OpenCompass/opencompass/datasets/srbench/Feynman/FeynmanEquations.csv

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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