2-ancestry mixing, zero discriminant

Percentage Accurate: 77.0% → 98.7%

Time: 6.1s

Alternatives: 7

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: 77.0% 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, 0.3× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt[3]{0.5} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. cbrt-div 98.7%

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

   2. clear-num 98.8%

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

3. Applied egg-rr 98.8%

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

   1. associate-/r/ 98.8%

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

   2. *-commutative 98.8%

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

5. Simplified 98.8%

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

   1. metadata-eval 98.8%

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

   2. metadata-eval 98.8%

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

   3. div-inv 98.8%

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

   4. cbrt-div 98.7%

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

   5. clear-num 98.7%

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

   6. div-inv 98.7%

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

   7. cbrt-prod 98.8%

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

7. Applied egg-rr 98.8%

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

8. Final simplification 98.8%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. cbrt-div 98.7%

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

   2. clear-num 98.8%

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

3. Applied egg-rr 98.8%

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

   1. associate-/r/ 98.8%

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

   2. *-commutative 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. pow1/3 39.8%

      \[\leadsto \color{blue}{{\left(\frac{g}{2 \cdot a}\right)}^{0.3333333333333333}} \]

   2. clear-num 39.5%

      \[\leadsto {\color{blue}{\left(\frac{1}{\frac{2 \cdot a}{g}}\right)}}^{0.3333333333333333} \]

   3. associate-/r/ 39.8%

      \[\leadsto {\color{blue}{\left(\frac{1}{2 \cdot a} \cdot g\right)}}^{0.3333333333333333} \]

   4. unpow-prod-down 26.5%

      \[\leadsto \color{blue}{{\left(\frac{1}{2 \cdot a}\right)}^{0.3333333333333333} \cdot {g}^{0.3333333333333333}} \]

   5. pow1/3 49.2%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{1}{2 \cdot a}}} \cdot {g}^{0.3333333333333333} \]

   6. associate-/r* 49.2%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{1}{2}}{a}}} \cdot {g}^{0.3333333333333333} \]

   7. metadata-eval 49.2%

      \[\leadsto \sqrt[3]{\frac{\color{blue}{0.5}}{a}} \cdot {g}^{0.3333333333333333} \]

   8. pow1/3 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 4: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. cbrt-div 98.7%

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

   2. clear-num 98.8%

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

3. Applied egg-rr 98.8%

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

   1. associate-/l* 98.7%

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

   2. *-lft-identity 98.7%

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

   3. *-commutative 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 5: 98.7% accurate, 0.5× 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 77.9%

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

   1. associate-/r* 77.9%

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

   2. cbrt-div 98.7%

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

   3. div-inv 98.7%

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

   4. metadata-eval 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

Alternative 6: 77.0% 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 77.9%

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

   1. add-log-exp 9.5%

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

   2. *-un-lft-identity 9.5%

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

   3. log-prod 9.5%

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

   4. metadata-eval 9.5%

      \[\leadsto \color{blue}{0} + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right) \]

   5. add-log-exp 77.9%

      \[\leadsto 0 + \color{blue}{\sqrt[3]{\frac{g}{2 \cdot a}}} \]

   6. *-un-lft-identity 77.9%

      \[\leadsto 0 + \sqrt[3]{\frac{\color{blue}{1 \cdot g}}{2 \cdot a}} \]

   7. times-frac 77.9%

      \[\leadsto 0 + \sqrt[3]{\color{blue}{\frac{1}{2} \cdot \frac{g}{a}}} \]

   8. metadata-eval 77.9%

      \[\leadsto 0 + \sqrt[3]{\color{blue}{0.5} \cdot \frac{g}{a}} \]

3. Applied egg-rr 77.9%

   \[\leadsto \color{blue}{0 + \sqrt[3]{0.5 \cdot \frac{g}{a}}} \]
4. Step-by-step derivation

   1. +-lft-identity 77.9%

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

   2. metadata-eval 77.9%

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

   3. times-frac 77.9%

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

   4. *-commutative 77.9%

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

   5. times-frac 77.9%

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

   6. rem-square-sqrt 40.3%

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

   7. associate-*r/ 40.3%

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

   8. /-rgt-identity 40.3%

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

   9. rem-square-sqrt 77.9%

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

5. Simplified 77.9%

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

6. Final simplification 77.9%

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

Alternative 7: 77.0% 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 77.9%

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

2. Final simplification 77.9%

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

Reproduce

herbie shell --seed 2023334 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))