2-ancestry mixing, zero discriminant

Percentage Accurate: 76.3% → 98.7%

Time: 8.8s

Alternatives: 8

Speedup: 1.0×

• could not determine a ground truth

  1. g = 3.593245393874437e-6
  2. a = 6.3911108159950165e-65

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: 76.3% 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: 98.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. pow1/3 42.6%

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

   2. *-un-lft-identity 42.6%

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

   3. times-frac 42.6%

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

   4. metadata-eval 42.6%

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

   5. unpow-prod-down 42.6%

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

4. Applied egg-rr 42.6%

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

   1. unpow1/3 42.6%

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

   2. unpow1/3 77.0%

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

6. Simplified 77.0%

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

   1. pow1/3 42.6%

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

   2. div-inv 42.6%

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

   3. unpow-prod-down 26.4%

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

   4. pow1/3 44.4%

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

8. Applied egg-rr 44.4%

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

   1. *-commutative 44.4%

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

   2. unpow1/3 98.9%

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

10. Simplified 98.9%

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

11. Final simplification 98.9%

    \[\leadsto \sqrt[3]{0.5} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{g}\right) \]
12. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. pow1/3 42.6%

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

   2. clear-num 42.6%

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

   3. associate-/r/ 42.6%

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

   4. unpow-prod-down 26.4%

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

   5. pow1/3 49.0%

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

   6. associate-/r* 49.0%

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

   7. metadata-eval 49.0%

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

   8. pow1/3 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. cbrt-div 98.8%

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

   2. clear-num 98.8%

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

4. Applied egg-rr 98.8%

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

   1. associate-/r/ 98.8%

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

   2. associate-*l/ 98.8%

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

   3. *-lft-identity 98.8%

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

   4. *-commutative 98.8%

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

6. Simplified 98.8%

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

7. Final simplification 98.8%

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

Alternative 4: 76.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. add-log-exp 9.0%

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

   2. *-un-lft-identity 9.0%

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

   3. log-prod 9.0%

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

   4. metadata-eval 9.0%

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

   5. add-log-exp 77.1%

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

   6. div-inv 77.1%

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

   7. associate-/r* 77.1%

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

   8. metadata-eval 77.1%

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

4. Applied egg-rr 77.1%

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

   1. +-lft-identity 77.1%

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

6. Simplified 77.1%

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

   1. *-commutative 77.1%

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

   2. associate-*l/ 77.1%

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

   3. associate-*r/ 77.1%

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

   4. add-exp-log 43.0%

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

8. Applied egg-rr 43.0%

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

   1. rem-exp-log 77.1%

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

   2. clear-num 76.9%

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

   3. div-inv 76.9%

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

   4. div-inv 76.9%

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

   5. associate-/r* 77.1%

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

10. Applied egg-rr 77.1%

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

11. Final simplification 77.1%

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

Alternative 5: 76.2% 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 77.1%

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

   1. clear-num 76.9%

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

   2. cbrt-div 77.2%

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

   3. metadata-eval 77.2%

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

   4. associate-/l* 77.2%

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

4. Applied egg-rr 77.2%

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

5. Final simplification 77.2%

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

Alternative 6: 76.2% 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 77.1%

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

   1. cbrt-div 98.8%

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

   2. clear-num 98.8%

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

4. Applied egg-rr 98.8%

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

   1. associate-/r/ 98.8%

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

   2. associate-*l/ 98.8%

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

   3. *-lft-identity 98.8%

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

   4. *-commutative 98.8%

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

6. Simplified 98.8%

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

   1. clear-num 98.8%

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

   2. *-commutative 98.8%

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

   3. frac-2neg 98.8%

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

   4. metadata-eval 98.8%

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

   5. div-inv 98.8%

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

   6. cbrt-undiv 77.2%

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

   7. *-commutative 77.2%

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

   8. associate-/l* 77.1%

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

8. Applied egg-rr 77.1%

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

   1. mul-1-neg 77.1%

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

   2. distribute-frac-neg2 77.1%

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

   3. remove-double-neg 77.1%

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

   4. associate-*r/ 77.2%

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

10. Simplified 77.2%

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

11. Final simplification 77.2%

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

Alternative 7: 76.3% 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 77.1%

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

   1. add-log-exp 9.0%

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

   2. *-un-lft-identity 9.0%

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

   3. log-prod 9.0%

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

   4. metadata-eval 9.0%

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

   5. add-log-exp 77.1%

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

   6. div-inv 77.1%

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

   7. associate-/r* 77.1%

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

   8. metadata-eval 77.1%

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

4. Applied egg-rr 77.1%

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

   1. +-lft-identity 77.1%

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

6. Simplified 77.1%

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

7. Final simplification 77.1%

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

Alternative 8: 76.3% 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 77.1%

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

3. Final simplification 77.1%

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

Reproduce

herbie shell --seed 2024046 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))