2-ancestry mixing, zero discriminant

Percentage Accurate: 76.4% → 98.7%

Time: 7.9s

Alternatives: 5

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: 76.4% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

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

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

   2. associate-/l/ N/A

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

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

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

   4. /-lowering-/.f64 77.1%

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

3. Simplified 77.1%

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

   1. associate-/l/ N/A

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

   2. associate-/r* N/A

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

   3. cbrt-div N/A

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

   4. clear-num N/A

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

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

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

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

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

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

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

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

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

   9. /-lowering-/.f64 98.9%

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

6. Applied egg-rr 98.9%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

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

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

   2. associate-/l/ N/A

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

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

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

   4. /-lowering-/.f64 77.1%

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

3. Simplified 77.1%

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

   1. associate-/l/ N/A

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

   2. associate-/r* N/A

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

   3. cbrt-div N/A

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

   4. /-lowering-/.f64 N/A

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

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

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

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{cbrt.f64}\left(\mathsf{/.f64}\left(g, 2\right)\right), \left(\sqrt[3]{a}\right)\right) \]

   7. cbrt-lowering-cbrt.f64 98.8%

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

6. Applied egg-rr 98.8%

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

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 77.1%

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

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

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

   2. associate-/l/ N/A

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

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

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

   4. /-lowering-/.f64 77.1%

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

3. Simplified 77.1%

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

   1. pow1/3 N/A

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

   2. frac-2neg N/A

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

   3. div-inv N/A

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

   4. unpow-prod-down N/A

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

   5. distribute-neg-frac2 N/A

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

   6. div-inv N/A

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

   7. unpow-prod-down N/A

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

   8. associate-*l* N/A

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

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

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

   10. pow1/3 N/A

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

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

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

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

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

   13. pow1/3 N/A

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

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

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

   15. metadata-eval N/A

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

   16. frac-2neg N/A

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

   17. /-lowering-/.f64 N/A

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

   18. pow1/3 N/A

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

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

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

   20. metadata-eval N/A

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

   21. metadata-eval 98.3%

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

6. Applied egg-rr 98.3%

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

   1. *-commutative N/A

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

   2. cbrt-unprod N/A

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

   3. associate-*r/ N/A

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

   4. metadata-eval N/A

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

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

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

   6. /-lowering-/.f64 98.3%

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

8. Applied egg-rr 98.3%

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

Alternative 4: 76.4% 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

Alternative 5: 76.4% 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. Step-by-step derivation

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

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

   2. associate-/l/ N/A

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

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

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

   4. /-lowering-/.f64 77.1%

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

3. Simplified 77.1%

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

   1. div-inv N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

   5. associate-/l/ N/A

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

   6. associate-/r* N/A

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

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

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

   8. metadata-eval 76.7%

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

6. Applied egg-rr 76.7%

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

7. Final simplification 76.7%

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

Reproduce

herbie shell --seed 2024144 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))