2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 2.8s

Alternatives: 5

Speedup: 0.7×

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: 76.1% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. 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. cbrt-prod N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. associate-/r* N/A

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

   10. lower-/.f64 N/A

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

   11. metadata-eval N/A

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

   12. lower-cbrt.f64 98.7%

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

3. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a}} \cdot \sqrt[3]{g}} \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. metadata-eval N/A

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

   5. associate-/r* N/A

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

   6. count-2 N/A

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

   7. lift-+.f64 N/A

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

   8. lift-cbrt.f64 N/A

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

   9. cbrt-prod N/A

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

   10. associate-/r/ N/A

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

   11. lift-/.f64 N/A

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

   12. mult-flip N/A

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

   13. lift-/.f64 N/A

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

   14. *-commutative N/A

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

   15. lift-/.f64 N/A

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

   16. lift-/.f64 N/A

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

   17. mult-flip N/A

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

   18. associate-/r* N/A

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

   19. lift-+.f64 N/A

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

   20. count-2 N/A

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

   21. associate-/r* N/A

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

   22. metadata-eval N/A

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

   23. lift-/.f64 N/A

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

   24. metadata-eval N/A

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

5. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{0.5}{a} \cdot 2}}{\sqrt[3]{\frac{2}{g}}}} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*l/ N/A

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

   4. metadata-eval N/A

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

   5. lower-/.f64 98.7%

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

7. Applied rewrites 98.7%

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

Alternative 2: 98.7% accurate, 0.6× speedup

Math

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

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 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. 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. cbrt-prod N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. associate-/r* N/A

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

   10. lower-/.f64 N/A

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

   11. metadata-eval N/A

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

   12. lower-cbrt.f64 98.7%

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

3. Applied rewrites 98.7%

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

Alternative 3: 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 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 4: 76.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.1%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. metadata-eval 76.1%

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

3. Applied rewrites 76.1%

   \[\leadsto \sqrt[3]{\color{blue}{\frac{0.5}{a} \cdot g}} \]
4. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. metadata-eval N/A

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

   4. times-frac N/A

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

   5. metadata-eval N/A

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

   6. count-2 N/A

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

   7. lift-+.f64 N/A

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

   8. *-inverses N/A

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

   9. associate-/r* N/A

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

   10. *-commutative N/A

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

   11. associate-/r* N/A

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

   12. mult-flip N/A

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

   13. lower-*.f64 N/A

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

   14. lower-/.f64 N/A

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

   15. lower-/.f64 76.1%

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

5. Applied rewrites 76.1%

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

Alternative 5: 76.1% 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 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.1%

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

3. Applied rewrites 76.1%

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

Reproduce

herbie shell --seed 2025185 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))