2-ancestry mixing, zero discriminant

Percentage Accurate: 75.7% → 98.7%

Time: 4.1s

Alternatives: 4

Speedup: 0.5×

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: 75.7% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 74.3%

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

   1. div-inv 74.3%

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

   2. cbrt-prod 98.4%

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

   3. associate-/r* 98.8%

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

   4. metadata-eval 98.8%

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

3. Applied egg-rr 98.8%

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

   1. clear-num 98.4%

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

   2. cbrt-div 98.2%

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

   3. metadata-eval 98.2%

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

   4. div-inv 98.2%

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

   5. metadata-eval 98.2%

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

   6. div-inv 98.3%

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

   7. clear-num 98.3%

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

   8. *-commutative 98.3%

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

   9. div-inv 98.2%

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

   10. associate-/r* 98.2%

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

   11. *-commutative 98.2%

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

   12. metadata-eval 98.2%

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

   13. metadata-eval 98.2%

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

   14. div-inv 98.2%

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

   15. cbrt-div 98.4%

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

   16. clear-num 98.7%

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

5. Applied egg-rr 98.7%

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

   1. frac-2neg 98.7%

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

   2. div-inv 98.8%

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

   3. distribute-neg-frac 98.8%

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

   4. metadata-eval 98.8%

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

7. Applied egg-rr 98.8%

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

8. Final simplification 98.8%

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

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 74.3%

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

   1. div-inv 74.3%

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

   2. cbrt-prod 98.4%

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

   3. associate-/r* 98.8%

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

   4. metadata-eval 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt[3]{\frac{a \cdot 2}{g}}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ 1.0 (cbrt (/ (* a 2.0) g))))

C

double code(double g, double a) {
	return 1.0 / cbrt(((a * 2.0) / g));
}

Java

public static double code(double g, double a) {
	return 1.0 / Math.cbrt(((a * 2.0) / g));
}

Julia

function code(g, a)
	return Float64(1.0 / cbrt(Float64(Float64(a * 2.0) / g)))
end

Wolfram

code[g_, a_] := N[(1.0 / N[Power[N[(N[(a * 2.0), $MachinePrecision] / g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.3%

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

   1. clear-num 73.6%

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

   2. cbrt-div 74.9%

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

   3. metadata-eval 74.9%

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

   4. *-un-lft-identity 74.9%

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

   5. times-frac 75.2%

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

   6. metadata-eval 75.2%

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

3. Applied egg-rr 75.2%

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

   1. associate-*r/ 74.9%

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

   2. *-commutative 74.9%

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

5. Simplified 74.9%

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

6. Final simplification 74.9%

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

Alternative 4: 75.7% 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 74.3%

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

2. Taylor expanded in g around 0 74.7%

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

3. Final simplification 74.7%

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

Reproduce

herbie shell --seed 2023193 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))