2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 11.9s

Alternatives: 3

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: 76.1% 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

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

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. Add Preprocessing
3. Step-by-step derivation

   1. pow1/3 35.5%

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

   2. clear-num 34.4%

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

   3. associate-/r/ 35.5%

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

   4. unpow-prod-down 24.3%

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

   5. pow1/3 48.2%

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

   6. associate-/r* 48.2%

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

   7. metadata-eval 48.2%

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

   8. pow1/3 98.8%

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

4. Applied egg-rr 98.8%

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

Alternative 2: 76.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.2%

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

   1. pow1/3 35.5%

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

   2. div-inv 35.5%

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

   3. associate-/r* 35.5%

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

   4. metadata-eval 35.5%

      \[\leadsto {\left(g \cdot \frac{\color{blue}{0.5}}{a}\right)}^{0.3333333333333333} \]

4. Applied egg-rr 35.5%

   \[\leadsto \color{blue}{{\left(g \cdot \frac{0.5}{a}\right)}^{0.3333333333333333}} \]
5. Step-by-step derivation

   1. unpow1/3 71.3%

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

   2. cbrt-prod 98.8%

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

   3. *-commutative 98.8%

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

   4. /-rgt-identity 98.8%

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

   5. clear-num 98.7%

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

   6. div-inv 98.7%

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

6. Applied egg-rr 98.7%

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

   1. clear-num 98.7%

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

   2. cbrt-div 98.7%

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

   3. associate-/r/ 98.6%

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

   4. associate-/r* 98.5%

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

   5. cbrt-prod 98.6%

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

   6. associate-/l/ 98.6%

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

   7. add-cbrt-cube 98.4%

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

   8. add-cbrt-cube 98.1%

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

   9. cbrt-undiv 70.8%

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

8. Applied egg-rr 71.3%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{\frac{1}{a}}{\frac{2}{g}}}} \]
9. Add Preprocessing

Alternative 3: 76.1% 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. Add Preprocessing
3. Step-by-step derivation

   1. add-log-exp 9.0%

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

   2. *-un-lft-identity 9.0%

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

   3. log-prod 9.0%

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

   4. metadata-eval 9.0%

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

   5. add-log-exp 71.2%

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

   6. div-inv 71.3%

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

   7. associate-/r* 71.3%

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

   8. metadata-eval 71.3%

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

4. Applied egg-rr 71.3%

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

   1. +-lft-identity 71.3%

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

6. Simplified 71.3%

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

7. Final simplification 71.3%

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

Reproduce

herbie shell --seed 2024107 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))