2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 3.1s

Alternatives: 3

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: 76.1% 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

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

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 70.7%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. lift-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. flip-+ N/A

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

   8. distribute-neg-frac N/A

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

   9. +-inverses N/A

      \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\mathsf{neg}\left(\color{blue}{0}\right)}{a - a}}} \]

   10. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lower-neg.f64 N/A

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

   18. lower-cbrt.f64 1.6

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

   19. lift-*.f64 N/A

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

   20. count-2-rev N/A

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

   21. flip-+ N/A

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

   22. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   23. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   24. +-inverses N/A

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

   25. distribute-neg-frac N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. metadata-eval N/A

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

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

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

   7. count-2-rev N/A

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

   8. lift-+.f64 N/A

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

   9. cbrt-div N/A

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

   10. lift-neg.f64 N/A

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

   11. frac-2neg N/A

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

   12. cbrt-div N/A

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

   13. lift-+.f64 N/A

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

   14. flip-+ N/A

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

   15. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   16. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   17. +-inverses N/A

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

   18. distribute-neg-frac N/A

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

   19. flip-+ N/A

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

   20. count-2-rev N/A

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

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

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

   22. metadata-eval N/A

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

   23. *-commutative N/A

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

6. Applied rewrites 98.8%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 98.8

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

8. Applied rewrites 98.8%

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

Alternative 2: 76.1% 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 70.7%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. 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 70.7

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

4. Applied rewrites 70.7%

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

5. Taylor expanded in g around 0

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

   1. associate-*r/ N/A

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

   2. associate-*l/ N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 70.8

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

7. Applied rewrites 70.8%

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

Alternative 3: 76.1% 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 70.7%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. Add Preprocessing
3. 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 70.7

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

4. Applied rewrites 70.7%

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

Reproduce

herbie shell --seed 2025003 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))