2-ancestry mixing, zero discriminant

Percentage Accurate: 76.3% → 98.7%

Time: 4.6s

Alternatives: 5

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: 76.3% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.2%

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

   1. expm1-log1p-u 56.4%

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

   2. expm1-udef 26.8%

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

   3. log1p-udef 26.8%

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

   4. add-exp-log 41.6%

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

   5. *-un-lft-identity 41.6%

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

   6. times-frac 41.6%

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

   7. metadata-eval 41.6%

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

3. Applied egg-rr 41.6%

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

   1. +-commutative 41.6%

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

   2. associate--l+ 71.2%

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

   3. metadata-eval 71.2%

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

   4. +-rgt-identity 71.2%

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

   5. associate-*r/ 71.2%

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

   6. associate-*l/ 71.2%

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

5. Simplified 71.2%

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

   1. associate-*l/ 71.2%

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

   2. *-un-lft-identity 71.2%

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

   3. times-frac 71.2%

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

   4. metadata-eval 71.2%

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

   5. metadata-eval 71.2%

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

   6. times-frac 71.2%

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

   7. *-un-lft-identity 71.2%

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

   8. *-commutative 71.2%

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

   9. cbrt-undiv 98.8%

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

   10. clear-num 98.8%

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

   11. div-inv 98.7%

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

   12. associate-/r* 98.6%

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

   13. clear-num 98.6%

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

   14. metadata-eval 98.6%

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

   15. /-rgt-identity 98.6%

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

   16. metadata-eval 98.6%

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

   17. div-inv 98.6%

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

   18. cbrt-div 98.7%

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

   19. clear-num 98.7%

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

7. Applied egg-rr 98.7%

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

   1. expm1-log1p-u 71.5%

      \[\leadsto \frac{\sqrt[3]{\frac{0.5}{a}}}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\sqrt[3]{g}}\right)\right)}} \]

   2. expm1-udef 30.8%

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

9. Applied egg-rr 30.8%

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

    1. expm1-def 71.5%

       \[\leadsto \frac{\sqrt[3]{\frac{0.5}{a}}}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\sqrt[3]{g}}\right)\right)}} \]

    2. expm1-log1p 98.7%

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

    3. rem-cbrt-cube 98.5%

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

    4. cube-div 98.5%

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

    5. metadata-eval 98.5%

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

    6. rem-cube-cbrt 98.8%

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

11. Simplified 98.8%

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

12. Final simplification 98.8%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.2%

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

   1. cbrt-div 98.8%

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

   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. Final simplification 98.8%

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

Alternative 3: 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 71.2%

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

   1. div-inv 71.2%

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

   2. cbrt-prod 98.7%

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

   3. associate-/r* 98.7%

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

   4. metadata-eval 98.7%

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

3. Applied egg-rr 98.7%

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

4. Final simplification 98.7%

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

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 71.2%

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

   1. cbrt-div 98.8%

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

   2. div-inv 98.7%

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

3. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.8%

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

   2. *-rgt-identity 98.8%

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

   3. *-commutative 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 5: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.2%

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

   1. expm1-log1p-u 56.4%

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

   2. expm1-udef 26.8%

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

   3. log1p-udef 26.8%

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

   4. add-exp-log 41.6%

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

   5. *-un-lft-identity 41.6%

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

   6. times-frac 41.6%

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

   7. metadata-eval 41.6%

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

3. Applied egg-rr 41.6%

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

   1. +-commutative 41.6%

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

   2. associate--l+ 71.2%

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

   3. metadata-eval 71.2%

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

   4. +-rgt-identity 71.2%

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

   5. associate-*r/ 71.2%

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

   6. associate-*l/ 71.2%

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

5. Simplified 71.2%

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

6. Final simplification 71.2%

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

Reproduce

herbie shell --seed 2023187 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))