collection stringclasses 15
values | task_ID stringlengths 6 15 | description stringlengths 10 4.11k | dtype stringclasses 2
values | expression stringlengths 3 338 | name stringlengths 5 47 | scientific_field stringclasses 6
values | support stringlengths 8 402 |
|---|---|---|---|---|---|---|---|
Densities | densities_0 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anglit.html#scipy.stats.anglit | float | cos(2*x_0) | anglit density | Mathematics | [[-0.7853981633974483, 0.7853981633974483]] |
Densities | densities_1 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.arcsine.html#scipy.stats.arcsine | float | 1/(pi*sqrt(x_0*(1 - x_0))) | arcsine density | Mathematics | [[0.001, 0.999]] |
Densities | densities_2 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genlogistic.html#scipy.stats.genlogistic | float | exp(-x_0)/(1+exp(-x_0))^2 | logistic density | Mathematics | [[-2, 2]] |
Densities | densities_3 | c = 2, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto | float | (1 + 2*x_0)^(-3/2) | generalized pareto density | Mathematics | [[0, 2]] |
Densities | densities_4 | a,b,c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genexpon.html#scipy.stats.genexpon | float | (1 + 2*(1 - exp(-2*x_0)))*exp(-3*x_0 + 1 - exp(-2*x_0)) | generalized exponential density | Mathematics | [[0, 2]] |
Densities | densities_5 | c = -1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme | float | exp(-(1 + x_0)^(-1))*(1 + x_0)^(-2) | generalized extreme value density | Mathematics | [[-0.5, 2]] |
Densities | densities_6 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gibrat.html#scipy.stats.gibrat | float | 1/(x_0*sqrt(2*pi))*exp(-0.5*(log(x_0)^2)) | gibrat density | Mathematics | [[3.4452751762614753e-10, 2]] |
Densities | densities_7 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gompertz.html#scipy.stats.gompertz | float | exp(x_0)*exp(1 - exp(x_0)) | gompertz density | Mathematics | [[0, 2]] |
Densities | densities_8 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r | float | exp(-(x_0 + exp(-x_0))) | right-skewed Gumbel density | Mathematics | [[-1.5, 2]] |
Densities | densities_9 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halfcauchy.html#scipy.stats.halfcauchy | float | 2/(pi*(1 + x_0^2)) | Half-Cauchy density | Mathematics | [[0, 2]] |
Densities | densities_10 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halflogistic.html#scipy.stats.halflogistic | float | (2*exp(-x_0))/((1 + exp(-x_0))^2) | Half-Logistic density | Mathematics | [[0, 2]] |
Densities | densities_11 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halfnorm.html#scipy.stats.halfnorm | float | sqrt(2/pi)*exp(-x_0^2/2) | Half-Normal density | Mathematics | [[0, 2]] |
Densities | densities_12 | c = 1.0, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bradford.html#scipy.stats.bradford | float | 1/(log(2)*(1 + x_0)) | bradford density | Mathematics | [[0, 1]] |
Densities | densities_13 | mu = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invgauss.html#scipy.stats.invgauss | float | 1/sqrt((2*pi*x_0^3))*exp(-((x_0-1)^2)/(2*x_0)) | Inverse Gaussian density | Mathematics | [[0.2, 2]] |
Densities | densities_14 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invweibull.html#scipy.stats.invweibull | float | exp(-1/x_0)/(x_0^2) | Inverse Weibull density | Mathematics | [[0.2, 2]] |
Densities | densities_15 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lomax.html#scipy.stats.lomax | float | 1/((1 +x_0)^2) | Lomax density | Mathematics | [[0.0, 2]] |
Densities | densities_16 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.maxwell.html#scipy.stats.maxwell | float | sqrt(2/pi)*x_0^2*exp(-x_0^2/2) | Maxwell density | Physics | [[0.0, 2]] |
Densities | densities_17 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.moyal.html#scipy.stats.moyal | float | (exp(-(x_0+exp(-x_0))/2))/(sqrt(2*pi)) | Moyal density | Physics | [[0.0, 2]] |
Densities | densities_18 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm | float | (exp(-x_0^2/2))/(sqrt(2*pi)) | standard normal density | Mathematics | [[-2, 2]] |
Densities | densities_19 | b = 2, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pareto.html#scipy.stats.pareto | float | 2/(x_0^3) | standard normal density | Mathematics | [[1, 2]] |
Densities | densities_20 | a = 0.5, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.powerlaw.html#scipy.stats.powerlaw | float | 1/(2*sqrt(x_0)) | power law density | Mathematics | [[5.213836029582808e-10, 1]] |
Densities | densities_21 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rayleigh.html#scipy.stats.rayleigh | float | x_0*exp(-x_0^2/2) | rayleigh density | Mathematics | [[0, 2]] |
Densities | densities_22 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.semicircular.html#scipy.stats.semicircular | float | 2/pi*sqrt(1 - x_0^2) | semicircular density | Mathematics | [[-1, 1]] |
Densities | densities_23 | c = 2.0, d = 1.0, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.burr.html#scipy.stats.burr | float | 2*(x_0^(-3))/((1+x_0^(-2))^2) | bradford density | Mathematics | [[2.235761575875017e-10, 1.8350870916695006]] |
Densities | densities_24 | lambda = 0.1, N = 100, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boltzmann.html#scipy.stats.boltzmann | int | 0.09516690253473127*exp(-0.1*x_0) | Boltzmann density | Mathematics | [[0, 50]] |
Densities | densities_25 | p = 0.2, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.geom.html#scipy.stats.geom | int | 0.8^(x_0-1)*0.2 | Geometric density | Mathematics | [[1, 20]] |
Densities | densities_26 | p = 0.9, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logser.html#scipy.stats.logser | int | -(0.9^x_0)/(x_0*log(0.1)) | Log Series density | Mathematics | [[1, 20]] |
Densities | densities_27 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cauchy.html#scipy.stats.cauchy | float | 1/(pi*(1 + x_0^2)) | cauchy density | Mathematics | [[-1, 1]] |
Densities | densities_28 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cosine.html#scipy.stats.cosine | float | (1 + cos(x_0))/(2*pi) | cosine density | Mathematics | [[-3.141592653589793, 3.141592653589793]] |
Densities | densities_29 | https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.expon.html#scipy.stats.expon | float | exp(-x_0) | exponential density | Mathematics | [[0, 2]] |
Densities | densities_30 | a = 2, c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.exponweib.html#scipy.stats.exponweib | float | 2*(1 - exp(-x_0))*exp(-x_0) | exponential weibull density | Mathematics | [[0, 1]] |
Densities | densities_31 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fatiguelife.html#scipy.stats.fatiguelife | float | (x_0+1)/(2*sqrt(2*pi*x_0^3))*exp(-(x_0-1)^2/(2*x_0)) | fatigue life density | Engineering | [[8.485969149596428e-10, 0.29538227738363126]] |
Densities | densities_32 | c = 1, https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.foldcauchy.html#scipy.stats.foldcauchy | float | 1/(pi*(1 + (x_0-1)^2)) + 1/(pi*(1 + (x_0+1)^2)) | folded cauchy density | Mathematics | [[0, 2]] |
Eponymous | eponymous_0 | The P-wave speed is determined by the elastic properties of the medium, including the bulk modulus, shear modulus, and density. | float | sqrt((x_0 + 4*x_1/3)/x_2) | Adams–Williamson equation | Physics | [[0, 95.05825033339732], [63.433589833745664, 63.43558983374566], [4.1390180172129476e-10, 10]] |
Eponymous | eponymous_1 | The S-wave speed is determined by the shear modulus and density of the medium. | float | sqrt(x_0/x_1) | Adams–Williamson equation | Physics | [[9.239684573003615e-10, 100], [1.3500667250809784e-10, 10]] |
Eponymous | eponymous_2 | Linear dispersion relation of the BBM equation. | float | x_0/(x_0**2 + 1) | Benjamin–Bona–Mahony equation | Physics | [[-100, 100]] |
Eponymous | eponymous_3 | The Hazen–Williams equation for full pipe flows relates the slope of the energy line to the flow rate, pipe roughness coefficient, and pipe diameter. | float | 19707*x_1**(463/250)/(2500*((x_2**(463/250)*x_3**(3044/625)))*(x_0**(463/250))) | Hazen–Williams equation | Engineering | [[0.001, 0.04], [0.001, 100], [0.001, 1], [0.001, 10]] |
Eponymous | eponymous_4 | The Henderson–Hasselbalch equation relates the pH of a solution to the acid dissociation constant and the ratio of the concentrations of the base and acid. | float | x_0 + log(x_1/x_2, 10) | Henderson–Hasselbalch equation | Chemistry | [[0, 14], [1e-06, 1], [1e-06, 1]] |
Eponymous | eponymous_5 | The Hill equation for response in terms of the total amount of receptor and ligand-bound receptor concentrations. | float | x_0/x_1 | Hill equation (biochemistry) | Biology | [[0, 100], [9.444676152270404e-10, 100]] |
Eponymous | eponymous_6 | The Michelson–Rayleigh line equation defines the relationship between pressure and density across a shock wave. | float | (-x_0 + x_1)/(1/x_3 - 1*1/x_2) | Hugoniot equation | Physics | [[0, 10], [0, 10], [1.8407984796296806, 2.785561249328673], [1.8387984794051082, 1.840798479405108]] |
Eponymous | eponymous_7 | The Hugoniot equation expresses the conservation of energy across a shock wave. | float | 1*(1/x_3 + 1/x_2)*(-x_0 + x_1)/2 | Hugoniot equation | Physics | [[0, 10], [0, 10], [4.237408202101278e-10, 3.6106334461630896], [1.5648993212380446e-10, 10]] |
Eponymous | eponymous_8 | The simplified Hugoniot equation relates pressure and density changes across a shock wave, incorporating heat release. | float | x_4*(-x_0/x_2 + x_1/x_3)/(x_4 - 1) - 1*1*(1/x_3 + 1/x_2)*(-x_0 + x_1)/2 | Hugoniot equation | Physics | [[0, 10], [0, 10], [4.601741210308319e-10, 10], [6.921494488665303e-10, 8.145417595604535], [1.0000000001300038, 2]] |
Eponymous | eponymous_9 | The non-dimensional Rayleigh line equation simplifies the relationship between pressure and density across a shock wave. | float | (x_0 - 1)/(x_1 - 1) | Hugoniot equation | Physics | [[0, 10], [0, 10]] |
Eponymous | eponymous_10 | The Kapustinskii equation calculates the lattice energy for an ionic crystal. | float | x_0*(x_1*Abs(x_2)*Abs(x_3))*(-x_6/(x_4 + x_5) + 1)/(x_4 + x_5) | Kapustinskii equation | Chemistry | [[0, 10], [0, 10], [-10, 10], [-10, 10], [0.01, 10], [0.01, 10], [0, 10]] |
Eponymous | eponymous_11 | A simpler form of the Kapustinskii equation for estimating lattice energy. | float | x_0*(x_1*Abs(x_2)*Abs(x_3))/(x_4 + x_5) | Kapustinskii equation | Chemistry | [[0, 10], [0, 10], [-10, 10], [-10, 10], [0.01, 10], [0.01, 10]] |
Eponymous | eponymous_12 | The Born–Landé equation for calculating lattice energy in ionic crystals. | float | -x_0*x_1*x_2*x_3*x_4**2*(1 - 1*1/x_7)/(4*pi*x_5*x_6) | Kapustinskii equation | Chemistry | [[0, 10], [0, 10], [-10, 10], [-10, 10], [0.01, 10], [0.01, 10], [0.01, 10], [1, 10]] |
Eponymous | eponymous_13 | Linear dispersion relation of the KdV equation. | float | -x_0**3 + x_0 | Benjamin–Bona–Mahony equation | Physics | [[-100, 100]] |
Eponymous | eponymous_14 | The Karplus equation describes the correlation between 3J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy. | float | x_0*cos(2*x_1) + x_2*cos(x_1) + x_3 | Karplus equation | Chemistry | [[0, 360], [-10, 10], [-10, 10], [-10, 10]] |
Eponymous | eponymous_15 | The radial Kepler equation for objects with enough energy to escape relates time and distance from the center of attraction. | float | 2*x_0**(3/2)/3 | Kepler's equation | Physics | [[0, 10]] |
Eponymous | eponymous_16 | The Kozeny-Carman equation describes the pressure drop of a fluid flowing through a packed bed of solids. | float | (150*x_0)*x_4*(1 - x_3)**2/(((x_1**2*x_2**2))*(x_3**3)) | Kozeny–Carman equation | Engineering | [[0.001, 10.0], [0.1, 1.0], [0.001, 0.1], [0.1, 0.6], [0.01, 1.0]] |
Eponymous | eponymous_17 | Darcy's law states that flow is proportional to the pressure gradient and inversely proportional to the fluid viscosity. | float | x_0*x_2/(x_1*x_3) | Kozeny–Carman equation | Engineering | [[0.001, 10.0], [0.001, 10.0], [0.01, 100.0], [0.1, 10.0]] |
Eponymous | eponymous_18 | The Kozeny equation for absolute permeability describes the permeability of a packed bed of solids. | float | x_0**2*(x_1**3*x_2**2)/((180*(1 - x_1)**2)) | Kozeny–Carman equation | Engineering | [[0.1, 1.0], [0.1, 0.6], [0.001, 0.1]] |
Eponymous | eponymous_19 | The polytropic equation of state relates pressure and density in a polytropic fluid. | float | x_0**(1 + 1/x_2)*x_1 | Lane–Emden equation | Physics | [[3.6948178544493615e-10, 0.04443330038779237], [0.34, 0.4], [-0.54, -0.48]] |
Eponymous | eponymous_20 | The density profile of a polytropic fluid is given by the polytropic index. | float | x_0**x_2*x_1 | Lane–Emden equation | Physics | [[0, 10], [0, 10], [0, 5]] |
Eponymous | eponymous_21 | The solution to the Lane–Emden equation for a polytropic index of 0. | float | -1*1*x_0**2/6 + 1 | Lane–Emden equation | Physics | [[0, 10]] |
Eponymous | eponymous_22 | Poisson's equation is a generalization of Laplace's equation with a specified right-hand side function. | float | x_0 | Laplace's equation | Physics | [[-10, 10]] |
Eponymous | eponymous_23 | The ideal gas law describes the relationship between pressure, volume, number of moles, and temperature of an ideal gas. | float | (x_0*x_1)/x_2 | List of equations | Physics | [[1000, 110000], [0.001, 100], [0.001, 100]] |
Eponymous | eponymous_24 | Transformed equation from the example Bernoulli equation using substitution u = 1/y. | float | x_0**2 | Bernoulli differential equation | Mathematics | [[0, 10]] |
Eponymous | eponymous_25 | Newton's second law of motion states that the force acting on an object is equal to its mass times its acceleration. | float | x_0*x_1 | List of equations | Physics | [[0.1, 1000], [0.01, 100]] |
Eponymous | eponymous_26 | Ohm's law describes the relationship between voltage, current, and resistance in an electrical circuit. | float | x_0*x_1 | List of equations | Physics | [[0.01, 1000], [0.001, 100]] |
Eponymous | eponymous_27 | The equation of a straight line in slope-intercept form describes the relationship between the y-coordinate and the x-coordinate. | float | x_0*x_1 + x_2 | List of equations | Mathematics | [[-100, 100], [-100, 100], [-100, 100]] |
Eponymous | eponymous_28 | The Arrhenius equation describes the temperature dependence of reaction rates. | float | x_0*exp(-x_1/x_2) | List of equations | Chemistry | [[0.01, 100], [1000, 100000], [200, 1000]] |
Eponymous | eponymous_29 | The Michaelis-Menten equation describes the rate of enzymatic reactions. | float | (x_0*x_1)/(x_1 + x_2) | List of equations | Biology | [[0.01, 100], [0.001, 100], [0.001, 100]] |
Eponymous | eponymous_30 | The Lorentz force law describes the electromagnetic force on a charge q due to electric field E and magnetic field B. | float | x_0*(x_1 + x_2*x_3) | Lorentz equation | Physics | [[-1e-06, 1e-06], [-1000000.0, 1000000.0], [-1000000.0, 1000000.0], [-1000000.0, 1000000.0]] |
Eponymous | eponymous_31 | The Lorentz force equation for a continuous charge distribution in motion describes the force density due to electric and magnetic fields. | float | x_0*(x_1 + x_2*x_3) | Lorentz equation | Physics | [[-1e-06, 1e-06], [-1000000.0, 1000000.0], [-1000000.0, 1000000.0], [-1000000.0, 1000000.0]] |
Eponymous | eponymous_32 | The Lorentz–Lorenz equation relates the refractive index of a substance to its polarizability. | float | (4*pi)*x_0*x_1/3 | Lorentz–Lorenz equation | Physics | [[1e+20, 1e+25], [1e-30, 1e-25]] |
Eponymous | eponymous_33 | The quadratic Lyapunov function for continuous-time systems. | float | x_0*x_1*(x_0) | Lyapunov equation | Mathematics | [[-10, 10], [-10, 10]] |
Eponymous | eponymous_34 | The quadratic Lyapunov function for discrete-time systems. | float | x_0*x_1*(x_0) | Lyapunov equation | Mathematics | [[-10, 10], [-10, 10]] |
Eponymous | eponymous_35 | Solution of the transformed equation using integrating factor M(x) = x^2. | float | x_0**4 | Bernoulli differential equation | Mathematics | [[0, 10]] |
Eponymous | eponymous_36 | The Mark–Houwink equation relates intrinsic viscosity to molecular weight for polymers. | float | x_0*x_1**x_2 | Mark–Houwink equation | Chemistry | [[0.01, 10], [1000, 1000000], [0.5, 2.0]] |
Eponymous | eponymous_37 | The Mason–Weaver sedimentation coefficient is defined as the ratio of buoyant mass to drag coefficient. | float | x_0/x_1 | Mason–Weaver equation | Physics | [[1e-10, 1e-05], [1e-10, 1e-05]] |
Eponymous | eponymous_38 | The ratio of the sedimentation coefficient to the diffusion constant is given by the buoyant mass and temperature. | float | x_0/x_1 | Mason–Weaver equation | Physics | [[1e-10, 1e-05], [1e-10, 1e-05]] |
Eponymous | eponymous_39 | The equilibrium concentration distribution in the Mason–Weaver equation. | float | x_0*exp(-x_1) | Mason–Weaver equation | Physics | [[1e-10, 1e-05], [1e-10, 1e-05]] |
Eponymous | eponymous_40 | The Morison equation describes the inline force on a body in oscillatory flow as the sum of an inertia force and a drag force. | float | x_0*x_1*x_2*x_3 + 1*x_0*x_4*x_5*x_6*Abs(x_6)/2 | Morison equation | Engineering | [[0.1, 1000], [0.1, 10], [0.1, 10], [0.1, 100], [0.1, 10], [0.1, 100], [-10, 10]] |
Eponymous | eponymous_41 | The Morison equation for a moving body in an oscillatory flow includes additional terms for the body's velocity and acceleration. | float | x_0*x_1*x_2 + x_0*x_1*x_3*(x_2 - x_4) + 1*x_0*x_5*x_6*(x_7 - x_8)*Abs(x_7 - x_8)/2 | Morison equation | Engineering | [[0.1, 1000], [0.1, 100], [-10, 10], [0.1, 10], [-10, 10], [0.1, 10], [0.1, 100], [-10, 10], [-10, 10]] |
Eponymous | eponymous_42 | The Nernst equation expressed in terms of base-10 logarithms for the cell potential as a function of standard cell potential, thermal voltage, number of electrons transferred, and activities of the reduced and oxidized forms. | float | x_0 - x_1*log(x_3/x_4, E)/x_2 | Nernst equation | Chemistry | [[273.15, 373.15], [0.02, 0.03], [1, 10], [0.1, 10], [0.1, 10]] |
Eponymous | eponymous_43 | The Ornstein–Zernike equation relates the total correlation function to the direct correlation function in statistical mechanics. | float | x_0/(x_0*x_1 + 1) | Ornstein–Zernike equation | Physics | [[0, 10], [0, 10]] |
Eponymous | eponymous_44 | The total correlation function is defined in terms of the pair correlation function. | float | x_0 - 1 | Ornstein–Zernike equation | Physics | [[0, 10]] |
Eponymous | eponymous_45 | The Landé g-factor in the Pauli equation for an electron in an isotropic constant magnetic field. | float | 3/2 + (-x_0*(x_0 + 1) + 3/4)/((2*x_1*(x_1 + 1))) | Pauli equation | Physics | [[0, 10], [0.5, 10.5]] |
Eponymous | eponymous_46 | The third-order Birch–Murnaghan isothermal equation of state relates pressure to volume. | float | (3*x_0)*((x_1/x_2)**(7/3) - (x_1/x_2)**(5/3))*(3*(x_3 - 4)*((x_1/x_2)**(2/3) - 1)/4 + 1)/2 | Birch–Murnaghan equation of state | Physics | [[1, 100], [1, 100], [1, 100], [1, 100]] |
Eponymous | eponymous_47 | The modified Penman equation by Shuttleworth simplifies the calculation of evaporation using SI units. | float | (x_0*x_1 + x_2*(643/100)*(67*x_3/125 + 1)*x_4)/((x_5*(x_0 + x_2))) | Penman equation | Engineering | [[0, 1000], [0, 1000], [734.4649426197814, 734.4669426197813], [0, 1000], [0, 1000], [8.997176337288693e-10, 745.7438253960154]] |
Eponymous | eponymous_48 | The saturated vapor pressure of air is approximated by an exponential function of temperature. | float | exp(2107/100 - 1*5336/x_0) | Penman equation | Engineering | [[200, 350]] |
Eponymous | eponymous_49 | The slope of the saturation vapor pressure curve is derived from the temperature and the saturated vapor pressure. | float | 5336*exp(2107/100 - 1*5336/x_0)/(x_0**2) | Penman equation | Engineering | [[200, 350]] |
Eponymous | eponymous_50 | This equation describes the periods of elliptic curves in terms of the j-invariant. | float | x_0**3/(x_0**3 - 1*27*x_1**2) | Picard–Fuchs equation | Mathematics | [[-100, 100], [-100, 100]] |
Eponymous | eponymous_51 | This is the Weierstrass form of an elliptic curve. | float | 4*x_0**3 - x_0*x_1 - x_2 | Picard–Fuchs equation | Mathematics | [[-100, 100], [-100, 100], [-100, 100]] |
Eponymous | eponymous_52 | Poisson's equation relating the electric potential to the free charge density. | float | -x_0/x_1 | Poisson's equation | Physics | [[0, 10], [1, 10]] |
Eponymous | eponymous_53 | The Prandtl–Glauert transformation scaling down dimensions and angle of attack by the Prandtl–Glauert factor. | float | x_0**2*x_1 | Prandtl–Glauert equation | Engineering | [[-10, 10], [-10, 10]] |
Eponymous | eponymous_54 | The lift coefficient for a flat elliptical wing using Lifting-Line Theory. | float | (2*pi*x_0)/(x_1 + 2/x_2) | Prandtl–Glauert equation | Engineering | [[-10, 10], [-10, 10], [-10, 10]] |
Eponymous | eponymous_55 | The Prony equation calculates the head loss due to friction within a given run of pipe. | float | x_0*(x_2*x_3 + x_3**2*x_4)/x_1 | Prony equation | Engineering | [[0.1, 100], [0.01, 10], [0.01, 5], [0.01, 10], [0.01, 10]] |
Eponymous | eponymous_56 | The Randles–Ševčík equation at 25 °C describes the peak current in a cyclic voltammetry experiment as a function of scan rate and other parameters. | float | (269/100)*10**5*x_0**(3/2)*x_1*x_2*sqrt(x_3*x_4) | Randles–Sevcik equation | Chemistry | [[1, 10], [1e-05, 0.001], [0.01, 1], [1e-06, 0.0001], [1e-06, 0.0001]] |
Eponymous | eponymous_57 | The finite strain parameter is defined in terms of volume. | float | 1*((x_0/x_1)**(2/3) - 1)/2 | Birch–Murnaghan equation of state | Physics | [[1, 100], [1, 100]] |
Eponymous | eponymous_58 | A general fit formula for the peak currents as a function of the scan rate in a cyclic voltammetry experiment. | float | x_0 + x_1*(x_2/(-3 + 1*E))**x_3 | Randles–Sevcik equation | Chemistry | [[-1.77, 0.23], [-1.78, 0.22], [-2.59, -0.59], [0.42, 2.42]] |
Eponymous | eponymous_59 | The Hugoniot equation describes the conservation of energy across a shock wave. | float | 1*(1/x_3 + 1/x_2)*(-x_0 + x_1)/2 | Rankine–Hugoniot equation | Physics | [[0, 100], [0, 100], [0.1, 10], [0.1, 10]] |
Eponymous | eponymous_60 | The mass entering the bubble is given by the product of density, area, and velocity. | float | x_0*4*pi*x_1**2*x_2 | Rayleigh–Plesset equation | Physics | [[900, 1100], [0.01, 1], [0.01, 1]] |
Eponymous | eponymous_61 | The van Deemter equation relates the height equivalent to a theoretical plate (HETP) to flow and kinetic parameters causing peak broadening in chromatography. | float | x_0 + x_1/x_2 + x_2*(x_3 + x_4) | Rodrigues equation | Chemistry | [[0, 1], [0, 1], [6.851221812098629e-10, 1], [0, 1], [0, 1]] |
Eponymous | eponymous_62 | The optimal velocity for minimizing HETP in chromatography. | float | sqrt(x_0/x_1) | Rodrigues equation | Chemistry | [[5.695283133988482e-10, 1], [3.772975265547984e-10, 1]] |
Eponymous | eponymous_63 | The plate height in chromatography is the ratio of column length to the number of theoretical plates. | float | x_0/x_1 | Rodrigues equation | Chemistry | [[0, 1], [9.085288493748678e-10, 0.027076785042440002]] |
Eponymous | eponymous_64 | The plate count in chromatography can be estimated using the retention time and standard deviation. | float | (x_0/x_1)**2 | Rodrigues equation | Chemistry | [[0, 1], [1.4354550881279238e-10, 1]] |
Eponymous | eponymous_65 | The plate count in chromatography can be estimated using the retention time and peak width at half height. | float | 8*(x_0/x_1)**2*log(2, E) | Rodrigues equation | Chemistry | [[0, 1], [7.666192125554971e-10, 0.42393999176393415]] |
Eponymous | eponymous_66 | The plate count in chromatography can be estimated using the retention time and the width at the base of the peak. | float | 16*(x_0/x_1)**2 | Rodrigues equation | Chemistry | [[0, 1], [2.5780477752590514e-10, 1]] |
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Equation Recovery Benchmark
This dataset contains the public regression tasks and evaluation metrics for the Equation Recovery Benchmark.
You find the different regression tasks inside train.csv.
Evaluation code to score a symbolic regression algorithm is located inside src.
An example is provided in src/quickstart.ipynb.
The dataset contains the following columns
- Collection: dataset name
- task ID: unique ID
- description: some string giving a description of the expression
- dtype: type of data, used for sampling (int or float)
- expression: expression that represents the target function
- name: sometimes the expressions have special names (e.g. gompertz density)
- scientific field: area of science, where expression applies
- support: list of intervals (a,b) for each independent variable. Within the hypercube of these intervals, the expression is valid.
The following licenses apply to the datasets:
- Densities: BSD 3-Clause
- Eponymous: CC-BY-SA 4.0
- Feynman: MIT
- Keijzer: BSD 3-Clause
- Korns: BSD 3-Clause
- Koza: BSD 3-Clause
- Livermore: BSD 3-Clause
- Nguyen: BSD 3-Clause
- OEIS: CC-BY-SA 4.0
- Pagie: BSD 3-Clause
- SynEq: MIT
- SRDS: MIT
- Strogatz: GPL-3.0
- Vladislavleva: BSD 3-Clause
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