2-ancestry mixing, zero discriminant

Percentage Accurate: 75.3% → 98.7%

Time: 6.0s

Alternatives: 4

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: 75.3% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

   1. associate-/r* 76.5%

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

   2. cbrt-div 98.7%

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

   3. div-inv 98.7%

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

   4. div-inv 98.7%

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

   5. metadata-eval 98.7%

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

3. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot \frac{1}{\sqrt[3]{a}}} \]
4. Step-by-step derivation

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

   1. div-inv 76.5%

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

   2. cbrt-prod 98.7%

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

   3. *-commutative 98.7%

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

   4. associate-/r* 98.7%

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

   5. metadata-eval 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 3: 75.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

   1. expm1-log1p-u 59.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)\right)} \]

   2. expm1-udef 24.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} - 1} \]

   3. sub-neg 24.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{\frac{g}{2 \cdot a}}\right)} + \left(-1\right)} \]

   4. div-inv 24.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\right)} + \left(-1\right) \]

   5. associate-/r* 24.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}}\right)} + \left(-1\right) \]

   6. metadata-eval 24.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}}\right)} + \left(-1\right) \]

   7. metadata-eval 24.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{-1} \]

3. Applied egg-rr 24.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + -1} \]
4. Step-by-step derivation

   1. metadata-eval 24.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} + \color{blue}{\left(-1\right)} \]

   2. sub-neg 24.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)} - 1} \]

   3. expm1-def 59.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{g \cdot \frac{0.5}{a}}\right)\right)} \]

   4. expm1-log1p 76.5%

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

5. Simplified 76.5%

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

6. Final simplification 76.5%

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

Alternative 4: 75.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

2. Final simplification 76.5%

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

Reproduce

herbie shell --seed 2023336 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))