2-ancestry mixing, zero discriminant

Percentage Accurate: 76.3% → 98.7%

Time: 4.0s

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: 76.3% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. cbrt-div N/A

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

   5. neg-mul-1 N/A

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

   6. cbrt-prod N/A

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

   7. pow1/3 N/A

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

   8. associate-/r* N/A

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

   9. lower-/.f64 N/A

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

   10. pow1/3 N/A

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

   11. sqr-pow N/A

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

   12. pow-prod-down N/A

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

   13. sqr-neg N/A

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

   14. remove-double-neg N/A

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

   15. remove-double-neg N/A

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

   16. pow-prod-down N/A

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

   17. sqr-pow N/A

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

   18. pow1/3 N/A

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

   19. lower-/.f64 N/A

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

   20. lower-cbrt.f64 N/A

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

   21. pow1/3 N/A

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

   22. lower-cbrt.f64 N/A

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

   23. lower-cbrt.f64 1.7

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

   24. remove-double-div N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. associate-/r* N/A

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

   5. associate-/l/ N/A

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

   6. lower-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. lift-cbrt.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. metadata-eval N/A

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

   12. div-inv N/A

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

   13. cbrt-div N/A

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

   14. clear-num N/A

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

   15. lift-/.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lift-cbrt.f64 N/A

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

   18. lift-cbrt.f64 N/A

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

   19. cbrt-undiv N/A

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

   20. lower-cbrt.f64 N/A

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

   21. lower-/.f64 98.8

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

6. Applied rewrites 98.8%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{-0.5}{a}}}{\sqrt[3]{\frac{-1}{g}}}} \]
7. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. cbrt-div N/A

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

   5. neg-mul-1 N/A

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

   6. cbrt-prod N/A

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

   7. pow1/3 N/A

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

   8. associate-/r* N/A

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

   9. lower-/.f64 N/A

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

   10. pow1/3 N/A

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

   11. sqr-pow N/A

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

   12. pow-prod-down N/A

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

   13. sqr-neg N/A

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

   14. remove-double-neg N/A

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

   15. remove-double-neg N/A

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

   16. pow-prod-down N/A

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

   17. sqr-pow N/A

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

   18. pow1/3 N/A

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

   19. lower-/.f64 N/A

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

   20. lower-cbrt.f64 N/A

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

   21. pow1/3 N/A

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

   22. lower-cbrt.f64 N/A

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

   23. lower-cbrt.f64 1.7

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

   24. remove-double-div N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/l/ N/A

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

   4. lower-/.f64 N/A

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

   5. *-commutative N/A

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

   6. lift-cbrt.f64 N/A

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

   7. lift-cbrt.f64 N/A

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

   8. cbrt-prod N/A

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

   9. neg-mul-1 N/A

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

   10. lower-cbrt.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. distribute-lft-neg-in N/A

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

   13. metadata-eval N/A

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

   14. lower-*.f64 98.8

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

6. Applied rewrites 98.8%

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

Alternative 3: 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 77.8%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. cbrt-div N/A

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

   5. neg-mul-1 N/A

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

   6. cbrt-prod N/A

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

   7. pow1/3 N/A

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

   8. associate-/r* N/A

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

   9. lower-/.f64 N/A

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

   10. pow1/3 N/A

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

   11. sqr-pow N/A

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

   12. pow-prod-down N/A

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

   13. sqr-neg N/A

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

   14. remove-double-neg N/A

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

   15. remove-double-neg N/A

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

   16. pow-prod-down N/A

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

   17. sqr-pow N/A

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

   18. pow1/3 N/A

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

   19. lower-/.f64 N/A

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

   20. lower-cbrt.f64 N/A

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

   21. pow1/3 N/A

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

   22. lower-cbrt.f64 N/A

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

   23. lower-cbrt.f64 1.7

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

   24. remove-double-div N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. lift-cbrt.f64 N/A

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

   5. cbrt-undiv N/A

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

   6. div-inv N/A

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

   7. metadata-eval N/A

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

   8. *-commutative N/A

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

   9. cbrt-prod N/A

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

   10. lift-cbrt.f64 N/A

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

   11. lift-cbrt.f64 N/A

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

   12. associate-*l/ N/A

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

   13. lift-cbrt.f64 N/A

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

   14. lift-cbrt.f64 N/A

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

   15. cbrt-undiv N/A

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

   16. lower-*.f64 N/A

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

6. Applied rewrites 98.8%

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

Alternative 4: 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]

Derivation

1. Initial program 77.8%

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

Alternative 5: 76.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. cbrt-div N/A

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

   5. neg-mul-1 N/A

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

   6. cbrt-prod N/A

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

   7. pow1/3 N/A

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

   8. associate-/r* N/A

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

   9. lower-/.f64 N/A

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

   10. pow1/3 N/A

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

   11. sqr-pow N/A

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

   12. pow-prod-down N/A

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

   13. sqr-neg N/A

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

   14. remove-double-neg N/A

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

   15. remove-double-neg N/A

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

   16. pow-prod-down N/A

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

   17. sqr-pow N/A

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

   18. pow1/3 N/A

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

   19. lower-/.f64 N/A

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

   20. lower-cbrt.f64 N/A

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

   21. pow1/3 N/A

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

   22. lower-cbrt.f64 N/A

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

   23. lower-cbrt.f64 1.7

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

   24. remove-double-div N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. div-inv N/A

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

   3. lift-/.f64 N/A

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

   4. lift-cbrt.f64 N/A

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

   5. lift-cbrt.f64 N/A

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

   6. cbrt-undiv N/A

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

   7. div-inv N/A

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

   8. metadata-eval N/A

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

   9. *-commutative N/A

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

   10. neg-mul-1 N/A

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

   11. lift-neg.f64 N/A

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

   12. metadata-eval N/A

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

   13. lift-cbrt.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. metadata-eval N/A

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

   17. div-inv N/A

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

   18. cbrt-div N/A

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

   19. clear-num N/A

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

   20. lift-/.f64 N/A

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

   21. cbrt-prod N/A

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

   22. *-commutative N/A

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

   23. lift-*.f64 N/A

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

   24. lift-cbrt.f64 77.7

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

   25. lift-*.f64 N/A

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

6. Applied rewrites 77.7%

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

Reproduce

herbie shell --seed 2024324 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))