2-ancestry mixing, zero discriminant

Percentage Accurate: 75.6% → 98.7%

Time: 3.6s

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: 75.6% 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

\[\begin{array}{l} \\ \left(\sqrt[3]{g \cdot 0.5} \cdot 0.5\right) \cdot \frac{2}{\sqrt[3]{a}} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (* (* (cbrt (* g 0.5)) 0.5) (/ 2.0 (cbrt a))))

C

double code(double g, double a) {
	return (cbrt((g * 0.5)) * 0.5) * (2.0 / cbrt(a));
}

Java

public static double code(double g, double a) {
	return (Math.cbrt((g * 0.5)) * 0.5) * (2.0 / Math.cbrt(a));
}

Julia

function code(g, a)
	return Float64(Float64(cbrt(Float64(g * 0.5)) * 0.5) * Float64(2.0 / cbrt(a)))
end

Wolfram

code[g_, a_] := N[(N[(N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision] * 0.5), $MachinePrecision] * N[(2.0 / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.6%

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

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. cbrt-prod N/A

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

   6. associate-/r* N/A

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

   7. metadata-eval N/A

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

   8. cbrt-undiv N/A

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

   9. frac-2neg-rev N/A

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

   10. cbrt-neg-rev N/A

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

   11. metadata-eval N/A

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

   12. associate-/l* N/A

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

   13. distribute-neg-frac2 N/A

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

   14. mult-flip N/A

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

   15. *-commutative N/A

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

   16. distribute-rgt-neg-in N/A

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

   17. mult-flip N/A

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

   18. associate-*l* N/A

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

   19. metadata-eval N/A

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

   20. *-commutative N/A

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

   21. mult-flip-rev N/A

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

3. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\left(\sqrt[3]{0.5 \cdot g} \cdot 2\right) \cdot \frac{1}{\sqrt[3]{a} \cdot 2}} \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-cbrt.f64 N/A

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

   6. associate-*l* N/A

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

   7. mult-flip-rev N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. times-frac N/A

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

   11. mult-flip-rev N/A

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

   12. lower-*.f64 N/A

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

   13. mult-flip N/A

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

   14. metadata-eval N/A

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

   15. lower-*.f64 N/A

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 N/A

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

   19. mult-flip-rev N/A

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

   20. lower-/.f64 N/A

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

   21. lift-cbrt.f64 98.7

       \[\leadsto \left(\sqrt[3]{g \cdot 0.5} \cdot 0.5\right) \cdot \frac{2}{\color{blue}{\sqrt[3]{a}}} \]

5. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\left(\sqrt[3]{g \cdot 0.5} \cdot 0.5\right) \cdot \frac{2}{\sqrt[3]{a}}} \]
6. Add Preprocessing

Alternative 2: 98.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.6%

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

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

   3. lift-/.f64 N/A

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

   4. cbrt-div N/A

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

   5. lower-/.f64 N/A

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

   6. lower-cbrt.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.6

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

3. Applied rewrites 98.6%

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

Alternative 3: 75.6% 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 75.6%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. mult-flip N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. metadata-eval N/A

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

   8. lower-/.f64 75.6

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

3. Applied rewrites 75.6%

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

Alternative 4: 75.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.6%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 75.6

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

3. Applied rewrites 75.6%

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

Reproduce

herbie shell --seed 2025136 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))