2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 1.5s

Alternatives: 6

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, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.1%

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

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

3. Applied rewrites 98.7%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lift-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.2

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

5. Applied rewrites 98.2%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. lower-pow.f64 98.7

      \[\leadsto \frac{\frac{\sqrt[3]{g}}{\color{blue}{{2}^{0.3333333333333333}}}}{\sqrt[3]{a}} \]

7. Applied rewrites 98.7%

   \[\leadsto \frac{\frac{\sqrt[3]{g}}{\color{blue}{{2}^{0.3333333333333333}}}}{\sqrt[3]{a}} \]

8. Taylor expanded in g around -inf

   \[\leadsto \frac{\color{blue}{-1 \cdot \left(\sqrt[3]{g} \cdot \frac{\sqrt[3]{-1}}{\sqrt[3]{2}}\right)}}{\sqrt[3]{a}} \]
9. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \frac{\mathsf{neg}\left(\sqrt[3]{g} \cdot \frac{\sqrt[3]{-1}}{\sqrt[3]{2}}\right)}{\sqrt[3]{a}} \]

   2. lower-neg.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. cbrt-undiv N/A

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

   6. metadata-eval N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lift-cbrt.f64 98.6

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

10. Applied rewrites 98.6%

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

Alternative 2: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g}}{\sqrt[3]{a} \cdot {2}^{0.3333333333333333}} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (/ (cbrt g) (* (cbrt a) (pow 2.0 0.3333333333333333))))

C

double code(double g, double a) {
	return cbrt(g) / (cbrt(a) * pow(2.0, 0.3333333333333333));
}

Java

public static double code(double g, double a) {
	return Math.cbrt(g) / (Math.cbrt(a) * Math.pow(2.0, 0.3333333333333333));
}

Julia

function code(g, a)
	return Float64(cbrt(g) / Float64(cbrt(a) * (2.0 ^ 0.3333333333333333)))
end

Wolfram

code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] / N[(N[Power[a, 1/3], $MachinePrecision] * N[Power[2.0, 0.3333333333333333], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.1%

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

   1. lift-+.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. count-2-rev N/A

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

   4. *-commutative N/A

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

   5. cbrt-unprod N/A

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

   6. lower-*.f64 N/A

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

   7. lift-cbrt.f64 N/A

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

   8. lower-cbrt.f64 98.2

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

5. Applied rewrites 98.2%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. lower-pow.f64 98.7

      \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{a} \cdot \color{blue}{{2}^{0.3333333333333333}}} \]

7. Applied rewrites 98.7%

   \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{a} \cdot \color{blue}{{2}^{0.3333333333333333}}} \]
8. Add Preprocessing

Alternative 3: 98.7% 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 76.1%

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

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

3. Applied rewrites 98.7%

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

4. Taylor expanded in g around 0

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

   1. lower-*.f64 98.7

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

6. Applied rewrites 98.7%

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

Alternative 4: 98.6% 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 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 5: 76.1% accurate, 1.0× speedup

Math

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

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(0.5 * Float64(g / a)))
end

Wolfram

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

Derivation

1. Initial program 76.1%

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

2. Taylor expanded in g around 0

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 76.1

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

4. Applied rewrites 76.1%

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

Alternative 6: 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 76.1%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.1

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

3. Applied rewrites 76.1%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))