2-ancestry mixing, zero discriminant

Percentage Accurate: 76.5% → 98.7%

Time: 8.4s

Alternatives: 4

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: 98.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.4%

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

   1. associate-/r* N/A

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

   2. frac-2neg N/A

      \[\leadsto \sqrt[3]{\frac{\mathsf{neg}\left(\frac{g}{2}\right)}{\mathsf{neg}\left(a\right)}} \]

   3. div-inv N/A

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

   4. cbrt-prod N/A

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

   5. pow1/3 N/A

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

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\mathsf{neg}\left(\frac{g}{2}\right)\right)}^{\frac{1}{3}}\right), \color{blue}{\left(\sqrt[3]{\frac{1}{\mathsf{neg}\left(a\right)}}\right)}\right) \]

   7. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\mathsf{neg}\left(\frac{g}{2}\right)\right), \frac{1}{3}\right), \left(\sqrt[3]{\color{blue}{\frac{1}{\mathsf{neg}\left(a\right)}}}\right)\right) \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{g}{\mathsf{neg}\left(2\right)}\right), \frac{1}{3}\right), \left(\sqrt[3]{\frac{\color{blue}{1}}{\mathsf{neg}\left(a\right)}}\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, \left(\mathsf{neg}\left(2\right)\right)\right), \frac{1}{3}\right), \left(\sqrt[3]{\frac{\color{blue}{1}}{\mathsf{neg}\left(a\right)}}\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, -2\right), \frac{1}{3}\right), \left(\sqrt[3]{\frac{1}{\mathsf{neg}\left(a\right)}}\right)\right) \]

   11. cbrt-lowering-cbrt.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, -2\right), \frac{1}{3}\right), \mathsf{cbrt.f64}\left(\left(\frac{1}{\mathsf{neg}\left(a\right)}\right)\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, -2\right), \frac{1}{3}\right), \mathsf{cbrt.f64}\left(\left(\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(a\right)}\right)\right)\right) \]

   13. frac-2neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, -2\right), \frac{1}{3}\right), \mathsf{cbrt.f64}\left(\left(\frac{-1}{a}\right)\right)\right) \]

   14. /-lowering-/.f64 43.9%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(g, -2\right), \frac{1}{3}\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, a\right)\right)\right) \]

4. Applied egg-rr 43.9%

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

   1. div-inv N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(g \cdot \frac{1}{-2}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(\color{blue}{-1}, a\right)\right)\right) \]

   2. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(g \cdot \frac{-1}{2}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, a\right)\right)\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(g \cdot \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, a\right)\right)\right) \]

   4. unpow-prod-down N/A

      \[\leadsto \mathsf{*.f64}\left(\left({g}^{\frac{1}{3}} \cdot {\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\color{blue}{\mathsf{/.f64}\left(-1, a\right)}\right)\right) \]

   5. pow1/3 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt[3]{g} \cdot {\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(\color{blue}{-1}, a\right)\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\sqrt[3]{g}\right), \left({\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}^{\frac{1}{3}}\right)\right), \mathsf{cbrt.f64}\left(\color{blue}{\mathsf{/.f64}\left(-1, a\right)}\right)\right) \]

   7. cbrt-lowering-cbrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(g\right), \left({\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}^{\frac{1}{3}}\right)\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(\color{blue}{-1}, a\right)\right)\right) \]

   8. pow1/3 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(g\right), \left(\sqrt[3]{\mathsf{neg}\left(\frac{1}{2}\right)}\right)\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, \color{blue}{a}\right)\right)\right) \]

   9. cbrt-lowering-cbrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(g\right), \mathsf{cbrt.f64}\left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, \color{blue}{a}\right)\right)\right) \]

   10. metadata-eval 98.7%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(g\right), \mathsf{cbrt.f64}\left(\frac{-1}{2}\right)\right), \mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(-1, a\right)\right)\right) \]

6. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{-0.5}\right)} \cdot \sqrt[3]{\frac{-1}{a}} \]
7. 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 77.4%

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

   1. div-inv N/A

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

   2. cbrt-prod N/A

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

   3. pow1/3 N/A

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{1}{2 \cdot a}\right)}^{\frac{1}{3}}\right), \color{blue}{\left(\sqrt[3]{g}\right)}\right) \]

   6. inv-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left({\left(2 \cdot a\right)}^{-1}\right)}^{\frac{1}{3}}\right), \left(\sqrt[3]{g}\right)\right) \]

   7. pow-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(2 \cdot a\right)}^{\left(-1 \cdot \frac{1}{3}\right)}\right), \left(\sqrt[3]{\color{blue}{g}}\right)\right) \]

   8. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(2 \cdot a\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{\color{blue}{g}}\right)\right) \]

   9. remove-double-div N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{1}{\frac{1}{2 \cdot a}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   10. associate-/r* N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{1}{\frac{\frac{1}{2}}{a}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   11. clear-num N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{a}{\frac{1}{2}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   12. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \left(\frac{1}{2}\right)\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \frac{-1}{3}\right), \left(\sqrt[3]{g}\right)\right) \]

   15. cbrt-lowering-cbrt.f64 45.7%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \frac{-1}{3}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

4. Applied egg-rr 45.7%

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

   1. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{a}{\frac{1}{2}}\right)}^{\left(-1 \cdot \frac{1}{3}\right)}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   2. pow-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left({\left(\frac{a}{\frac{1}{2}}\right)}^{-1}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   3. inv-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{1}{\frac{a}{\frac{1}{2}}}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   4. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{\frac{1}{2}}{a}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   5. pow1/3 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt[3]{\frac{\frac{1}{2}}{a}}\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   6. cbrt-lowering-cbrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(\left(\frac{\frac{1}{2}}{a}\right)\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   7. /-lowering-/.f64 98.7%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right)\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

6. Applied egg-rr 98.7%

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

7. Final simplification 98.7%

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

Alternative 3: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.4%

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

   1. div-inv N/A

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

   2. cbrt-prod N/A

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

   3. pow1/3 N/A

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{1}{2 \cdot a}\right)}^{\frac{1}{3}}\right), \color{blue}{\left(\sqrt[3]{g}\right)}\right) \]

   6. inv-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left({\left(2 \cdot a\right)}^{-1}\right)}^{\frac{1}{3}}\right), \left(\sqrt[3]{g}\right)\right) \]

   7. pow-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(2 \cdot a\right)}^{\left(-1 \cdot \frac{1}{3}\right)}\right), \left(\sqrt[3]{\color{blue}{g}}\right)\right) \]

   8. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(2 \cdot a\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{\color{blue}{g}}\right)\right) \]

   9. remove-double-div N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{1}{\frac{1}{2 \cdot a}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   10. associate-/r* N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{1}{\frac{\frac{1}{2}}{a}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   11. clear-num N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(\frac{a}{\frac{1}{2}}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   12. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \left(\frac{1}{2}\right)\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \left(-1 \cdot \frac{1}{3}\right)\right), \left(\sqrt[3]{g}\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \frac{-1}{3}\right), \left(\sqrt[3]{g}\right)\right) \]

   15. cbrt-lowering-cbrt.f64 45.7%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{/.f64}\left(a, \frac{1}{2}\right), \frac{-1}{3}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

4. Applied egg-rr 45.7%

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

   1. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{a}{\frac{1}{2}}\right)}^{\left(-1 \cdot \frac{1}{3}\right)}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   2. pow-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left({\left(\frac{a}{\frac{1}{2}}\right)}^{-1}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   3. inv-pow N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{1}{\frac{a}{\frac{1}{2}}}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   4. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\left({\left(\frac{\frac{1}{2}}{a}\right)}^{\frac{1}{3}}\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

   5. pow1/3 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt[3]{\frac{\frac{1}{2}}{a}}\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   6. cbrt-lowering-cbrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(\left(\frac{\frac{1}{2}}{a}\right)\right), \mathsf{cbrt.f64}\left(\color{blue}{g}\right)\right) \]

   7. /-lowering-/.f64 98.7%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right)\right), \mathsf{cbrt.f64}\left(g\right)\right) \]

6. Applied egg-rr 98.7%

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

8. Applied egg-rr 78.2%

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

Alternative 4: 76.5% 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 77.4%

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

   1. clear-num N/A

      \[\leadsto \mathsf{cbrt.f64}\left(\left(\frac{1}{\frac{2 \cdot a}{g}}\right)\right) \]

   2. associate-/r/ N/A

      \[\leadsto \mathsf{cbrt.f64}\left(\left(\frac{1}{2 \cdot a} \cdot g\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{cbrt.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), g\right)\right) \]

   4. associate-/r* N/A

      \[\leadsto \mathsf{cbrt.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), g\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{cbrt.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), g\right)\right) \]

   6. metadata-eval 77.5%

      \[\leadsto \mathsf{cbrt.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), g\right)\right) \]

4. Applied egg-rr 77.5%

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

5. Final simplification 77.5%

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

Reproduce

herbie shell --seed 2024161 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))