2-ancestry mixing, zero discriminant

Percentage Accurate: 76.5% → 98.6%

Time: 6.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{2 \cdot a}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))

C

double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g / (2.0 * a)));
}

Julia

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end

Wolfram

code[g_, a_] := N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Initial Program: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{2 \cdot a}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))

C

double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g / (2.0 * a)));
}

Julia

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end

Wolfram

code[g_, a_] := N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Alternative 1: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{\frac{1}{a}}}{\sqrt[3]{\frac{2}{g}}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ (cbrt (/ 1.0 a)) (cbrt (/ 2.0 g))))

C

double code(double g, double a) {
	return cbrt((1.0 / a)) / cbrt((2.0 / g));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((1.0 / a)) / Math.cbrt((2.0 / g));
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(1.0 / a)) / cbrt(Float64(2.0 / g)))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(1.0 / a), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[N[(2.0 / g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-log-exp 8.8%

      \[\leadsto \color{blue}{\log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   2. *-un-lft-identity 8.8%

      \[\leadsto \log \color{blue}{\left(1 \cdot e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   3. log-prod 8.8%

      \[\leadsto \color{blue}{\log 1 + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   4. metadata-eval 8.8%

      \[\leadsto \color{blue}{0} + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right) \]

   5. add-log-exp 78.6%

      \[\leadsto 0 + \color{blue}{\sqrt[3]{\frac{g}{2 \cdot a}}} \]

   6. div-inv 78.5%

      \[\leadsto 0 + \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

   7. associate-/r* 78.5%

      \[\leadsto 0 + \sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}} \]

   8. metadata-eval 78.5%

      \[\leadsto 0 + \sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}} \]

4. Applied egg-rr 78.5%

   \[\leadsto \color{blue}{0 + \sqrt[3]{g \cdot \frac{0.5}{a}}} \]
5. Step-by-step derivation

   1. +-lft-identity 78.5%

      \[\leadsto \color{blue}{\sqrt[3]{g \cdot \frac{0.5}{a}}} \]

6. Simplified 78.5%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot \frac{0.5}{a}}} \]
7. Step-by-step derivation

   1. clear-num 78.5%

      \[\leadsto \sqrt[3]{g \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}}} \]

   2. div-inv 78.5%

      \[\leadsto \sqrt[3]{g \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}}} \]

   3. metadata-eval 78.5%

      \[\leadsto \sqrt[3]{g \cdot \frac{1}{a \cdot \color{blue}{2}}} \]

   4. un-div-inv 78.6%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{g}{a \cdot 2}}} \]

   5. add-sqr-sqrt 41.9%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{\sqrt{g} \cdot \sqrt{g}}}{a \cdot 2}} \]

   6. *-commutative 41.9%

      \[\leadsto \sqrt[3]{\frac{\sqrt{g} \cdot \sqrt{g}}{\color{blue}{2 \cdot a}}} \]

   7. frac-times 41.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\sqrt{g}}{2} \cdot \frac{\sqrt{g}}{a}}} \]

   8. clear-num 41.9%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{2}{\sqrt{g}}}} \cdot \frac{\sqrt{g}}{a}} \]

   9. clear-num 41.9%

      \[\leadsto \sqrt[3]{\frac{1}{\frac{2}{\sqrt{g}}} \cdot \color{blue}{\frac{1}{\frac{a}{\sqrt{g}}}}} \]

   10. frac-times 41.9%

       \[\leadsto \sqrt[3]{\color{blue}{\frac{1 \cdot 1}{\frac{2}{\sqrt{g}} \cdot \frac{a}{\sqrt{g}}}}} \]

   11. metadata-eval 41.9%

       \[\leadsto \sqrt[3]{\frac{\color{blue}{1}}{\frac{2}{\sqrt{g}} \cdot \frac{a}{\sqrt{g}}}} \]

   12. times-frac 41.9%

       \[\leadsto \sqrt[3]{\frac{1}{\color{blue}{\frac{2 \cdot a}{\sqrt{g} \cdot \sqrt{g}}}}} \]

   13. *-commutative 41.9%

       \[\leadsto \sqrt[3]{\frac{1}{\frac{\color{blue}{a \cdot 2}}{\sqrt{g} \cdot \sqrt{g}}}} \]

   14. add-sqr-sqrt 78.4%

       \[\leadsto \sqrt[3]{\frac{1}{\frac{a \cdot 2}{\color{blue}{g}}}} \]

   15. associate-/l* 78.4%

       \[\leadsto \sqrt[3]{\frac{1}{\color{blue}{a \cdot \frac{2}{g}}}} \]

8. Applied egg-rr 78.4%

   \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{a \cdot \frac{2}{g}}}} \]
9. Step-by-step derivation

   1. associate-/r* 78.5%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{a}}{\frac{2}{g}}}} \]

   2. cbrt-div 98.7%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{a}}}{\sqrt[3]{\frac{2}{g}}}} \]

10. Applied egg-rr 98.7%

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{a}}}{\sqrt[3]{\frac{2}{g}}}} \]
11. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{g \cdot 0.5} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (* (cbrt (/ 1.0 a)) (cbrt (* g 0.5))))

C

double code(double g, double a) {
	return cbrt((1.0 / a)) * cbrt((g * 0.5));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((1.0 / a)) * Math.cbrt((g * 0.5));
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(1.0 / a)) * cbrt(Float64(g * 0.5)))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(1.0 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1/3 37.3%

      \[\leadsto \color{blue}{{\left(\frac{g}{2 \cdot a}\right)}^{0.3333333333333333}} \]

   2. associate-/r* 37.3%

      \[\leadsto {\color{blue}{\left(\frac{\frac{g}{2}}{a}\right)}}^{0.3333333333333333} \]

   3. div-inv 37.3%

      \[\leadsto {\color{blue}{\left(\frac{g}{2} \cdot \frac{1}{a}\right)}}^{0.3333333333333333} \]

   4. unpow-prod-down 24.8%

      \[\leadsto \color{blue}{{\left(\frac{g}{2}\right)}^{0.3333333333333333} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333}} \]

   5. pow1/3 46.2%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{2}}} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333} \]

   6. div-inv 46.2%

      \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2}}} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333} \]

   7. metadata-eval 46.2%

      \[\leadsto \sqrt[3]{g \cdot \color{blue}{0.5}} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333} \]

4. Applied egg-rr 46.2%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333}} \]
5. Step-by-step derivation

   1. unpow1/3 98.7%

      \[\leadsto \sqrt[3]{g \cdot 0.5} \cdot \color{blue}{\sqrt[3]{\frac{1}{a}}} \]

6. Simplified 98.7%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot \sqrt[3]{\frac{1}{a}}} \]

7. Final simplification 98.7%

   \[\leadsto \sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{g \cdot 0.5} \]
8. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ (cbrt (* g 0.5)) (cbrt a)))

C

double code(double g, double a) {
	return cbrt((g * 0.5)) / cbrt(a);
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g * 0.5)) / Math.cbrt(a);
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(g * 0.5)) / cbrt(a))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/r* 78.6%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]

   2. cbrt-div 98.7%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{g}{2}}}{\sqrt[3]{a}}} \]

   3. div-inv 98.7%

      \[\leadsto \frac{\sqrt[3]{\color{blue}{g \cdot \frac{1}{2}}}}{\sqrt[3]{a}} \]

   4. metadata-eval 98.7%

      \[\leadsto \frac{\sqrt[3]{g \cdot \color{blue}{0.5}}}{\sqrt[3]{a}} \]

4. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}}} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{0.5}{a}} \cdot \sqrt[3]{g} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (* (cbrt (/ 0.5 a)) (cbrt g)))

C

double code(double g, double a) {
	return cbrt((0.5 / a)) * cbrt(g);
}

Java

public static double code(double g, double a) {
	return Math.cbrt((0.5 / a)) * Math.cbrt(g);
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(0.5 / a)) * cbrt(g))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(0.5 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1/3 37.3%

      \[\leadsto \color{blue}{{\left(\frac{g}{2 \cdot a}\right)}^{0.3333333333333333}} \]

   2. clear-num 37.3%

      \[\leadsto {\color{blue}{\left(\frac{1}{\frac{2 \cdot a}{g}}\right)}}^{0.3333333333333333} \]

   3. associate-/r/ 37.3%

      \[\leadsto {\color{blue}{\left(\frac{1}{2 \cdot a} \cdot g\right)}}^{0.3333333333333333} \]

   4. unpow-prod-down 24.8%

      \[\leadsto \color{blue}{{\left(\frac{1}{2 \cdot a}\right)}^{0.3333333333333333} \cdot {g}^{0.3333333333333333}} \]

   5. pow1/3 48.6%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{1}{2 \cdot a}}} \cdot {g}^{0.3333333333333333} \]

   6. associate-/r* 48.6%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{2}}{a}}} \cdot {g}^{0.3333333333333333} \]

   7. metadata-eval 48.6%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{0.5}}{a}} \cdot {g}^{0.3333333333333333} \]

   8. pow1/3 98.6%

      \[\leadsto \sqrt[3]{\frac{0.5}{a}} \cdot \color{blue}{\sqrt[3]{g}} \]

4. Applied egg-rr 98.6%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a}} \cdot \sqrt[3]{g}} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt[3]{\frac{a \cdot 2}{g}}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ 1.0 (cbrt (/ (* a 2.0) g))))

C

double code(double g, double a) {
	return 1.0 / cbrt(((a * 2.0) / g));
}

Java

public static double code(double g, double a) {
	return 1.0 / Math.cbrt(((a * 2.0) / g));
}

Julia

function code(g, a)
	return Float64(1.0 / cbrt(Float64(Float64(a * 2.0) / g)))
end

Wolfram

code[g_, a_] := N[(1.0 / N[Power[N[(N[(a * 2.0), $MachinePrecision] / g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/r* 78.6%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{g}{2}}{a}}} \]

   2. cbrt-div 98.7%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{g}{2}}}{\sqrt[3]{a}}} \]

   3. div-inv 98.7%

      \[\leadsto \frac{\sqrt[3]{\color{blue}{g \cdot \frac{1}{2}}}}{\sqrt[3]{a}} \]

   4. metadata-eval 98.7%

      \[\leadsto \frac{\sqrt[3]{g \cdot \color{blue}{0.5}}}{\sqrt[3]{a}} \]

4. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}}} \]
5. Step-by-step derivation

   1. clear-num 98.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{g \cdot 0.5}}}} \]

   2. inv-pow 98.6%

      \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{a}}{\sqrt[3]{g \cdot 0.5}}\right)}^{-1}} \]

   3. div-inv 98.5%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{a} \cdot \frac{1}{\sqrt[3]{g \cdot 0.5}}\right)}}^{-1} \]

   4. metadata-eval 98.5%

      \[\leadsto {\left(\sqrt[3]{a} \cdot \frac{\color{blue}{\sqrt[3]{1}}}{\sqrt[3]{g \cdot 0.5}}\right)}^{-1} \]

   5. metadata-eval 98.5%

      \[\leadsto {\left(\sqrt[3]{a} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{g \cdot \color{blue}{\frac{1}{2}}}}\right)}^{-1} \]

   6. div-inv 98.5%

      \[\leadsto {\left(\sqrt[3]{a} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\color{blue}{\frac{g}{2}}}}\right)}^{-1} \]

   7. cbrt-div 98.7%

      \[\leadsto {\left(\sqrt[3]{a} \cdot \color{blue}{\sqrt[3]{\frac{1}{\frac{g}{2}}}}\right)}^{-1} \]

   8. clear-num 98.7%

      \[\leadsto {\left(\sqrt[3]{a} \cdot \sqrt[3]{\color{blue}{\frac{2}{g}}}\right)}^{-1} \]

   9. cbrt-prod 79.0%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{a \cdot \frac{2}{g}}\right)}}^{-1} \]

   10. associate-*r/ 79.1%

       \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{a \cdot 2}{g}}}\right)}^{-1} \]

   11. associate-*l/ 79.0%

       \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{a}{g} \cdot 2}}\right)}^{-1} \]

   12. cbrt-unprod 78.6%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}\right)}}^{-1} \]

   13. *-commutative 78.6%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{2} \cdot \sqrt[3]{\frac{a}{g}}\right)}}^{-1} \]

   14. *-commutative 78.6%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}\right)}}^{-1} \]

   15. add-cube-cbrt 78.1%

       \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}} \cdot \sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}}\right)}}^{-1} \]

   16. unpow-prod-down 78.1%

       \[\leadsto \color{blue}{{\left(\sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}} \cdot \sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}}\right)}^{-1} \cdot {\left(\sqrt[3]{\sqrt[3]{\frac{a}{g}} \cdot \sqrt[3]{2}}\right)}^{-1}} \]

6. Applied egg-rr 78.1%

   \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2}\right)}^{-1} \cdot {\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{-1}} \]
7. Step-by-step derivation

   1. unpow-1 78.1%

      \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2}\right)}^{-1} \cdot \color{blue}{\frac{1}{\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}}} \]

   2. associate-*r/ 78.2%

      \[\leadsto \color{blue}{\frac{{\left({\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2}\right)}^{-1} \cdot 1}{\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}}} \]

   3. *-rgt-identity 78.2%

      \[\leadsto \frac{\color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2}\right)}^{-1}}}{\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]

   4. unpow-1 78.2%

      \[\leadsto \frac{\color{blue}{\frac{1}{{\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2}}}}{\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]

   5. associate-/r* 78.1%

      \[\leadsto \color{blue}{\frac{1}{{\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}}} \]

   6. unpow2 78.1%

      \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}} \cdot \sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}\right)} \cdot \sqrt[3]{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]

   7. rem-3cbrt-lft 79.0%

      \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]

   8. associate-*r/ 79.1%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{\frac{2 \cdot a}{g}}}} \]

   9. *-commutative 79.1%

      \[\leadsto \frac{1}{\sqrt[3]{\frac{\color{blue}{a \cdot 2}}{g}}} \]

8. Simplified 79.1%

   \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{\frac{a \cdot 2}{g}}}} \]
9. Add Preprocessing

Alternative 6: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ 1.0 (cbrt (* 2.0 (/ a g)))))

C

double code(double g, double a) {
	return 1.0 / cbrt((2.0 * (a / g)));
}

Java

public static double code(double g, double a) {
	return 1.0 / Math.cbrt((2.0 * (a / g)));
}

Julia

function code(g, a)
	return Float64(1.0 / cbrt(Float64(2.0 * Float64(a / g))))
end

Wolfram

code[g_, a_] := N[(1.0 / N[Power[N[(2.0 * N[(a / g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 78.4%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\frac{2 \cdot a}{g}}}} \]

   2. cbrt-div 79.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}}} \]

   3. metadata-eval 79.1%

      \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{\frac{2 \cdot a}{g}}} \]

   4. associate-/l* 79.0%

      \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{2 \cdot \frac{a}{g}}}} \]

4. Applied egg-rr 79.0%

   \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}}} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{g}{a \cdot 2}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* a 2.0))))

C

double code(double g, double a) {
	return cbrt((g / (a * 2.0)));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g / (a * 2.0)));
}

Julia

function code(g, a)
	return cbrt(Float64(g / Float64(a * 2.0)))
end

Wolfram

code[g_, a_] := N[Power[N[(g / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing

3. Final simplification 78.6%

   \[\leadsto \sqrt[3]{\frac{g}{a \cdot 2}} \]
4. Add Preprocessing

Alternative 8: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{g \cdot \frac{0.5}{a}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt (* g (/ 0.5 a))))

C

double code(double g, double a) {
	return cbrt((g * (0.5 / a)));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g * (0.5 / a)));
}

Julia

function code(g, a)
	return cbrt(Float64(g * Float64(0.5 / a)))
end

Wolfram

code[g_, a_] := N[Power[N[(g * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-log-exp 8.8%

      \[\leadsto \color{blue}{\log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   2. *-un-lft-identity 8.8%

      \[\leadsto \log \color{blue}{\left(1 \cdot e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   3. log-prod 8.8%

      \[\leadsto \color{blue}{\log 1 + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right)} \]

   4. metadata-eval 8.8%

      \[\leadsto \color{blue}{0} + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right) \]

   5. add-log-exp 78.6%

      \[\leadsto 0 + \color{blue}{\sqrt[3]{\frac{g}{2 \cdot a}}} \]

   6. div-inv 78.5%

      \[\leadsto 0 + \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

   7. associate-/r* 78.5%

      \[\leadsto 0 + \sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}} \]

   8. metadata-eval 78.5%

      \[\leadsto 0 + \sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}} \]

4. Applied egg-rr 78.5%

   \[\leadsto \color{blue}{0 + \sqrt[3]{g \cdot \frac{0.5}{a}}} \]
5. Step-by-step derivation

   1. +-lft-identity 78.5%

      \[\leadsto \color{blue}{\sqrt[3]{g \cdot \frac{0.5}{a}}} \]

6. Simplified 78.5%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot \frac{0.5}{a}}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024097 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))