user: Converte this assembly snippet into its equivalent C code:

```asm
<gsw_alpha>:
  endbr64
  sub    $0x28,%rsp
  movapd %xmm0,%xmm5
  movsd  %xmm0,0x10(%rsp)
  movsd  %xmm1,0x18(%rsp)
  movsd  %xmm2,0x8(%rsp)
  pxor   %xmm0,%xmm0
  ucomisd %xmm5,%xmm0
  ja     L9
  sqrtsd %xmm5,%xmm5
L16:
  movsd  0x18(%rsp),%xmm6
  movapd %xmm6,%xmm1
  mulsd  D496(%rip),%xmm1
  subsd  D361(%rip),%xmm1
  mulsd  %xmm6,%xmm1
  movsd  D414(%rip),%xmm10
  addsd  %xmm10,%xmm1
  mulsd  %xmm6,%xmm1
  subsd  D318(%rip),%xmm1
  mulsd  %xmm5,%xmm1
  movapd %xmm6,%xmm0
  mulsd  D356(%rip),%xmm0
  movsd  D694(%rip),%xmm9
  subsd  %xmm9,%xmm0
  mulsd  %xmm6,%xmm0
  subsd  D604(%rip),%xmm0
  addsd  %xmm0,%xmm1
  movsd  0x10(%rsp),%xmm4
  mulsd  %xmm4,%xmm1
  movapd %xmm6,%xmm0
  mulsd  D5(%rip),%xmm0
  subsd  D298(%rip),%xmm0
  mulsd  %xmm6,%xmm0
  movsd  D104(%rip),%xmm8
  addsd  %xmm8,%xmm0
  mulsd  %xmm6,%xmm0
  addsd  D606(%rip),%xmm0
  addsd  %xmm0,%xmm1
  movapd %xmm6,%xmm0
  mulsd  D294(%rip),%xmm0
  subsd  D144(%rip),%xmm0
  mulsd  %xmm6,%xmm0
  subsd  D148(%rip),%xmm0
  movsd  D80(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D238(%rip),%xmm2
  mulsd  %xmm4,%xmm2
  addsd  %xmm2,%xmm0
  movapd %xmm6,%xmm2
  mulsd  D585(%rip),%xmm2
  subsd  D197(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D85(%rip),%xmm2
  movapd %xmm4,%xmm3
  mulsd  D353(%rip),%xmm3
  addsd  %xmm3,%xmm2
  movsd  0x8(%rsp),%xmm13
  mulsd  %xmm13,%xmm2
  addsd  %xmm2,%xmm0
  mulsd  %xmm13,%xmm0
  addsd  %xmm0,%xmm1
  movapd %xmm4,%xmm11
  mulsd  D89(%rip),%xmm11
  movapd %xmm6,%xmm0
  mulsd  D244(%rip),%xmm0
  addsd  D84(%rip),%xmm0
  mulsd  %xmm6,%xmm0
  addsd  D616(%rip),%xmm0
  mulsd  %xmm6,%xmm0
  movsd  D510(%rip),%xmm14
  subsd  %xmm14,%xmm0
  mulsd  %xmm6,%xmm0
  subsd  D412(%rip),%xmm0
  movapd %xmm4,%xmm2
  mulsd  D345(%rip),%xmm2
  addsd  %xmm2,%xmm0
  movapd %xmm6,%xmm2
  mulsd  D327(%rip),%xmm2
  subsd  D258(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D707(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  movsd  D365(%rip),%xmm15
  addsd  %xmm15,%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D433(%rip),%xmm2
  mulsd  %xmm5,%xmm2
  addsd  %xmm2,%xmm0
  mulsd  %xmm4,%xmm0
  movapd %xmm6,%xmm2
  mulsd  D396(%rip),%xmm2
  addsd  D125(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D625(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  movsd  D183(%rip),%xmm13
  addsd  %xmm13,%xmm2
  mulsd  %xmm6,%xmm2
  addsd  D352(%rip),%xmm2
  addsd  %xmm2,%xmm0
  movapd %xmm6,%xmm2
  mulsd  D240(%rip),%xmm2
  addsd  D286(%rip),%xmm2
  mulsd  %xmm6,%xmm2
  movsd  D386(%rip),%xmm12
  subsd  %xmm12,%xmm2
  mulsd  %xmm6,%xmm2
  subsd  D179(%rip),%xmm2
  movsd  D671(%rip),%xmm7
  movapd %xmm6,%xmm3
  mulsd  %xmm7,%xmm3
  subsd  D13(%rip),%xmm3
  mulsd  %xmm4,%xmm3
  addsd  %xmm3,%xmm2
  movapd %xmm6,%xmm3
  mulsd  D341(%rip),%xmm3
  subsd  D17(%rip),%xmm3
  addsd  %xmm11,%xmm3
  movapd %xmm6,%xmm4
  mulsd  %xmm6,%xmm3
  subsd  D572(%rip),%xmm3
  movsd  D566(%rip),%xmm6
  mulsd  %xmm6,%xmm4
  subsd  D262(%rip),%xmm4
  mulsd  0x8(%rsp),%xmm4
  addsd  %xmm4,%xmm3
  movsd  0x8(%rsp),%xmm4
  mulsd  %xmm4,%xmm3
  addsd  %xmm3,%xmm2
  mulsd  %xmm4,%xmm2
  addsd  %xmm0,%xmm2
  movsd  0x18(%rsp),%xmm4
  movapd %xmm4,%xmm0
  mulsd  D354(%rip),%xmm0
  subsd  D586(%rip),%xmm0
  mulsd  %xmm4,%xmm0
  subsd  D619(%rip),%xmm0
  mulsd  %xmm4,%xmm0
  addsd  %xmm15,%xmm0
  mulsd  %xmm5,%xmm0
  movapd %xmm4,%xmm3
  mulsd  D23(%rip),%xmm3
  addsd  D214(%rip),%xmm3
  mulsd  %xmm4,%xmm3
  addsd  D423(%rip),%xmm3
  mulsd  %xmm4,%xmm3
  subsd  %xmm14,%xmm3
  addsd  %xmm3,%xmm0
  movsd  0x10(%rsp),%xmm14
  mulsd  %xmm14,%xmm0
  movapd %xmm4,%xmm3
  mulsd  D160(%rip),%xmm3
  addsd  D658(%rip),%xmm3
  mulsd  %xmm4,%xmm3
  subsd  D706(%rip),%xmm3
  mulsd  %xmm4,%xmm3
  addsd  %xmm13,%xmm3
  addsd  %xmm0,%xmm3
  movapd %xmm4,%xmm0
  mulsd  D301(%rip),%xmm0
  addsd  D90(%rip),%xmm0
  mulsd  %xmm4,%xmm0
  subsd  %xmm12,%xmm0
  mulsd  %xmm14,%xmm7
  addsd  %xmm0,%xmm7
  movapd %xmm4,%xmm0
  mulsd  D381(%rip),%xmm0
  subsd  D17(%rip),%xmm0
  addsd  %xmm11,%xmm0
  movsd  0x8(%rsp),%xmm13
  mulsd  %xmm13,%xmm6
  addsd  %xmm0,%xmm6
  mulsd  %xmm13,%xmm6
  addsd  %xmm6,%xmm7
  mulsd  %xmm13,%xmm7
  addsd  %xmm7,%xmm3
  movapd %xmm3,%xmm0
  mulsd  %xmm1,%xmm0
  movapd %xmm4,%xmm6
  mulsd  D293(%rip),%xmm4
  subsd  D519(%rip),%xmm4
  mulsd  %xmm6,%xmm4
  addsd  %xmm10,%xmm4
  mulsd  %xmm4,%xmm5
  movapd %xmm6,%xmm3
  mulsd  D633(%rip),%xmm3
  subsd  %xmm9,%xmm3
  addsd  %xmm3,%xmm5
  mulsd  %xmm14,%xmm5
  movapd %xmm6,%xmm3
  mulsd  D79(%rip),%xmm3
  subsd  D523(%rip),%xmm3
  mulsd  %xmm6,%xmm3
  addsd  %xmm8,%xmm3
  addsd  %xmm3,%xmm5
  movapd %xmm6,%xmm3
  mulsd  D53(%rip),%xmm3
  subsd  D144(%rip),%xmm3
  movsd  D80(%rip),%xmm4
  mulsd  %xmm14,%xmm4
  addsd  %xmm4,%xmm3
  movapd %xmm6,%xmm4
  mulsd  D86(%rip),%xmm4
  subsd  D197(%rip),%xmm4
  mulsd  %xmm13,%xmm4
  addsd  %xmm4,%xmm3
  mulsd  %xmm13,%xmm3
  addsd  %xmm3,%xmm5
  movapd %xmm5,%xmm4
  mulsd  %xmm2,%xmm4
  subsd  %xmm4,%xmm0
  mulsd  %xmm2,%xmm1
  divsd  %xmm1,%xmm0
  add    $0x28,%rsp
  ret
L9:
  movsd  0x10(%rsp),%xmm0
  call   <sqrt@plt>
  movapd %xmm0,%xmm5
  jmp    L16
```

tool_calls: name: retrieve_data
arguments: label: D496
type: byte[8]
name: retrieve_data
arguments: label: D361
type: byte[8]
name: retrieve_data
arguments: label: D414
type: byte[8]
name: retrieve_data
arguments: label: D318
type: byte[8]
name: retrieve_data
arguments: label: D356
type: byte[8]
name: retrieve_data
arguments: label: D694
type: byte[8]
name: retrieve_data
arguments: label: D604
type: f64
name: retrieve_data
arguments: label: D5
type: byte[8]
name: retrieve_data
arguments: label: D298
type: byte[8]
name: retrieve_data
arguments: label: D104
type: f64
name: retrieve_data
arguments: label: D606
type: byte[8]
name: retrieve_data
arguments: label: D294
type: byte[8]
name: retrieve_data
arguments: label: D144
type: byte[8]
name: retrieve_data
arguments: label: D148
type: byte[8]
name: retrieve_data
arguments: label: D80
type: byte[8]
name: retrieve_data
arguments: label: D238
type: byte[8]
name: retrieve_data
arguments: label: D585
type: byte[8]
name: retrieve_data
arguments: label: D197
type: byte[8]
name: retrieve_data
arguments: label: D85
type: byte[8]
name: retrieve_data
arguments: label: D353
type: byte[8]
name: retrieve_data
arguments: label: D89
type: byte[8]
name: retrieve_data
arguments: label: D244
type: byte[8]
name: retrieve_data
arguments: label: D84
type: byte[8]
name: retrieve_data
arguments: label: D616
type: byte[8]
name: retrieve_data
arguments: label: D510
type: byte[8]
name: retrieve_data
arguments: label: D412
type: byte[8]
name: retrieve_data
arguments: label: D345
type: byte[8]
name: retrieve_data
arguments: label: D327
type: byte[8]
name: retrieve_data
arguments: label: D258
type: byte[8]
name: retrieve_data
arguments: label: D707
type: byte[8]
name: retrieve_data
arguments: label: D365
type: byte[8]
name: retrieve_data
arguments: label: D433
type: byte[8]
name: retrieve_data
arguments: label: D396
type: byte[8]
name: retrieve_data
arguments: label: D125
type: byte[8]
name: retrieve_data
arguments: label: D625
type: byte[8]
name: retrieve_data
arguments: label: D183
type: byte[8]
name: retrieve_data
arguments: label: D352
type: f64
name: retrieve_data
arguments: label: D240
type: byte[8]
name: retrieve_data
arguments: label: D286
type: byte[8]
name: retrieve_data
arguments: label: D386
type: byte[8]
name: retrieve_data
arguments: label: D179
type: byte[8]
name: retrieve_data
arguments: label: D671
type: byte[8]
name: retrieve_data
arguments: label: D13
type: byte[8]
name: retrieve_data
arguments: label: D341
type: byte[8]
name: retrieve_data
arguments: label: D17
type: byte[8]
name: retrieve_data
arguments: label: D572
type: byte[8]
name: retrieve_data
arguments: label: D566
type: byte[8]
name: retrieve_data
arguments: label: D262
type: byte[8]
name: retrieve_data
arguments: label: D354
type: byte[8]
name: retrieve_data
arguments: label: D586
type: byte[8]
name: retrieve_data
arguments: label: D619
type: byte[8]
name: retrieve_data
arguments: label: D23
type: byte[8]
name: retrieve_data
arguments: label: D214
type: byte[8]
name: retrieve_data
arguments: label: D423
type: byte[8]
name: retrieve_data
arguments: label: D160
type: byte[8]
name: retrieve_data
arguments: label: D658
type: byte[8]
name: retrieve_data
arguments: label: D706
type: byte[8]
name: retrieve_data
arguments: label: D301
type: byte[8]
name: retrieve_data
arguments: label: D90
type: byte[8]
name: retrieve_data
arguments: label: D381
type: byte[8]
name: retrieve_data
arguments: label: D293
type: byte[8]
name: retrieve_data
arguments: label: D519
type: byte[8]
name: retrieve_data
arguments: label: D633
type: byte[8]
name: retrieve_data
arguments: label: D79
type: byte[8]
name: retrieve_data
arguments: label: D523
type: byte[8]
name: retrieve_data
arguments: label: D53
type: byte[8]
name: retrieve_data
arguments: label: D86
type: byte[8]

tool: {"D496": [0x73,0x33,0x84,0xef,0x4f,0x14,0x86,0x3e]}

tool: {"D361": [0xd6,0xa6,0x84,0xcc,0x10,0xed,0xed,0x3e]}

tool: {"D414": [0xbf,0xb2,0x6b,0xaa,0x59,0xb2,0x40,0x3f]}

tool: {"D318": [0xfc,0x2d,0x58,0xb1,0x3a,0x6c,0xa4,0x3f]}

tool: {"D356": [0xfc,0x2c,0x45,0x01,0x00,0x83,0x2e,0x3f]}

tool: {"D694": [0xf2,0xa0,0x4f,0x84,0xed,0x94,0x9e,0x3f]}

tool: D604: 6.698001071123802

tool: {"D5": [0x1f,0x14,0xa5,0x0a,0xda,0x5c,0x53,0x3f]}

tool: {"D298": [0x8e,0x15,0x07,0xbe,0xd4,0x1d,0xa0,0x3f]}

tool: D104: 2.839940833161907

tool: {"D606": [0x2f,0x19,0x8d,0x99,0xbc,0x3e,0x8f,0x40]}

tool: {"D294": [0x6e,0xb3,0xdd,0x0b,0xa2,0x41,0xcf,0x3e]}

tool: {"D144": [0xd1,0x33,0xb0,0x73,0xcd,0x84,0x36,0x3f]}

tool: {"D148": [0xb8,0x52,0x81,0xe0,0x61,0xde,0x96,0x3f]}

tool: {"D80": [0x0d,0x0d,0x3e,0x7f,0x28,0x13,0xa7,0x3e]}

tool: {"D238": [0xea,0x40,0xd6,0x96,0x94,0xae,0x27,0x3f]}

tool: {"D585": [0x18,0xe6,0x61,0x34,0xd2,0x57,0xa7,0xbd]}

tool: {"D197": [0x40,0x72,0xfa,0x98,0x94,0x59,0x55,0x3e]}

tool: {"D85": [0xb4,0x8a,0x75,0x40,0x7b,0xb7,0x94,0x3e]}

tool: {"D353": [0x3d,0xae,0x24,0x03,0xdc,0x50,0xe5,0x3d]}

tool: {"D89": [0x3e,0xd3,0xdc,0x5f,0x9b,0x35,0x09,0x3d]}

tool: {"D244": [0x25,0x50,0x24,0x19,0xed,0xe9,0xb3,0xbd]}

tool: {"D84": [0xda,0x54,0xdf,0x5d,0x67,0x5e,0x10,0x3e]}

tool: {"D616": [0x9b,0x60,0x15,0x69,0x6b,0xf3,0x80,0x3e]}

tool: {"D510": [0xbc,0xe6,0xbd,0x4a,0x61,0xfc,0xfc,0x3e]}

tool: {"D412": [0x0f,0x4d,0x4a,0x59,0xcf,0xce,0x7e,0x3f]}

tool: {"D345": [0xf6,0x68,0xb1,0x23,0xf5,0xba,0xd6,0x3e]}

tool: {"D327": [0x8b,0x87,0x54,0x54,0x4b,0x95,0x87,0x3d]}

tool: {"D258": [0x61,0xf7,0x2f,0x26,0x08,0x7a,0xc9,0x3d]}

tool: {"D707": [0x57,0x27,0x46,0x6b,0x35,0x7a,0x40,0x3e]}

tool: {"D365": [0x2d,0xaf,0xa5,0xc9,0x09,0x83,0x99,0x3e]}

tool: {"D433": [0xe4,0x53,0x23,0x49,0xa0,0x51,0x01,0x3f]}

tool: {"D396": [0x40,0x56,0x29,0xd6,0xcf,0x2b,0x07,0x3e]}

tool: {"D125": [0x42,0xd1,0x39,0xf4,0x45,0xc8,0xb2,0x3e]}

tool: {"D625": [0x63,0xc6,0xe2,0xf0,0x2d,0xa3,0xf8,0x3e]}

tool: {"D183": [0xb6,0xcd,0x91,0xdc,0x8a,0xbd,0x66,0x3f]}

tool: D352: 1

tool: {"D240": [0xb7,0x34,0xcf,0x2a,0x41,0xfc,0x80,0xbd]}

tool: {"D286": [0x58,0xd0,0xf2,0x4f,0xfe,0x69,0x2b,0x3e]}

tool: {"D386": [0xa4,0xa8,0x06,0xd8,0x74,0x8f,0x95,0x3e]}

tool: {"D179": [0x9b,0xcc,0x5a,0x74,0xff,0xc0,0xfc,0x3e]}

tool: {"D671": [0xe8,0x94,0x78,0xf4,0xa0,0x57,0x05,0x3e]}

tool: {"D13": [0x8f,0x77,0xaa,0x37,0x2c,0xaa,0x7d,0x3e]}

tool: {"D341": [0x10,0xf7,0x4c,0x08,0xff,0xfe,0x14,0xbd]}

tool: {"D17": [0x61,0xf3,0x4c,0xa2,0x49,0x59,0xb5,0x3d]}

tool: {"D572": [0x5a,0x66,0xbb,0x13,0x58,0xc2,0xde,0x3d]}

tool: {"D566": [0x2c,0x35,0x32,0x6d,0xf1,0x75,0x91,0x3c]}

tool: {"D262": [0xeb,0xc5,0x77,0x63,0x5d,0xa0,0xd5,0x3c]}

tool: {"D354": [0x89,0x87,0x54,0x54,0x4b,0x95,0xa7,0x3d]}

tool: {"D586": [0x88,0xf9,0xa3,0x1c,0x86,0x1b,0xe3,0x3d]}

tool: {"D619": [0x58,0x27,0x46,0x6b,0x35,0x7a,0x50,0x3e]}

tool: {"D23": [0x25,0x50,0x24,0x19,0xed,0xe9,0xd3,0xbd]}

tool: {"D214": [0x48,0xff,0xce,0x0c,0x9b,0x8d,0x28,0x3e]}

tool: {"D423": [0x99,0x60,0x15,0x69,0x6b,0xf3,0x90,0x3e]}

tool: {"D160": [0x3f,0x56,0x29,0xd6,0xcf,0x2b,0x27,0x3e]}

tool: {"D658": [0xe6,0xb9,0x56,0xee,0x68,0x2c,0xcc,0x3e]}

tool: {"D706": [0x63,0xc6,0xe2,0xf0,0x2d,0xa3,0x08,0x3f]}

tool: {"D301": [0x14,0xcf,0x36,0xc0,0x61,0x7a,0x99,0xbd]}

tool: {"D90": [0x58,0xd0,0xf2,0x4f,0xfe,0x69,0x3b,0x3e]}

tool: {"D381": [0x11,0xf7,0x4c,0x08,0xff,0xfe,0x24,0xbd]}

tool: {"D293": [0x98,0x26,0xa3,0xf3,0x3b,0x8f,0xa0,0x3e]}

tool: {"D519": [0xd3,0xa6,0x84,0xcc,0x10,0xed,0xfd,0x3e]}

tool: {"D633": [0xfc,0x2c,0x45,0x01,0x00,0x83,0x3e,0x3f]}

tool: {"D79": [0x2f,0x9e,0xf7,0x0f,0x47,0x0b,0x6d,0x3f]}

tool: {"D523": [0x8f,0x15,0x07,0xbe,0xd4,0x1d,0xb0,0x3f]}

tool: {"D53": [0x6f,0xb3,0xdd,0x0b,0xa2,0x41,0xdf,0x3e]}

tool: {"D86": [0x18,0xe6,0x61,0x34,0xd2,0x57,0xb7,0xbd]}

assistant: ```c
double gsw_alpha(double sa, double ct, double p) {
  double v01 = 9.998420897506056e+2, v02 = 2.839940833161907e0, v03 = -3.147759265588511e-2, v04 = 1.181805545074306e-3, v05 = -6.698001071123802e0, v06 = -2.986498947203215e-2, v07 = 2.327859407479162e-4, v08 = -3.988822378968490e-2, v09 = 5.095422573880500e-4, v10 = -1.426984671633621e-5, v11 = 1.645039373682922e-7, v12 = -2.233269627352527e-2, v13 = -3.436090079851880e-4, v14 = 3.726050720345733e-6, v15 = -1.806789763745328e-4, v16 = 6.876837219536232e-7, v17 = -3.087032500374211e-7, v18 = -1.988366587925593e-8, v19 = -1.061519070296458e-11, v20 = 1.550932729220080e-10, v21 = 1.0e0, v22 = 2.775927747785646e-3, v23 = -2.349607444135925e-5, v24 = 1.119513357486743e-6, v25 = 6.743689325042773e-10, v26 = -7.521448093615448e-3, v27 = -2.764306979894411e-5, v28 = 1.262937315098546e-7, v29 = 9.527875081696435e-10, v30 = -1.811147201949891e-11, v31 = -3.303308871386421e-5, v32 = 3.801564588876298e-7, v33 = -7.672876869259043e-9, v34 = -4.634182341116144e-11, v35 = 2.681097235569143e-12, v36 = 5.419326551148740e-6, v37 = -2.742185394906099e-5, v38 = -3.212746477974189e-7, v39 = 3.191413910561627e-9, v40 = -1.931012931541776e-12, v41 = -1.105097577149576e-7, v42 = 6.211426728363857e-10, v43 = -1.119011592875110e-10, v44 = -1.941660213148725e-11, v45 = -1.864826425365600e-14, v46 = 1.119522344879478e-14, v47 = -1.200507748551599e-15, v48 = 6.057902487546866e-17, a01 = 2.839940833161907e0, a02 = -6.295518531177023e-2, a03 = 3.545416635222918e-3, a04 = -2.986498947203215e-2, a05 = 4.655718814958324e-4, a06 = 5.095422573880500e-4, a07 = -2.853969343267241e-5, a08 = 4.935118121048767e-7, a09 = -3.436090079851880e-4, a10 = 7.452101440691467e-6, a11 = 6.876837219536232e-7, a12 = -1.988366587925593e-8, a13 = -2.123038140592916e-11, a14 = 2.775927747785646e-3, a15 = -4.699214888271850e-5, a16 = 3.358540072460230e-6, a17 = 2.697475730017109e-9, a18 = -2.764306979894411e-5, a19 = 2.525874630197091e-7, a20 = 2.858362524508931e-9, a21 = -7.244588807799565e-11, a22 = 3.801564588876298e-7, a23 = -1.534575373851809e-8, a24 = -1.390254702334843e-10, a25 = 1.072438894227657e-11, a26 = -3.212746477974189e-7, a27 = 6.382827821123254e-9, a28 = -5.793038794625329e-12, a29 = 6.211426728363857e-10, a30 = -1.941660213148725e-11, a31 = -3.729652850731201e-14, a32 = 1.119522344879478e-14, a33 = 6.057902487546866e-17;
  double sqrtsa, v_hat_denominator, v_hat_numerator;
  double dvhatden_dct, dvhatnum_dct;
  sqrtsa = sqrt(sa);
  v_hat_denominator = v01 + ct * (v02 + ct * (v03 + v04 * ct)) + sa * (v05 + ct * (v06 + v07 * ct) + sqrtsa * (v08 + ct * (v09 + ct * (v10 + v11 * ct)))) + p * (v12 + ct * (v13 + v14 * ct) + sa * (v15 + v16 * ct) + p * (v17 + ct * (v18 + v19 * ct) + v20 * sa));
  v_hat_numerator = v21 + ct * (v22 + ct * (v23 + ct * (v24 + v25 * ct))) + sa * (v26 + ct * (v27 + ct * (v28 + ct * (v29 + v30 * ct))) + v36 * sa + sqrtsa * (v31 + ct * (v32 + ct * (v33 + ct * (v34 + v35 * ct))))) + p * (v37 + ct * (v38 + ct * (v39 + v40 * ct)) + sa * (v41 + v42 * ct) + p * (v43 + ct * (v44 + v45 * ct + v46 * sa) + p * (v47 + v48 * ct)));
  dvhatden_dct = a01 + ct * (a02 + a03 * ct) + sa * (a04 + a05 * ct + sqrtsa * (a06 + ct * (a07 + a08 * ct))) + p * (a09 + a10 * ct + a11 * sa + p * (a12 + a13 * ct));
  dvhatnum_dct = a14 + ct * (a15 + ct * (a16 + a17 * ct)) + sa * (a18 + ct * (a19 + ct * (a20 + a21 * ct)) + sqrtsa * (a22 + ct * (a23 + ct * (a24 + a25 * ct)))) + p * (a26 + ct * (a27 + a28 * ct) + a29 * sa + p * (a30 + a31 * ct + a32 * sa + a33 * p));
  return ((v_hat_denominator * dvhatnum_dct - v_hat_numerator * dvhatden_dct) / (v_hat_numerator * v_hat_denominator));
}
```