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srbench_add

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16
opencompass/datasets/srbench/2d/Feynman_2d.csv Normal file
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Formula,Filename,n_variables
y = exp(-(x1/x0)**2/2) / (sqrt(2*pi)*x0),I.6.2,2
y = x0 * x1,I.12.1,2
y = x0 * x1,I.12.5,2
y = 1/2 * x0 * x1**2,I.14.4,2
y = x0 / x1,I.25.13,2
y = arcsin(x0 * sin(x1)),I.26.2,2
y = x0 / x1,I.29.4,2
y = (x1 / (2 * pi)) * x0,I.34.27,2
y = (3/2) * x0 * x1,I.39.1,2
y = x0 / (4 * pi * x1**2),II.3.24,2
y = x0 * x1**2 / 2,II.8.31,2
y = 1 + x0 * x1 / (1 - (x0 * x1 / 3)),II.11.28,2
y = x0 * x1**2,II.27.18,2
y = x0 / (2 * (1 + x1)),II.38.14,2
y = x0 * (x1 / (2 * pi)),III.12.43,2
1 Formula Filename n_variables
2 y = exp(-(x1/x0)**2/2) / (sqrt(2*pi)*x0) I.6.2 2
3 y = x0 * x1 I.12.1 2
4 y = x0 * x1 I.12.5 2
5 y = 1/2 * x0 * x1**2 I.14.4 2
6 y = x0 / x1 I.25.13 2
7 y = arcsin(x0 * sin(x1)) I.26.2 2
8 y = x0 / x1 I.29.4 2
9 y = (x1 / (2 * pi)) * x0 I.34.27 2
10 y = (3/2) * x0 * x1 I.39.1 2
11 y = x0 / (4 * pi * x1**2) II.3.24 2
12 y = x0 * x1**2 / 2 II.8.31 2
13 y = 1 + x0 * x1 / (1 - (x0 * x1 / 3)) II.11.28 2
14 y = x0 * x1**2 II.27.18 2
15 y = x0 / (2 * (1 + x1)) II.38.14 2
16 y = x0 * (x1 / (2 * pi)) III.12.43 2

33
opencompass/datasets/srbench/3d/Feynman_3d.csv Normal file
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Formula,Filename,n_variables
y = exp(-((x1 - x2) / x0)**2 / 2) / (sqrt(2 * pi) * x0),I.6.2b,3
y = x0 / sqrt(1 - x1**2 / x2**2),I.10.7,3
y = x0*x2/(4*pi*x1*x2**3),I.12.4,3
y = x0 * x1 * x2,I.14.3,3
y = (x1 + x2) / (1 + x1 * x2 / x0**2),I.16.6,3
y = 1 / (1 / x0 + x2 / x1),I.27.6,3
y = x0 * sin(x2 * x1 / 2)**2 / sin(x1 / 2)**2,I.30.3,3
y = arcsin(x0 / (x2 * x1)),I.30.5,3
y = x2 / (1 - x1 / x0),I.34.1,3
y = (1 + x1/x0) / sqrt(1 - x1**2/x0**2) * x2,I.34.14,3
y = x0 + x1 + 2 * sqrt(x0 * x1) * cos(x2),I.37.4,3
y = 1/(x0-1) * x1 * x2,I.39.11,3
y = x0 * x2 * x1,I.43.31,3
y = sqrt(x0 * x1 / x2),I.47.23,3
y = x0 / (4 * pi * x1 * x2),II.4.23,3
y = (3/5)*x0**2/(4*pi*x1*x2),II.8.7,3
y = x0 / (x1 * (1 + x2)),II.10.9,3
y = x0 / sqrt(1 - x1**2 / x2**2),II.13.23,3
y = x0 * x1 / sqrt(1 - x1**2 / x2**2),II.13.34,3
y = -x0 * x1 * cos(x2),II.15.4,3
y = -x0 * x1 * cos(x2),II.15.5,3
y = sqrt(x0**2/x1**2 - pi**2/x2**2),II.24.17,3
y = x0 * x1 * x2**2,II.27.16,3
y = x0 * x1 / (2 * pi * x2),II.34.2a,3
y = x0 * x1 * x2 / 2,II.34.2,3
y = x0 * x1 / (4 * pi * x2),II.34.29a,3
y = 2*x0*x1/(x2/(2*pi)),III.7.38,3
y = sin(x0 * x1 / (x2 / (2 * pi)))**2,III.8.54,3
y = 2*x0*(1 - cos(x1*x2)),III.15.12,3
y = (x0 / (2 * pi))**2 / (2 * x1 * x2**2),III.15.14,3
y = 2*pi*x0/(x1*x2),III.15.27,3
y = x0 * (1 + x1 * cos(x2)),III.17.37,3
1 Formula Filename n_variables
2 y = exp(-((x1 - x2) / x0)**2 / 2) / (sqrt(2 * pi) * x0) I.6.2b 3
3 y = x0 / sqrt(1 - x1**2 / x2**2) I.10.7 3
4 y = x0*x2/(4*pi*x1*x2**3) I.12.4 3
5 y = x0 * x1 * x2 I.14.3 3
6 y = (x1 + x2) / (1 + x1 * x2 / x0**2) I.16.6 3
7 y = 1 / (1 / x0 + x2 / x1) I.27.6 3
8 y = x0 * sin(x2 * x1 / 2)**2 / sin(x1 / 2)**2 I.30.3 3
9 y = arcsin(x0 / (x2 * x1)) I.30.5 3
10 y = x2 / (1 - x1 / x0) I.34.1 3
11 y = (1 + x1/x0) / sqrt(1 - x1**2/x0**2) * x2 I.34.14 3
12 y = x0 + x1 + 2 * sqrt(x0 * x1) * cos(x2) I.37.4 3
13 y = 1/(x0-1) * x1 * x2 I.39.11 3
14 y = x0 * x2 * x1 I.43.31 3
15 y = sqrt(x0 * x1 / x2) I.47.23 3
16 y = x0 / (4 * pi * x1 * x2) II.4.23 3
17 y = (3/5)*x0**2/(4*pi*x1*x2) II.8.7 3
18 y = x0 / (x1 * (1 + x2)) II.10.9 3
19 y = x0 / sqrt(1 - x1**2 / x2**2) II.13.23 3
20 y = x0 * x1 / sqrt(1 - x1**2 / x2**2) II.13.34 3
21 y = -x0 * x1 * cos(x2) II.15.4 3
22 y = -x0 * x1 * cos(x2) II.15.5 3
23 y = sqrt(x0**2/x1**2 - pi**2/x2**2) II.24.17 3
24 y = x0 * x1 * x2**2 II.27.16 3
25 y = x0 * x1 / (2 * pi * x2) II.34.2a 3
26 y = x0 * x1 * x2 / 2 II.34.2 3
27 y = x0 * x1 / (4 * pi * x2) II.34.29a 3
28 y = 2*x0*x1/(x2/(2*pi)) III.7.38 3
29 y = sin(x0 * x1 / (x2 / (2 * pi)))**2 III.8.54 3
30 y = 2*x0*(1 - cos(x1*x2)) III.15.12 3
31 y = (x0 / (2 * pi))**2 / (2 * x1 * x2**2) III.15.14 3
32 y = 2*pi*x0/(x1*x2) III.15.27 3
33 y = x0 * (1 + x1 * cos(x2)) III.17.37 3

131
opencompass/datasets/srbench/Feynman/FeynmanEquations.csv Normal file
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Filename,Number,Output,Formula,# variables,v1_name,v1_low,v1_high,v2_name,v2_low,v2_high,v3_name,v3_low,v3_high,v4_name,v4_low,v4_high,v5_name,v5_low,v5_high,v6_name,v6_low,v6_high,v7_name,v7_low,v7_high,v8_name,v8_low,v8_high,v9_name,v9_low,v9_high,v10_name,v10_low,v10_high
I.6.2a,1,f,exp(-theta**2/2)/sqrt(2*pi),1,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,,,,
I.6.2,2,f,exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma),2,sigma,1,3,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,
I.6.2b,3,f,exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma),3,sigma,1,3,theta,1,3,theta1,1,3,,,,,,,,,,,,,,,,,,,,,
I.8.14,4,d,sqrt((x2-x1)**2+(y2-y1)**2),4,x1,1,5,x2,1,5,y1,1,5,y2,1,5,,,,,,,,,,,,,,,,,,
I.9.18,5,F,G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2),9,m1,1,2,m2,1,2,G,1,2,x1,3,4,x2,1,2,y1,3,4,y2,1,2,z1,3,4,z2,1,2,,,
I.10.7,6,m,m_0/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
I.11.19,7,A,x1*y1+x2*y2+x3*y3,6,x1,1,5,x2,1,5,x3,1,5,y1,1,5,y2,1,5,y3,1,5,,,,,,,,,,,,
I.12.1,8,F,mu*Nn,2,mu,1,5,Nn,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.12.2,10,F,q1*q2*r/(4*pi*epsilon*r**3),4,q1,1,5,q2,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,
I.12.4,11,Ef,q1*r/(4*pi*epsilon*r**3),3,q1,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
I.12.5,12,F,q2*Ef,2,q2,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.12.11,13,F,q*(Ef+B*v*sin(theta)),5,q,1,5,Ef,1,5,B,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,
I.13.4,9,K,1/2*m*(v**2+u**2+w**2),4,m,1,5,v,1,5,u,1,5,w,1,5,,,,,,,,,,,,,,,,,,
I.13.12,14,U,G*m1*m2*(1/r2-1/r1),5,m1,1,5,m2,1,5,r1,1,5,r2,1,5,G,1,5,,,,,,,,,,,,,,,
I.14.3,15,U,m*g*z,3,m,1,5,g,1,5,z,1,5,,,,,,,,,,,,,,,,,,,,,
I.14.4,16,U,1/2*k_spring*x**2,2,k_spring,1,5,x,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.15.3x,17,x1,(x-u*t)/sqrt(1-u**2/c**2),4,x,5,10,u,1,2,c,3,20,t,1,2,,,,,,,,,,,,,,,,,,
I.15.3t,18,t1,(t-u*x/c**2)/sqrt(1-u**2/c**2),4,x,1,5,c,3,10,u,1,2,t,1,5,,,,,,,,,,,,,,,,,,
I.15.1,19,p,m_0*v/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
I.16.6,20,v1,(u+v)/(1+u*v/c**2),3,c,1,5,v,1,5,u,1,5,,,,,,,,,,,,,,,,,,,,,
I.18.4,21,r,(m1*r1+m2*r2)/(m1+m2),4,m1,1,5,m2,1,5,r1,1,5,r2,1,5,,,,,,,,,,,,,,,,,,
I.18.12,22,tau,r*F*sin(theta),2,r,1,5,F,1,5,theta,0,5,,,,,,,,,,,,,,,,,,,,,
I.18.14,23,L,m*r*v*sin(theta),3,m,1,5,r,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,,,,
I.24.6,24,E_n,1/2*m*(omega**2+omega_0**2)*1/2*x**2,4,m,1,3,omega,1,3,omega_0,1,3,x,1,3,,,,,,,,,,,,,,,,,,
I.25.13,25,Volt,q/C,2,q,1,5,C,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.26.2,26,theta1,arcsin(n*sin(theta2)),2,n,0,1,theta2,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.27.6,27,foc,1/(1/d1+n/d2),3,d1,1,5,d2,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
I.29.4,28,k,omega/c,2,omega,1,10,c,1,10,,,,,,,,,,,,,,,,,,,,,,,,
I.29.16,29,x,sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2)),4,x1,1,5,x2,1,5,theta1,1,5,theta2,1,5,,,,,,,,,,,,,,,,,,
I.30.3,30,Int,Int_0*sin(n*theta/2)**2/sin(theta/2)**2,3,Int_0,1,5,theta,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
I.30.5,31,theta,arcsin(lambd/(n*d)),3,lambd,1,2,d,2,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
I.32.5,32,Pwr,q**2*a**2/(6*pi*epsilon*c**3),4,q,1,5,a,1,5,epsilon,1,5,c,1,5,,,,,,,,,,,,,,,,,,
I.32.17,33,Pwr,(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2),6,epsilon,1,2,c,1,2,Ef,1,2,r,1,2,omega,1,2,omega_0,3,5,,,,,,,,,,,,
I.34.8,34,omega,q*v*B/p,4,q,1,5,v,1,5,B,1,5,p,1,5,,,,,,,,,,,,,,,,,,
I.34.1,35,omega,omega_0/(1-v/c),3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
I.34.14,36,omega,(1+v/c)/sqrt(1-v**2/c**2)*omega_0,3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
I.34.27,37,E_n,(h/(2*pi))*omega,2,omega,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.37.4,38,Int,I1+I2+2*sqrt(I1*I2)*cos(delta),3,I1,1,5,I2,1,5,delta,1,5,,,,,,,,,,,,,,,,,,,,,
I.38.12,39,r,4*pi*epsilon*(h/(2*pi))**2/(m*q**2),3,m,1,5,q,1,5,h,1,5,epsilon,1,5,,,,,,,,,,,,,,,,,,
I.39.1,40,E_n,3/2*pr*V,2,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,,,,
I.39.11,41,E_n,1/(gamma-1)*pr*V,3,gamma,2,5,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,
I.39.22,42,pr,n*kb*T/V,4,n,1,5,T,1,5,V,1,5,kb,1,5,,,,,,,,,,,,,,,,,,
I.40.1,43,n,n_0*exp(-m*g*x/(kb*T)),6,n_0,1,5,m,1,5,x,1,5,T,1,5,g,1,5,kb,1,5,,,,,,,,,,,,
I.41.16,44,L_rad,h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1)),5,omega,1,5,T,1,5,h,1,5,kb,1,5,c,1,5,,,,,,,,,,,,,,,
I.43.16,45,v,mu_drift*q*Volt/d,4,mu_drift,1,5,q,1,5,Volt,1,5,d,1,5,,,,,,,,,,,,,,,,,,
I.43.31,46,D,mob*kb*T,3,mob,1,5,T,1,5,kb,1,5,,,,,,,,,,,,,,,,,,,,,
I.43.43,47,kappa,1/(gamma-1)*kb*v/A,4,gamma,2,5,kb,1,5,A,1,5,v,1,5,,,,,,,,,,,,,,,,,,
I.44.4,48,E_n,n*kb*T*ln(V2/V1),5,n,1,5,kb,1,5,T,1,5,V1,1,5,V2,1,5,,,,,,,,,,,,,,,
I.47.23,49,c,sqrt(gamma*pr/rho),3,gamma,1,5,pr,1,5,rho,1,5,,,,,,,,,,,,,,,,,,,,,
I.48.2,50,E_n,m*c**2/sqrt(1-v**2/c**2),3,m,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
I.50.26,51,x,x1*(cos(omega*t)+alpha*cos(omega*t)**2),4,x1,1,3,omega,1,3,t,1,3,alpha,1,3,,,,,,,,,,,,,,,,,,
II.2.42,52,Pwr,kappa*(T2-T1)*A/d,5,kappa,1,5,T1,1,5,T2,1,5,A,1,5,d,1,5,,,,,,,,,,,,,,,
II.3.24,53,flux,Pwr/(4*pi*r**2),2,Pwr,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,,,,
II.4.23,54,Volt,q/(4*pi*epsilon*r),3,q,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
II.6.11,55,Volt,1/(4*pi*epsilon)*p_d*cos(theta)/r**2,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
II.6.15a,56,Ef,p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2),6,epsilon,1,3,p_d,1,3,r,1,3,x,1,3,y,1,3,z,1,3,,,,,,,,,,,,
II.6.15b,57,Ef,p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
II.8.7,58,E_n,3/5*q**2/(4*pi*epsilon*d),3,q,1,5,epsilon,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
II.8.31,59,E_den,epsilon*Ef**2/2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
II.10.9,60,Ef,sigma_den/epsilon*1/(1+chi),3,sigma_den,1,5,epsilon,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
II.11.3,61,x,q*Ef/(m*(omega_0**2-omega**2)),5,q,1,3,Ef,1,3,m,1,3,omega_0,3,5,omega,1,2,,,,,,,,,,,,,,,
II.11.17,62,n,n_0*(1+p_d*Ef*cos(theta)/(kb*T)),6,n_0,1,3,kb,1,3,T,1,3,theta,1,3,p_d,1,3,Ef,1,3,,,,,,,,,,,,
II.11.20,63,Pol,n_rho*p_d**2*Ef/(3*kb*T),5,n_rho,1,5,p_d,1,5,Ef,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
II.11.27,64,Pol,n*alpha/(1-(n*alpha/3))*epsilon*Ef,4,n,0,1,alpha,0,1,epsilon,1,2,Ef,1,2,,,,,,,,,,,,,,,,,,
II.11.28,65,theta,1+n*alpha/(1-(n*alpha/3)),2,n,0,1,alpha,0,1,,,,,,,,,,,,,,,,,,,,,,,,
II.13.17,66,B,1/(4*pi*epsilon*c**2)*2*I/r,4,epsilon,1,5,c,1,5,I,1,5,r,1,5,,,,,,,,,,,,,,,,,,
II.13.23,67,rho_c,rho_c_0/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
II.13.34,68,j,rho_c_0*v/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
II.15.4,69,E_n,-mom*B*cos(theta),3,mom,1,5,B,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
II.15.5,70,E_n,-p_d*Ef*cos(theta),3,p_d,1,5,Ef,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
II.21.32,71,Volt,q/(4*pi*epsilon*r*(1-v/c)),5,q,1,5,epsilon,1,5,r,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,
II.24.17,72,k,sqrt(omega**2/c**2-pi**2/d**2),3,omega,4,6,c,1,2,d,2,4,,,,,,,,,,,,,,,,,,,,,
II.27.16,73,flux,epsilon*c*Ef**2,3,epsilon,1,5,c,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,
II.27.18,74,E_den,epsilon*Ef**2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
II.34.2a,75,I,q*v/(2*pi*r),3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
II.34.2,76,mom,q*v*r/2,3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
II.34.11,77,omega,g_*q*B/(2*m),4,g_,1,5,q,1,5,B,1,5,m,1,5,,,,,,,,,,,,,,,,,,
II.34.29a,78,mom,q*h/(4*pi*m),3,q,1,5,h,1,5,m,1,5,,,,,,,,,,,,,,,,,,,,,
II.34.29b,79,E_n,g_*mom*B*Jz/(h/(2*pi)),5,g_,1,5,h,1,5,Jz,1,5,mom,1,5,B,1,5,,,,,,,,,,,,,,,
II.35.18,80,n,n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T))),5,n_0,1,3,kb,1,3,T,1,3,mom,1,3,B,1,3,,,,,,,,,,,,,,,
II.35.21,81,M,n_rho*mom*tanh(mom*B/(kb*T)),5,n_rho,1,5,mom,1,5,B,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
II.36.38,82,f,mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M,8,mom,1,3,H,1,3,kb,1,3,T,1,3,alpha,1,3,epsilon,1,3,c,1,3,M,1,3,,,,,,
II.37.1,83,E_n,mom*(1+chi)*B,6,mom,1,5,B,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
II.38.3,84,F,Y*A*x/d,4,Y,1,5,A,1,5,d,1,5,x,1,5,,,,,,,,,,,,,,,,,,
II.38.14,85,mu_S,Y/(2*(1+sigma)),2,Y,1,5,sigma,1,5,,,,,,,,,,,,,,,,,,,,,,,,
III.4.32,86,n,1/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
III.4.33,87,E_n,(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
III.7.38,88,omega,2*mom*B/(h/(2*pi)),3,mom,1,5,B,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,
III.8.54,89,prob,sin(E_n*t/(h/(2*pi)))**2,3,E_n,1,2,t,1,2,h,1,4,,,,,,,,,,,,,,,,,,,,,
III.9.52,90,prob,(p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2,6,p_d,1,3,Ef,1,3,t,1,3,h,1,3,omega,1,5,omega_0,1,5,,,,,,,,,,,,
III.10.19,91,E_n,mom*sqrt(Bx**2+By**2+Bz**2),3,mom,1,5,Bx,1,5,By,1,5,Bz,1,5,,,,,,,,,,,,,,,,,,
III.12.43,92,L,n*(h/(2*pi)),2,n,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
III.13.18,93,v,2*E_n*d**2*k/(h/(2*pi)),4,E_n,1,5,d,1,5,k,1,5,h,1,5,,,,,,,,,,,,,,,,,,
III.14.14,94,I,I_0*(exp(q*Volt/(kb*T))-1),5,I_0,1,5,q,1,2,Volt,1,2,kb,1,2,T,1,2,,,,,,,,,,,,,,,
III.15.12,95,E_n,2*U*(1-cos(k*d)),3,U,1,5,k,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
III.15.14,96,m,(h/(2*pi))**2/(2*E_n*d**2),3,h,1,5,E_n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
III.15.27,97,k,2*pi*alpha/(n*d),3,alpha,1,5,n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
III.17.37,98,f,beta*(1+alpha*cos(theta)),3,beta,1,5,alpha,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
III.19.51,99,E_n,-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2),4,m,1,5,q,1,5,h,1,5,n,1,5,epsilon,1,5,,,,,,,,,,,,,,,
III.21.20,100,j,-rho_c_0*q*A_vec/m,4,rho_c_0,1,5,q,1,5,A_vec,1,5,m,1,5,,,,,,,,,,,,,,,,,,
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1 Filename Number Output Formula # variables v1_name v1_low v1_high v2_name v2_low v2_high v3_name v3_low v3_high v4_name v4_low v4_high v5_name v5_low v5_high v6_name v6_low v6_high v7_name v7_low v7_high v8_name v8_low v8_high v9_name v9_low v9_high v10_name v10_low v10_high
2 I.6.2a 1 f exp(-theta**2/2)/sqrt(2*pi) 1 theta 1 3
3 I.6.2 2 f exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma) 2 sigma 1 3 theta 1 3
4 I.6.2b 3 f exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma) 3 sigma 1 3 theta 1 3 theta1 1 3
5 I.8.14 4 d sqrt((x2-x1)**2+(y2-y1)**2) 4 x1 1 5 x2 1 5 y1 1 5 y2 1 5
6 I.9.18 5 F G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2) 9 m1 1 2 m2 1 2 G 1 2 x1 3 4 x2 1 2 y1 3 4 y2 1 2 z1 3 4 z2 1 2
7 I.10.7 6 m m_0/sqrt(1-v**2/c**2) 3 m_0 1 5 v 1 2 c 3 10
8 I.11.19 7 A x1*y1+x2*y2+x3*y3 6 x1 1 5 x2 1 5 x3 1 5 y1 1 5 y2 1 5 y3 1 5
9 I.12.1 8 F mu*Nn 2 mu 1 5 Nn 1 5
10 I.12.2 10 F q1*q2*r/(4*pi*epsilon*r**3) 4 q1 1 5 q2 1 5 epsilon 1 5 r 1 5
11 I.12.4 11 Ef q1*r/(4*pi*epsilon*r**3) 3 q1 1 5 epsilon 1 5 r 1 5
12 I.12.5 12 F q2*Ef 2 q2 1 5 Ef 1 5
13 I.12.11 13 F q*(Ef+B*v*sin(theta)) 5 q 1 5 Ef 1 5 B 1 5 v 1 5 theta 1 5
14 I.13.4 9 K 1/2*m*(v**2+u**2+w**2) 4 m 1 5 v 1 5 u 1 5 w 1 5
15 I.13.12 14 U G*m1*m2*(1/r2-1/r1) 5 m1 1 5 m2 1 5 r1 1 5 r2 1 5 G 1 5
16 I.14.3 15 U m*g*z 3 m 1 5 g 1 5 z 1 5
17 I.14.4 16 U 1/2*k_spring*x**2 2 k_spring 1 5 x 1 5
18 I.15.3x 17 x1 (x-u*t)/sqrt(1-u**2/c**2) 4 x 5 10 u 1 2 c 3 20 t 1 2
19 I.15.3t 18 t1 (t-u*x/c**2)/sqrt(1-u**2/c**2) 4 x 1 5 c 3 10 u 1 2 t 1 5
20 I.15.1 19 p m_0*v/sqrt(1-v**2/c**2) 3 m_0 1 5 v 1 2 c 3 10
21 I.16.6 20 v1 (u+v)/(1+u*v/c**2) 3 c 1 5 v 1 5 u 1 5
22 I.18.4 21 r (m1*r1+m2*r2)/(m1+m2) 4 m1 1 5 m2 1 5 r1 1 5 r2 1 5
23 I.18.12 22 tau r*F*sin(theta) 2 r 1 5 F 1 5 theta 0 5
24 I.18.14 23 L m*r*v*sin(theta) 3 m 1 5 r 1 5 v 1 5 theta 1 5
25 I.24.6 24 E_n 1/2*m*(omega**2+omega_0**2)*1/2*x**2 4 m 1 3 omega 1 3 omega_0 1 3 x 1 3
26 I.25.13 25 Volt q/C 2 q 1 5 C 1 5
27 I.26.2 26 theta1 arcsin(n*sin(theta2)) 2 n 0 1 theta2 1 5
28 I.27.6 27 foc 1/(1/d1+n/d2) 3 d1 1 5 d2 1 5 n 1 5
29 I.29.4 28 k omega/c 2 omega 1 10 c 1 10
30 I.29.16 29 x sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2)) 4 x1 1 5 x2 1 5 theta1 1 5 theta2 1 5
31 I.30.3 30 Int Int_0*sin(n*theta/2)**2/sin(theta/2)**2 3 Int_0 1 5 theta 1 5 n 1 5
32 I.30.5 31 theta arcsin(lambd/(n*d)) 3 lambd 1 2 d 2 5 n 1 5
33 I.32.5 32 Pwr q**2*a**2/(6*pi*epsilon*c**3) 4 q 1 5 a 1 5 epsilon 1 5 c 1 5
34 I.32.17 33 Pwr (1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2) 6 epsilon 1 2 c 1 2 Ef 1 2 r 1 2 omega 1 2 omega_0 3 5
35 I.34.8 34 omega q*v*B/p 4 q 1 5 v 1 5 B 1 5 p 1 5
36 I.34.1 35 omega omega_0/(1-v/c) 3 c 3 10 v 1 2 omega_0 1 5
37 I.34.14 36 omega (1+v/c)/sqrt(1-v**2/c**2)*omega_0 3 c 3 10 v 1 2 omega_0 1 5
38 I.34.27 37 E_n (h/(2*pi))*omega 2 omega 1 5 h 1 5
39 I.37.4 38 Int I1+I2+2*sqrt(I1*I2)*cos(delta) 3 I1 1 5 I2 1 5 delta 1 5
40 I.38.12 39 r 4*pi*epsilon*(h/(2*pi))**2/(m*q**2) 3 m 1 5 q 1 5 h 1 5 epsilon 1 5
41 I.39.1 40 E_n 3/2*pr*V 2 pr 1 5 V 1 5
42 I.39.11 41 E_n 1/(gamma-1)*pr*V 3 gamma 2 5 pr 1 5 V 1 5
43 I.39.22 42 pr n*kb*T/V 4 n 1 5 T 1 5 V 1 5 kb 1 5
44 I.40.1 43 n n_0*exp(-m*g*x/(kb*T)) 6 n_0 1 5 m 1 5 x 1 5 T 1 5 g 1 5 kb 1 5
45 I.41.16 44 L_rad h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1)) 5 omega 1 5 T 1 5 h 1 5 kb 1 5 c 1 5
46 I.43.16 45 v mu_drift*q*Volt/d 4 mu_drift 1 5 q 1 5 Volt 1 5 d 1 5
47 I.43.31 46 D mob*kb*T 3 mob 1 5 T 1 5 kb 1 5
48 I.43.43 47 kappa 1/(gamma-1)*kb*v/A 4 gamma 2 5 kb 1 5 A 1 5 v 1 5
49 I.44.4 48 E_n n*kb*T*ln(V2/V1) 5 n 1 5 kb 1 5 T 1 5 V1 1 5 V2 1 5
50 I.47.23 49 c sqrt(gamma*pr/rho) 3 gamma 1 5 pr 1 5 rho 1 5
51 I.48.2 50 E_n m*c**2/sqrt(1-v**2/c**2) 3 m 1 5 v 1 2 c 3 10
52 I.50.26 51 x x1*(cos(omega*t)+alpha*cos(omega*t)**2) 4 x1 1 3 omega 1 3 t 1 3 alpha 1 3
53 II.2.42 52 Pwr kappa*(T2-T1)*A/d 5 kappa 1 5 T1 1 5 T2 1 5 A 1 5 d 1 5
54 II.3.24 53 flux Pwr/(4*pi*r**2) 2 Pwr 1 5 r 1 5
55 II.4.23 54 Volt q/(4*pi*epsilon*r) 3 q 1 5 epsilon 1 5 r 1 5
56 II.6.11 55 Volt 1/(4*pi*epsilon)*p_d*cos(theta)/r**2 4 epsilon 1 3 p_d 1 3 theta 1 3 r 1 3
57 II.6.15a 56 Ef p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2) 6 epsilon 1 3 p_d 1 3 r 1 3 x 1 3 y 1 3 z 1 3
58 II.6.15b 57 Ef p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3 4 epsilon 1 3 p_d 1 3 theta 1 3 r 1 3
59 II.8.7 58 E_n 3/5*q**2/(4*pi*epsilon*d) 3 q 1 5 epsilon 1 5 d 1 5
60 II.8.31 59 E_den epsilon*Ef**2/2 2 epsilon 1 5 Ef 1 5
61 II.10.9 60 Ef sigma_den/epsilon*1/(1+chi) 3 sigma_den 1 5 epsilon 1 5 chi 1 5
62 II.11.3 61 x q*Ef/(m*(omega_0**2-omega**2)) 5 q 1 3 Ef 1 3 m 1 3 omega_0 3 5 omega 1 2
63 II.11.17 62 n n_0*(1+p_d*Ef*cos(theta)/(kb*T)) 6 n_0 1 3 kb 1 3 T 1 3 theta 1 3 p_d 1 3 Ef 1 3
64 II.11.20 63 Pol n_rho*p_d**2*Ef/(3*kb*T) 5 n_rho 1 5 p_d 1 5 Ef 1 5 kb 1 5 T 1 5
65 II.11.27 64 Pol n*alpha/(1-(n*alpha/3))*epsilon*Ef 4 n 0 1 alpha 0 1 epsilon 1 2 Ef 1 2
66 II.11.28 65 theta 1+n*alpha/(1-(n*alpha/3)) 2 n 0 1 alpha 0 1
67 II.13.17 66 B 1/(4*pi*epsilon*c**2)*2*I/r 4 epsilon 1 5 c 1 5 I 1 5 r 1 5
68 II.13.23 67 rho_c rho_c_0/sqrt(1-v**2/c**2) 3 rho_c_0 1 5 v 1 2 c 3 10
69 II.13.34 68 j rho_c_0*v/sqrt(1-v**2/c**2) 3 rho_c_0 1 5 v 1 2 c 3 10
70 II.15.4 69 E_n -mom*B*cos(theta) 3 mom 1 5 B 1 5 theta 1 5
71 II.15.5 70 E_n -p_d*Ef*cos(theta) 3 p_d 1 5 Ef 1 5 theta 1 5
72 II.21.32 71 Volt q/(4*pi*epsilon*r*(1-v/c)) 5 q 1 5 epsilon 1 5 r 1 5 v 1 2 c 3 10
73 II.24.17 72 k sqrt(omega**2/c**2-pi**2/d**2) 3 omega 4 6 c 1 2 d 2 4
74 II.27.16 73 flux epsilon*c*Ef**2 3 epsilon 1 5 c 1 5 Ef 1 5
75 II.27.18 74 E_den epsilon*Ef**2 2 epsilon 1 5 Ef 1 5
76 II.34.2a 75 I q*v/(2*pi*r) 3 q 1 5 v 1 5 r 1 5
77 II.34.2 76 mom q*v*r/2 3 q 1 5 v 1 5 r 1 5
78 II.34.11 77 omega g_*q*B/(2*m) 4 g_ 1 5 q 1 5 B 1 5 m 1 5
79 II.34.29a 78 mom q*h/(4*pi*m) 3 q 1 5 h 1 5 m 1 5
80 II.34.29b 79 E_n g_*mom*B*Jz/(h/(2*pi)) 5 g_ 1 5 h 1 5 Jz 1 5 mom 1 5 B 1 5
81 II.35.18 80 n n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T))) 5 n_0 1 3 kb 1 3 T 1 3 mom 1 3 B 1 3
82 II.35.21 81 M n_rho*mom*tanh(mom*B/(kb*T)) 5 n_rho 1 5 mom 1 5 B 1 5 kb 1 5 T 1 5
83 II.36.38 82 f mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M 8 mom 1 3 H 1 3 kb 1 3 T 1 3 alpha 1 3 epsilon 1 3 c 1 3 M 1 3
84 II.37.1 83 E_n mom*(1+chi)*B 6 mom 1 5 B 1 5 chi 1 5
85 II.38.3 84 F Y*A*x/d 4 Y 1 5 A 1 5 d 1 5 x 1 5
86 II.38.14 85 mu_S Y/(2*(1+sigma)) 2 Y 1 5 sigma 1 5
87 III.4.32 86 n 1/(exp((h/(2*pi))*omega/(kb*T))-1) 4 h 1 5 omega 1 5 kb 1 5 T 1 5
88 III.4.33 87 E_n (h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1) 4 h 1 5 omega 1 5 kb 1 5 T 1 5
89 III.7.38 88 omega 2*mom*B/(h/(2*pi)) 3 mom 1 5 B 1 5 h 1 5
90 III.8.54 89 prob sin(E_n*t/(h/(2*pi)))**2 3 E_n 1 2 t 1 2 h 1 4
91 III.9.52 90 prob (p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2 6 p_d 1 3 Ef 1 3 t 1 3 h 1 3 omega 1 5 omega_0 1 5
92 III.10.19 91 E_n mom*sqrt(Bx**2+By**2+Bz**2) 3 mom 1 5 Bx 1 5 By 1 5 Bz 1 5
93 III.12.43 92 L n*(h/(2*pi)) 2 n 1 5 h 1 5
94 III.13.18 93 v 2*E_n*d**2*k/(h/(2*pi)) 4 E_n 1 5 d 1 5 k 1 5 h 1 5
95 III.14.14 94 I I_0*(exp(q*Volt/(kb*T))-1) 5 I_0 1 5 q 1 2 Volt 1 2 kb 1 2 T 1 2
96 III.15.12 95 E_n 2*U*(1-cos(k*d)) 3 U 1 5 k 1 5 d 1 5
97 III.15.14 96 m (h/(2*pi))**2/(2*E_n*d**2) 3 h 1 5 E_n 1 5 d 1 5
98 III.15.27 97 k 2*pi*alpha/(n*d) 3 alpha 1 5 n 1 5 d 1 5
99 III.17.37 98 f beta*(1+alpha*cos(theta)) 3 beta 1 5 alpha 1 5 theta 1 5
100 III.19.51 99 E_n -m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2) 4 m 1 5 q 1 5 h 1 5 n 1 5 epsilon 1 5
101 III.21.20 100 j -rho_c_0*q*A_vec/m 4 rho_c_0 1 5 q 1 5 A_vec 1 5 m 1 5
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