><td>63.00e-6</td><td>23.17</td><td>5135.8</td><td>24.03</td></tr><tr><td>ApproxMinVolume</td><td>63.48</td><td>298.2</td><td>438.4</td><td>07:18</td><td>2714059</td><td>64.00e-6</td><td>23.35</td><td>5055.6</td><td>24.08</td></tr><tr><td>Recursive</td><td>45.54</td><td>217.5</td><td>318.2</td><td>05:18</td><td>2087414</td><td>62.00e-6</td><td>19.24</td><td>3590.0</td><td>20.86</td></tr><tr><td>Recursive2</td><td>52.07</td><td>222.0</td><td>335.6</td><td>05:35</td><td>2087932</td><td>62.00e-6</td><td>19.41</td><td>4029.8</td><td>20.90</td></tr><tr><td>Interval</td><td>38.00e-6</td><td>19.14</td><td>19.14</td><td>19:138</td><td>306036</td><td>63.00e-6</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Bernstein</td><td>41.20</td><td>6.705</td><td>94.26</td><td>01:34</td><td>72424</td><td>67.00e-6</td><td>21.81</td><td>3335.1</td><td>21.01</td></tr><tr><td>MinVariance</td><td>72.95</td><td>7.779</td><td>168.4</td><td>02:48</td><td>78200</td><td>69.00e-6</td><td>23.82</td><td>6160.4</td><td>22.02</td></tr><tr><td>BSplines</td><td>43.92</td><td>15.29</td><td>112.4</td><td>01:52</td><td>152933</td><td>69.00e-6</td><td>40.28</td><td>3780.0</td><td>35.14</td></tr><tr><td>MinNorm</td><td>70.18</td><td>7.492</td><td>164.3</td><td>02:44</td><td>75509</td><td>70.00e-6</td><td>23.27</td><td>6046.8</td><td>21.54</td></tr><tr><td>MinVolume</td><td>68.33</td><td>8.484</td><td>161.3</td><td>02:41</td><td>84924</td><td>70.00e-6</td><td>25.57</td><td>5953.2</td><td>23.19</td></tr><tr><td>ApproxMinVolume</td><td>67.21</td><td>8.511</td><td>158.2</td><td>02:38</td><td>85144</td><td>70.00e-6</td><td>25.75</td><td>5842.8</td><td>23.23</td></tr><tr><td>Recursive</td><td>48.00</td><td>6.977</td><td>112.7</td><td>01:52</td><td>73986</td><td>68.00e-6</td><td>22.48</td><td>4125.0</td><td>21.35</td></tr><tr><td>Recursive2</td><td>54.91</td><td>7.215</td><td>129.0</td><td>02:09</td><td>74118</td><td>69.00e-6</td><td>23.04</td><td>4744.4</td><td>21.44</td></tr></tbody></table>