2-ancestry mixing, zero discriminant

Percentage Accurate: 77.1% → 98.7%

Time: 5.9s

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: 77.1% 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, 0.5× 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 75.6%

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

   1. cbrt-div 98.8%

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

   2. clear-num 98.7%

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

4. Applied egg-rr 98.7%

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

   1. associate-/l* 98.8%

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

   2. *-lft-identity 98.8%

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

   3. *-commutative 98.8%

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

6. Simplified 98.8%

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

7. Final simplification 98.8%

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

Alternative 2: 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 75.6%

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

   1. pow1/3 28.6%

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

   2. clear-num 28.1%

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

   3. associate-/r/ 28.6%

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

   4. unpow-prod-down 17.2%

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

   5. pow1/3 43.8%

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

   6. associate-/r* 43.8%

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

   7. metadata-eval 43.8%

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

   8. pow1/3 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 3: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.6%

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

   1. add-log-exp 8.4%

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

   2. *-un-lft-identity 8.4%

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

   3. log-prod 8.4%

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

   4. metadata-eval 8.4%

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

   5. add-log-exp 75.6%

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

   6. *-un-lft-identity 75.6%

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

   7. times-frac 75.6%

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

   8. metadata-eval 75.6%

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

4. Applied egg-rr 75.6%

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

   1. +-lft-identity 75.6%

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

   2. metadata-eval 75.6%

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

   3. times-frac 75.6%

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

   4. *-commutative 75.6%

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

   5. times-frac 75.7%

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

   6. rem-square-sqrt 38.0%

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

   7. associate-*r/ 38.0%

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

   8. /-rgt-identity 38.0%

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

   9. rem-square-sqrt 75.7%

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

6. Simplified 75.7%

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

   1. clear-num 75.7%

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

   2. div-inv 75.7%

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

   3. metadata-eval 75.7%

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

   4. div-inv 75.6%

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

   5. clear-num 74.0%

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

   6. div-inv 74.0%

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

   7. associate-/r* 75.7%

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

   8. metadata-eval 75.7%

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

   9. div-inv 75.7%

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

   10. clear-num 75.7%

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

8. Applied egg-rr 75.7%

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

9. Final simplification 75.7%

   \[\leadsto \sqrt[3]{\frac{\frac{0.5}{a}}{\frac{1}{g}}} \]
10. Add Preprocessing

Alternative 4: 77.1% 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 75.6%

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

   1. add-log-exp 8.4%

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

   2. *-un-lft-identity 8.4%

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

   3. log-prod 8.4%

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

   4. metadata-eval 8.4%

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

   5. add-log-exp 75.6%

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

   6. *-un-lft-identity 75.6%

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

   7. times-frac 75.6%

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

   8. metadata-eval 75.6%

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

4. Applied egg-rr 75.6%

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

   1. +-lft-identity 75.6%

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

   2. metadata-eval 75.6%

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

   3. times-frac 75.6%

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

   4. *-commutative 75.6%

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

   5. times-frac 75.7%

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

   6. rem-square-sqrt 38.0%

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

   7. associate-*r/ 38.0%

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

   8. /-rgt-identity 38.0%

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

   9. rem-square-sqrt 75.7%

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

6. Simplified 75.7%

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

7. Final simplification 75.7%

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

Reproduce

herbie shell --seed 2024011 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))