Table 5. Tested Feynman equations, part 2 (same notation as in Table 4).

Feynman Eq.	Equation	Solution Time (s)	Methods Used	Data Needed	Solved By Eureqa	Solved W/o da	Noise Tolerance
II.2.42	$\mathrm{P}=\frac{\mathrm{\kappa }(T_2-T_1)A}{d}$	54	da, bf	10	Yes	Yes	10−3
II.3.24	$F_E=\frac{P}{4\mathrm{\pi }{r}^2}$	8	da	10	Yes	Yes	10−2
II.4.23	$V_e=\frac{q}{4\mathrm{\pi }\mathrm{ϵ}r}$	10	da	10	Yes	Yes	10−2
II.6.11	$V_e=\frac{1}{4\mathrm{\pi }\mathrm{ϵ}}\frac{p_d\text{cos} \mathrm{\theta }}{r^2}$	18	da, bf	10	Yes	Yes	10−3
II.6.15a	$E_f=\frac{3}{4\mathrm{\pi }\mathrm{ϵ}}\frac{p_{d}z}{r^5}\sqrt{x^2+y^2}$	2801	da, sm, bf	104	No	Yes	10−3
II.6.15b	$E_f=\frac{3}{4\mathrm{\pi }\mathrm{ϵ}}\frac{p_d}{r^3}\text{cos} \mathrm{\theta }\text{sin} \mathrm{\theta }$	23	da, bf	10	Yes	Yes	10−2
II.8.7	$E=\frac{3}{5}\frac{q^2}{4\mathrm{\pi }\mathrm{ϵ}d}$	10	da	10	Yes	Yes	10−2
II.8.31	$E_{\text{den}}=\frac{\mathrm{ϵ}{E}_f^2}{2}$	8	da	10	Yes	Yes	10−2
II.10.9	$E_f=\frac{{\mathrm{\sigma }}_{\text{den}}}{\mathrm{ϵ}}\frac{1}{1+\mathrm{\chi }}$	13	da, bf	10	Yes	Yes	10−2
II.11.3	$x=\frac{{\mathrm{qE}}_f}{m({\mathrm{\omega }}_0^2-{\mathrm{\omega }}^2)}$	25	da, bf	10	Yes	Yes	10−3
II.11.17	$n=n_0(1+\frac{p_{\mathrm{d}}{E}_f\text{cos} \mathrm{\theta }}{k_{b}T})$	28	da, bf	10	Yes	Yes	10−2
II.11.20	$P*=\frac{n_{\mathrm{\rho }}{p}_{\mathrm{d}}^2{E}_f}{3k_{b}T}$	18	da, bf	10	Yes	Yes	10−3
II.11.27	$P*=\frac{n\mathrm{\alpha }}{1-n\mathrm{\alpha }/3}\mathrm{ϵ}{E}_f$	337	da bf-inverse	102	No	Yes	10−3
II.11.28	$\mathrm{\theta }=1+\frac{n\mathrm{\alpha }}{1-(n\mathrm{\alpha }/3)}$	1708	da, sym*, bf	102	No	Yes	10−4
II.13.17	$B=\frac{1}{4\mathrm{\pi }\mathrm{ϵ}{c}^2}\frac{2I}{r}$	13	da	10	Yes	Yes	10−2
II.13.23	${\mathrm{\rho }}_c=\frac{{\mathrm{\rho }}_{c_0}}{\sqrt{1-v^2/c^2}}$	13	da, bf	102	No	Yes	10−4
II.13.34	$j=\frac{{\mathrm{\rho }}_{c_0}v}{\sqrt{1-v^2/c^2}}$	14	da, bf	10	No	Yes	10−4
II.15.4	E = − μMB cos θ	14	da, bf	10	Yes	Yes	10−3
II.15.5	E = − pdEf cos θ	14	da, bf	10	Yes	Yes	10−3
II.21.32	$V_e=\frac{q}{4\mathrm{\pi }\mathrm{ϵ}r(1-v/c)}$	21	da, bf	10	Yes	Yes	10−3
II.24.17	$k=\sqrt{\frac{{\mathrm{\omega }}^2}{c^2}-\frac{{\mathrm{\pi }}^2}{d^2}}$	62	da bf	10	No	Yes	10−5
II.27.16	$F_E=\mathrm{ϵ}{\mathrm{cE}}_f^2$	13	da	10	Yes	Yes	10−2
II.27.18	$E_{\text{den}}=\mathrm{ϵ}{E}_f^2$	9	da	10	Yes	Yes	10−2
II.34.2a	$I=\frac{\mathit{qv}}{2\mathrm{\pi }r}$	11	da	10	Yes	Yes	10−2
II.34.2	${\mathrm{\mu }}_M=\frac{\mathit{qvr}}{2}$	11	da	10	Yes	Yes	10−2
II.34.11	$\mathrm{\omega }=\frac{g_{\text{\_}}\mathit{qB}}{2m}$	16	da, bf	10	Yes	Yes	10−4
II.34.29a	${\mathrm{\mu }}_M=\frac{\mathit{qh}}{4\mathrm{\pi }m}$	12	da	10	Yes	Yes	10−2
II.34.29b	$E=\frac{g_{\text{\_}}{\mathrm{\mu }}_{M}B{J}_z}{\mathrm{\hslash }}$	18	da, bf	10	Yes	Yes	10−4
II.35.18	$n=\frac{n_0}{\text{exp}({\mathrm{\mu }}_{m}B/(k_{b}T))+\text{exp}(-{\mathrm{\mu }}_{m}B/(k_{b}T))}$	30	da, bf	10	No	Yes	10−2
II.35.21	$M=n_{\mathrm{\rho }}{\mathrm{\mu }}_M\text{tanh}\left(\frac{{\mathrm{\mu }}_{M}B}{k_{b}T}\right)$	1597	da, halve-input, bf	10	Yes	No	10−4
II.36.38	$f=\frac{{\mathrm{\mu }}_{m}B}{k_{b}T}+\frac{{\mathrm{\mu }}_m\mathrm{\alpha }M}{\mathrm{ϵ}{c}^2{k}_{b}T}$	77	da bf	10	Yes	Yes	10−2
II.37.1	E = μM(1 + χ)B	15	da, bf	10	Yes	Yes	10−3
II.38.3	$F=\frac{\mathit{YAx}}{d}$	47	da, bf	10	Yes	Yes	10−3
II.38.14	${\mathrm{\mu }}_{\mathrm{S}}=\frac{Y}{2(1+\mathrm{\sigma })}$	13	da, bf	10	Yes	Yes	10−3
III.4.32	$n=\frac{1}{e^{\frac{\mathrm{\hslash }\mathrm{\omega }}{k_{b}T}}-1}$	20	da, bf	10	No	Yes	10−3
III.4.33	$E=\frac{\mathrm{\hslash }\mathrm{\omega }}{e^{\frac{\mathrm{\hslash }\mathrm{\omega }}{k_{b}T}}-1}$	19	da, bf	10	No	Yes	10−3
III.7.38	$\mathrm{\omega }=\frac{2{\mathrm{\mu }}_{M}B}{\mathrm{\hslash }}$	13	da	10	Yes	Yes	10−2
III.8.54	$p_{\mathrm{\gamma }}=\text{sin}{\left(\frac{\mathit{Et}}{\mathrm{\hslash }}\right)}^2$	39	da, bf	10	No	Yes	10−3
III.9.52	$p_{\mathrm{\gamma }}=\frac{p_{\mathrm{d}}{E}_{f}t}{\mathrm{\hslash }}\frac{\text{sin}{((\mathrm{\omega }-{\mathrm{\omega }}_0)t/2)}^2}{{((\mathrm{\omega }-{\mathrm{\omega }}_0)t/2)}^2}$	3162	da, sym–, sm, bf	103	No	Yes	10−3
III.10.19	$E={\mathrm{\mu }}_M\sqrt{B_x^2+B_y^2+B_z^2}$	410	da, bf-squared	102	Yes	Yes	10−4
III.12.43	L = nℏ	11	da, bf	10	Yes	Yes	10−3
III.13.18	$v=\frac{2E{d}^{2}k}{\mathrm{\hslash }}$	16	da, bf	10	Yes	Yes	10−4
III.14.14	$I=I_0(e^{\frac{q{V}_e}{k_{b}T}}-1)$	18	da, bf	10	No	Yes	10−3
III.15.12	E = 2U(1 − cos (kd))	14	da, bf	10	Yes	Yes	10−4
III.15.14	$m=\frac{{\mathrm{\hslash }}^2}{2E{d}^2}$	10	da	10	Yes	Yes	10−2
III.15.27	$k=\frac{2\mathrm{\pi }\mathrm{\alpha }}{\mathit{nd}}$	14	da, bf	10	Yes	Yes	10−3
III.17.37	f = β(1 + αcos θ)	27	bf	10	Yes	Yes	10−3
III.19.51	$E=\frac{-m{q}^4}{2{(4\mathrm{\pi }\mathrm{ϵ})}^2{\mathrm{\hslash }}^2}\frac{1}{n^2}$	18	da, bf	10	Yes	Yes	10−5
III.21.20	$j=\frac{-{\mathrm{\rho }}_{c_0}{\mathit{qA}}_{\text{vec}}}{m}$	13	da	10	Yes	Yes	10−2