2-ancestry mixing, zero discriminant

Percentage Accurate: 76.5% → 98.7%

Time: 2.4s

Alternatives: 3

Speedup: 1.0×

Specification

Math

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

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

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

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, 0.6× speedup

Math

\[\sqrt[3]{\frac{0.25}{a}} \cdot \sqrt[3]{g + g} \]

FPCore

(FPCore (g a) :precision binary64 (* (cbrt (/ 0.25 a)) (cbrt (+ g g))))

C

double code(double g, double a) {
	return cbrt((0.25 / a)) * cbrt((g + g));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((0.25 / a)) * Math.cbrt((g + g));
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(0.25 / a)) * cbrt(Float64(g + g)))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(0.25 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(g + g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.5%

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

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.7%

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.7%

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

3. Applied rewrites 98.7%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. lift-+.f64 N/A

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

   6. count-2 N/A

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

   7. *-commutative N/A

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

   8. associate-/l/ N/A

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

   9. lift-/.f64 N/A

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

   10. div-flip-rev N/A

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

   11. lift-/.f64 N/A

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

   12. lift-/.f64 N/A

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

   13. *-rgt-identity N/A

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

   14. lift-/.f64 N/A

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

   15. lift-/.f64 N/A

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

   16. div-flip-rev N/A

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

   17. lift-/.f64 N/A

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

   18. associate-/l/ N/A

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

   19. *-commutative N/A

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

   20. count-2 N/A

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

   21. lift-+.f64 N/A

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

   22. metadata-eval N/A

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

   23. frac-times N/A

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

   24. cbrt-div N/A

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

   25. lower-/.f64 N/A

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

5. Applied rewrites 98.6%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. mult-flip N/A

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

   6. cbrt-prod N/A

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

   7. lift-cbrt.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. count-2-rev N/A

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

   12. lower-+.f64 N/A

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

   13. lower-cbrt.f64 N/A

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

   14. metadata-eval N/A

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

   15. lower-/.f64 N/A

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

   16. metadata-eval 98.6%

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lift-+.f64 N/A

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

   20. count-2 N/A

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

   21. associate-*r* N/A

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

   22. lower-*.f64 N/A

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

   23. metadata-eval 98.6%

       \[\leadsto \sqrt[3]{g + g} \cdot \sqrt[3]{\frac{1}{\color{blue}{4} \cdot a}} \]

7. Applied rewrites 98.6%

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

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\sqrt[3]{g + g} \cdot \sqrt[3]{\frac{1}{4 \cdot a}}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\sqrt[3]{\frac{1}{4 \cdot a}} \cdot \sqrt[3]{g + g}} \]

   3. lower-*.f64 98.6%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{1}{4 \cdot a}} \cdot \sqrt[3]{g + g}} \]

   4. lift-/.f64 N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{4 \cdot a}}} \cdot \sqrt[3]{g + g} \]

   5. lift-*.f64 N/A

      \[\leadsto \sqrt[3]{\frac{1}{\color{blue}{4 \cdot a}}} \cdot \sqrt[3]{g + g} \]

   6. associate-/r* N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{4}}{a}}} \cdot \sqrt[3]{g + g} \]

   7. lower-/.f64 N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{4}}{a}}} \cdot \sqrt[3]{g + g} \]

   8. metadata-eval 98.7%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{0.25}}{a}} \cdot \sqrt[3]{g + g} \]

9. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.25}{a}} \cdot \sqrt[3]{g + g}} \]
10. Add Preprocessing

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\frac{\sqrt[3]{g}}{\sqrt[3]{a + a}} \]

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 76.5%

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

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.7%

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.7%

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

3. Applied rewrites 98.7%

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

Alternative 3: 76.5% accurate, 1.0× speedup

Math

\[\sqrt[3]{\frac{g}{a + a}} \]

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 76.5%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.5%

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

3. Applied rewrites 76.5%

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

Reproduce

herbie shell --seed 2025196 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))