2-ancestry mixing, zero discriminant

Percentage Accurate: 76.2% → 98.7%

Time: 3.6s

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: 76.2% 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, 0.3× speedup

Math

\[\begin{array}{l} \\ \frac{{\left({\left(\sqrt[3]{0.5 \cdot g}\right)}^{-1}\right)}^{-1}}{\sqrt[3]{a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

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

   4. associate-/r* N/A

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

   5. cbrt-div N/A

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

   6. lower-/.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-cbrt.f64 98.7

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

4. Applied rewrites 98.7%

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

5. Taylor expanded in g around 0

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

   1. lower-*.f64 98.7

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

7. Applied rewrites 98.7%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. lower-pow.f64 37.9

      \[\leadsto \frac{\color{blue}{{\left(0.5 \cdot g\right)}^{0.3333333333333333}}}{\sqrt[3]{a}} \]

9. Applied rewrites 37.9%

   \[\leadsto \frac{\color{blue}{{\left(0.5 \cdot g\right)}^{0.3333333333333333}}}{\sqrt[3]{a}} \]
10. Step-by-step derivation

    1. lift-pow.f64 N/A

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

    2. pow-to-exp N/A

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

    3. sinh-+-cosh-rev N/A

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

    4. flip-+ N/A

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

    5. sinh-cosh N/A

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

    6. sinh---cosh-rev N/A

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

    7. lower-/.f64 N/A

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

    8. exp-neg N/A

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

    9. pow-to-exp N/A

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

    10. lift-pow.f64 N/A

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

    11. lower-/.f64 37.9

        \[\leadsto \frac{\frac{1}{\color{blue}{\frac{1}{{\left(0.5 \cdot g\right)}^{0.3333333333333333}}}}}{\sqrt[3]{a}} \]

    12. lift-pow.f64 N/A

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

    13. unpow1/3 N/A

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

    14. lower-cbrt.f64 98.7

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

11. Applied rewrites 98.7%

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

12. Final simplification 98.7%

    \[\leadsto \frac{{\left({\left(\sqrt[3]{0.5 \cdot g}\right)}^{-1}\right)}^{-1}}{\sqrt[3]{a}} \]
13. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

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

   4. associate-/r* N/A

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

   5. cbrt-div N/A

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

   6. lower-/.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-cbrt.f64 98.7

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

4. Applied rewrites 98.7%

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

5. Taylor expanded in g around 0

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

   1. lower-*.f64 98.7

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

7. Applied rewrites 98.7%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

3. Taylor expanded in g around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-cbrt.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-/.f64 77.0

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

5. Applied rewrites 77.0%

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

7. Applied rewrites 98.7%

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

9. Applied rewrites 98.3%

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

Alternative 4: 76.2% 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 77.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 77.0

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

4. Applied rewrites 77.0%

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

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 77.1

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

7. Applied rewrites 77.1%

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

Alternative 5: 76.2% 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 77.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 77.0

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

4. Applied rewrites 77.0%

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

Reproduce

herbie shell --seed 2024350 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))