2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 7.4s

Alternatives: 7

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: 76.1% 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, 0.5× 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 73.9%

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

   1. expm1-log1p-u 54.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. sub-neg 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} + \left(-1\right)} \]

   4. div-inv 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\right)} + \left(-1\right) \]

   5. associate-/r* 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}}\right)} + \left(-1\right) \]

   6. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}}\right)} + \left(-1\right) \]

   7. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{-1} \]

3. Applied egg-rr 24.1%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + -1} \]
4. Step-by-step derivation

   1. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{\left(-1\right)} \]

   2. sub-neg 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} - 1} \]

   3. expm1-def 54.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)\right)} \]

   4. expm1-log1p 73.8%

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

5. Simplified 73.8%

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

   1. associate-*r/ 73.9%

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

   2. metadata-eval 73.9%

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

   3. div-inv 73.9%

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

   4. add-cube-cbrt 73.5%

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

   5. cbrt-undiv 73.4%

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

   6. cbrt-undiv 73.3%

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

   7. cbrt-undiv 73.1%

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

   8. cbrt-undiv 98.0%

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

   9. add-cbrt-cube 98.3%

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

   10. div-inv 98.3%

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

   11. clear-num 98.2%

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

   12. associate-*l/ 98.2%

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

   13. div-inv 98.2%

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

   14. cbrt-undiv 98.7%

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

7. Applied egg-rr 98.7%

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

   1. add-cbrt-cube 98.5%

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

   2. pow1/3 48.8%

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

   3. un-div-inv 48.8%

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

   4. frac-times 48.8%

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

   5. metadata-eval 48.8%

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

   6. associate-/r* 48.8%

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

   7. add-cube-cbrt 48.8%

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

9. Applied egg-rr 48.8%

   \[\leadsto \frac{\color{blue}{{\left(\frac{1}{a}\right)}^{0.3333333333333333}}}{\sqrt[3]{\frac{2}{g}}} \]
10. Step-by-step derivation

    1. unpow1/3 98.8%

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

11. Simplified 98.8%

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

12. Final simplification 98.8%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

   1. cbrt-div 98.7%

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

   2. clear-num 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 3: 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 73.9%

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

   1. div-inv 73.8%

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

   2. cbrt-prod 98.7%

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

   3. *-commutative 98.7%

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

   4. associate-/r* 98.7%

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

   5. metadata-eval 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 4: 98.6% 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 73.9%

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

   1. cbrt-div 98.7%

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

   2. div-inv 98.7%

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

3. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.7%

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

   2. associate-/l* 98.7%

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

   3. /-rgt-identity 98.7%

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

   4. *-commutative 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 5: 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 73.9%

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

   1. associate-/r* 73.9%

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

   2. cbrt-div 98.7%

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

   3. div-inv 98.6%

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

   4. div-inv 98.6%

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

   5. metadata-eval 98.6%

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

3. Applied egg-rr 98.6%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot \frac{1}{\sqrt[3]{a}}} \]
4. Step-by-step derivation

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 6: 76.1% 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 73.9%

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

   1. expm1-log1p-u 54.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. sub-neg 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} + \left(-1\right)} \]

   4. div-inv 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\right)} + \left(-1\right) \]

   5. associate-/r* 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}}\right)} + \left(-1\right) \]

   6. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}}\right)} + \left(-1\right) \]

   7. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{-1} \]

3. Applied egg-rr 24.1%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + -1} \]
4. Step-by-step derivation

   1. metadata-eval 24.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{\left(-1\right)} \]

   2. sub-neg 24.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} - 1} \]

   3. expm1-def 54.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)\right)} \]

   4. expm1-log1p 73.8%

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

5. Simplified 73.8%

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

6. Final simplification 73.8%

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

Alternative 7: 76.1% 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 73.9%

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

2. Final simplification 73.9%

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

Reproduce

herbie shell --seed 2023326 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))