Table 4. Tested Feynman equations, part 1.

Abbreviations in the “Methods used” column: da, dimensional analysis; bf, brute force; pf, polyfit; ev, set two variables equal; sym, symmetry; sep, separability. Suffixes denote the type of symmetry or separability (sym–, translational symmetry; sep*, multiplicative separability; etc.) or the preprocessing before brute force (e.g., bf-inverse means inverting the mystery function before bf).

Feynman Eq.	Equation	Solution Time (s)	Methods Used	Data Needed	Solved By Eureqa	Solved W/o da	Noise Tolerance
I.6.20a	$f=e^{-{\mathrm{\theta }}^2/2}/\sqrt{2\mathrm{\pi }}$	16	bf	10	No	Yes	10−2
I.6.20	$f=e^{-\frac{{\mathrm{\theta }}^2}{2{\mathrm{\sigma }}^2}}/\sqrt{2{\mathrm{\pi }\mathrm{\sigma }}^2}$	2992	ev, bf-log	102	No	Yes	10−4
I.6.20b	$f=e^{-\frac{{(\mathrm{\theta }-{\mathrm{\theta }}_1)}^2}{2{\mathrm{\sigma }}^2}}/\sqrt{2{\mathrm{\pi }\mathrm{\sigma }}^2}$	4792	sym–, ev, bf-log	103	No	Yes	10−4
I.8.14	$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$	544	da, pf-squared	102	No	Yes	10−4
I.9.18	$F=\frac{G{m}_1{m}_2}{{(x_2-x_1)}^2+{(y_2-y_1)}^2+{(z_2-z_1)}^2}$	5975	da, sym–, sym–, sep∗, pf-inv	106	No	Yes	10−5
I.10.7	$m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$	14	da, bf	10	No	Yes	10−4
I.11.19	A = x1y1 + x2y2 + x3y3	184	da, pf	102	Yes	Yes	10−3
I.12.1	F = μNn	12	da, bf	10	Yes	Yes	10−3
I.12.2	$F=\frac{q_1{q}_2}{4\mathrm{\pi }\mathrm{ϵ}{r}^2}$	17	da, bf	10	Yes	Yes	10−2
I.12.4	$E_f=\frac{q_1}{4\mathrm{\pi }\mathrm{ϵ}{r}^2}$	12	da	10	Yes	Yes	10−2
I.12.5	F = q2Ef	8	da	10	Yes	Yes	10−2
I.12.11	F = q(Ef + Bv sin θ)	19	da, bf	10	Yes	Yes	10−3
I.13.4	$K=\frac{1}{2}m(v^2+u^2+w^2)$	22	da, bf	10	Yes	Yes	10−4
I.13.12	$U=G{m}_1{m}_2(\frac{1}{r_2}-\frac{1}{r_1})$	20	da, bf	10	Yes	Yes	10−4
I.14.3	U = mgz	12	da	10	Yes	Yes	10−2
I.14.4	$U=\frac{k_{\text{spring}}{x}^2}{2}$	9	da	10	Yes	Yes	10−2
I.15.3x	$x_1=\frac{x-\mathit{ut}}{\sqrt{1-u^2/c^2}}$	22	da, bf	10	No	No	10−3
I.15.3t	$t_1=\frac{t-\mathit{ux}/c^2}{\sqrt{1-u^2/c^2}}$	20	da, bf	102	No	No	10−4
I.15.10	$p=\frac{m_{0}v}{\sqrt{1-v^2/c^2}}$	13	da, bf	10	No	Yes	10−4
I.16.6	$v_1=\frac{u+v}{1+\mathit{uv}/c^2}$	18	da, bf	10	No	Yes	10−3
I.18.4	$r=\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}$	17	da, bf	10	Yes	Yes	10−2
I.18.12	τ = rF sin θ	15	da, bf	10	Yes	Yes	10−3
I.18.16	L = mrv sin θ	17	da, bf	10	Yes	Yes	10−3
I.24.6	$E=\frac{1}{4}m({\mathrm{\omega }}^2+{\mathrm{\omega }}_0^2)x^2$	22	da, bf	10	Yes	Yes	10−4
I.25.13	$V_e=\frac{q}{C}$	10	da	10	Yes	Yes	10−2
I.26.2	θ1 = arcsin (n sin θ2)	530	da, bf-sin	102	Yes	Yes	10−2
I.27.6	$f_f=\frac{1}{\frac{1}{d_1}+\frac{n}{d_2}}$	14	da, bf	10	Yes	Yes	10−2
I.29.4	$k=\frac{\mathrm{\omega }}{c}$	8	da	10	Yes	Yes	10−2
I.29.16	$x=\sqrt{x_1^2+x_2^2-2x_1{x}_2\text{cos}({\mathrm{\theta }}_1-{\mathrm{\theta }}_2)}$	2135	da, sym–, bf-squared	103	No	No	10−4
I.30.3	$I*=I{*}_0\frac{{\text{sin}}^2(n\mathrm{\theta }/2)}{{\text{sin}}^2(\mathrm{\theta }/2)}$	118	da, bf	102	Yes	Yes	10−3
I.30.5	$\mathrm{\theta }=\text{arcsin}\left(\frac{\mathrm{\lambda }}{\mathit{nd}}\right)$	529	da, bf-sin	102	Yes	Yes	10−3
I.32.5	$P=\frac{q^2{a}^2}{6\mathrm{\pi }\mathrm{ϵ}{c}^3}$	13	da	10	Yes	Yes	10−2
I.32.17	$P=\left(\frac{1}{2}\mathrm{ϵ}{\mathrm{cE}}_f^2\right)(8\mathrm{\pi }{r}^2/3)({\mathrm{\omega }}^4/{({\mathrm{\omega }}^2-{\mathrm{\omega }}_0^2)}^2)$	698	da, bf-sqrt	10	No	Yes	10−4
I.34.8	$\mathrm{\omega }=\frac{\mathit{qvB}}{p}$	13	da	10	Yes	Yes	10−2
I.34.10	$\mathrm{\omega }=\frac{{\mathrm{\omega }}_0}{1-v/c}$	13	da, bf	10	No	Yes	10−3
I.34.14	$\mathrm{\omega }=\frac{1+v/c}{\sqrt{1-v^2/c^2}}{\mathrm{\omega }}_0$	14	da, bf	10	No	Yes	10−3
I.34.27	E = ℏω	8	da	10	Yes	Yes	10−2
I.37.4	$I*=I_1+I_2+2\sqrt{I_1{I}_2}\text{cos}\mathrm{\delta }$	7032	da, bf	102	Yes	No	10−3
I.38.12	$r=\frac{4\mathrm{\pi }\mathrm{ϵ}{\mathrm{\hslash }}^2}{m{q}^2}$	13	da	10	Yes	Yes	10−2
I.39.10	$E=\frac{3}{2}{p}_{F}V$	8	da	10	Yes	Yes	10−2
I.39.11	$E=\frac{1}{\mathrm{\gamma }-1}{p}_{F}V$	13	da, bf	10	Yes	Yes	10−3
I.39.22	$P_F=\frac{n{k}_{b}T}{V}$	16	da, bf	10	Yes	Yes	10−4
I.40.1	$n=n_0{e}^{-\frac{\mathrm{mgx}}{k_{b}T}}$	20	da, bf	10	No	Yes	10−2
I.41.16	$L_{\text{rad}}=\frac{\mathrm{\hslash }{\mathrm{\omega }}^3}{{\mathrm{\pi }}^2{c}^2(e^{\frac{\mathrm{\hslash }\mathrm{\omega }}{k_{b}T}}-1)}$	22	da, bf	10	No	No	10−5
I.43.16	$v=\frac{{\mathrm{\mu }}_{\text{drift}}q{V}_e}{d}$	14	da	10	Yes	Yes	10−2
I.43.31	D = μekbT	11	da	10	Yes	Yes	10−2
I.43.43	$\mathrm{\kappa }=\frac{1}{\mathrm{\gamma }-1}\frac{k_{b}v}{A}$	16	da, bf	10	Yes	Yes	10−3
I.44.4	$E=n{k}_{b}T\text{ln}\left(\frac{V_2}{V_1}\right)$	18	da, bf	10	Yes	Yes	10−3
I.47.23	$c=\sqrt{\frac{\mathrm{\gamma }\mathrm{pr}}{\mathrm{\rho }}}$	14	da, bf	10	Yes	Yes	10−2
I.48.20	$E=\frac{m{c}^2}{\sqrt{1-v^2/c^2}}$	108	da, bf	102	No	No	10−5
I.50.26	x = x1[ cos (ωt) + α cos (ωt)2]	29	da bf	10	Yes	Yes	10−2