2-ancestry mixing, zero discriminant

Percentage Accurate: 76.2% → 98.8%

Time: 1.4s

Alternatives: 4

Speedup: 0.9×

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: 98.8% accurate, 0.6× 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 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

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. cbrt-prod N/A

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

   6. associate-/r* N/A

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

   7. metadata-eval N/A

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

   8. cbrt-undiv N/A

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

   9. associate-/l* N/A

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

   10. lower-/.f64 N/A

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

   11. cbrt-unprod N/A

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

   12. metadata-eval N/A

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

   13. mult-flip N/A

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

   14. lower-cbrt.f64 N/A

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

   15. mult-flip N/A

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

   16. metadata-eval N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 N/A

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

   19. lower-cbrt.f64 98.8

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

3. Applied rewrites 98.8%

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

Alternative 2: 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 76.2%

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

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

   3. lift-/.f64 N/A

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

   4. cbrt-div N/A

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

   5. lower-/.f64 N/A

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

   6. lower-cbrt.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   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 3: 76.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[g_, a_] := N[Power[N[(N[(0.5 / a), $MachinePrecision] / N[(1.0 / g), $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. lift-/.f64 N/A

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

   3. div-flip N/A

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

   4. associate-/r/ N/A

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

   5. lower-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. metadata-eval N/A

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

   8. lower-/.f64 76.2

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

3. Applied rewrites 76.2%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*l/ N/A

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

   4. associate-*r/ N/A

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

   5. div-flip N/A

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

   6. mult-flip-rev N/A

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

   7. lift-/.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. mult-flip N/A

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

   10. lift-*.f64 N/A

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

   11. lift-/.f64 N/A

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

   12. associate-/r* N/A

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

   13. lower-/.f64 N/A

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

   14. lift-/.f64 N/A

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

   15. lift-/.f64 76.2

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

5. Applied rewrites 76.2%

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

Alternative 4: 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 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%

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

Reproduce

herbie shell --seed 2025142 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))