2-ancestry mixing, zero discriminant

Percentage Accurate: 76.2% → 98.6%

Time: 3.9s

Alternatives: 6

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: 76.2% 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: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := {\left(\frac{1}{\left|g\right|}\right)}^{\left(\frac{1}{2}\right)}\\ \mathsf{copysign}\left(1, g\right) \cdot \frac{\sqrt[3]{\frac{1}{t\_0 \cdot t\_0}}}{\sqrt[3]{a + a}} \end{array} \]

FPCore

(FPCore (g a)
  :precision binary64
  (let* ((t_0 (pow (/ 1.0 (fabs g)) (/ 1.0 2.0))))
  (* (copysign 1.0 g) (/ (cbrt (/ 1.0 (* t_0 t_0))) (cbrt (+ a a))))))

C

double code(double g, double a) {
	double t_0 = pow((1.0 / fabs(g)), (1.0 / 2.0));
	return copysign(1.0, g) * (cbrt((1.0 / (t_0 * t_0))) / cbrt((a + a)));
}

Java

public static double code(double g, double a) {
	double t_0 = Math.pow((1.0 / Math.abs(g)), (1.0 / 2.0));
	return Math.copySign(1.0, g) * (Math.cbrt((1.0 / (t_0 * t_0))) / Math.cbrt((a + a)));
}

Julia

function code(g, a)
	t_0 = Float64(1.0 / abs(g)) ^ Float64(1.0 / 2.0)
	return Float64(copysign(1.0, g) * Float64(cbrt(Float64(1.0 / Float64(t_0 * t_0))) / cbrt(Float64(a + a))))
end

Wolfram

code[g_, a_] := Block[{t$95$0 = N[Power[N[(1.0 / N[Abs[g], $MachinePrecision]), $MachinePrecision], N[(1.0 / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[Power[N[(1.0 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[N[(a + a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 98.6%

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

   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 98.6%

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

3. Applied rewrites 98.6%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. metadata-eval N/A

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

   4. metadata-eval N/A

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

   5. pow-flip N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. cbrt-pow N/A

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

   9. inv-pow N/A

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

   10. metadata-eval N/A

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

   11. cbrt-undiv N/A

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

   12. lower-cbrt.f64 N/A

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

   13. lower-/.f64 N/A

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

   14. lower-/.f64 98.6%

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

5. Applied rewrites 98.6%

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

   1. unpow1 N/A

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

   2. sqr-pow N/A

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

   3. lower-unsound-*.f64 N/A

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

   4. lower-unsound-pow.f64 N/A

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

   5. lower-unsound-/.f64 N/A

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

   6. lower-unsound-pow.f64 N/A

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

   7. lower-unsound-/.f64 48.9%

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

7. Applied rewrites 48.9%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 98.6%

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

   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 98.6%

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

3. Applied rewrites 98.6%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. metadata-eval N/A

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

   4. metadata-eval N/A

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

   5. pow-flip N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. cbrt-pow N/A

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

   9. inv-pow N/A

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

   10. metadata-eval N/A

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

   11. cbrt-undiv N/A

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

   12. lower-cbrt.f64 N/A

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

   13. lower-/.f64 N/A

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

   14. lower-/.f64 98.6%

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

5. Applied rewrites 98.6%

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

Alternative 3: 98.6% 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 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 98.6%

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

   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 98.6%

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

3. Applied rewrites 98.6%

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

Alternative 4: 76.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 98.6%

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

   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 98.6%

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

3. Applied rewrites 98.6%

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

   1. lift-/.f64 N/A

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

   2. div-flip N/A

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

   3. lower-unsound-/.f32 N/A

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

   4. lower-/.f32 N/A

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

   5. lift-cbrt.f64 N/A

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

   6. lift-cbrt.f64 N/A

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

   7. cbrt-div N/A

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

   8. lift-/.f64 N/A

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

   9. lower-unsound-/.f64 N/A

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

   10. lower-cbrt.f64 76.2%

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

5. Applied rewrites 76.2%

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

Alternative 5: 76.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.2%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

   5. mult-flip N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 76.2%

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

3. Applied rewrites 76.2%

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

Alternative 6: 76.2% 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 76.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.2%

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

3. Applied rewrites 76.2%

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

Reproduce

herbie shell --seed 2025214 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))