2-ancestry mixing, zero discriminant

Percentage Accurate: 76.9% → 98.7%

Time: 1.9s

Alternatives: 5

Speedup: 0.8×

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: 76.9% 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, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{g}}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. count-2-rev N/A

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

   10. lower-+.f64 N/A

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

   11. lower-cbrt.f64 98.7

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

3. Applied rewrites 98.7%

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

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{0.5 \cdot g} \cdot \frac{1}{\sqrt[3]{a}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower-cbrt.f64 98.7

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

3. Applied rewrites 98.7%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. lower-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-/.f64 98.7

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

5. Applied rewrites 98.7%

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

Alternative 3: 98.7% 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 76.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{\frac{1}{a + a}}{\frac{1}{g}}} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

   1. lift-/.f64 N/A

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

   2. div-flip N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 76.2

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

   5. lift-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. lower-+.f64 76.2

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

3. Applied rewrites 76.2%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 76.2

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

5. Applied rewrites 76.2%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

   5. lower-/.f64 76.9

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

7. Applied rewrites 76.9%

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

Alternative 5: 76.9% 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 76.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.9

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

3. Applied rewrites 76.9%

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

Reproduce

herbie shell --seed 2025145 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))