2-ancestry mixing, zero discriminant

Percentage Accurate: 76.5% → 98.7%

Time: 6.5s

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: 76.5% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

   1. clear-num 76.9%

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

   2. cbrt-div 77.5%

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

   3. metadata-eval 77.5%

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

   4. associate-/l* 77.5%

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

4. Applied egg-rr 77.5%

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

   1. associate-*r/ 77.5%

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

   2. *-commutative 77.5%

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

   3. associate-/l* 77.5%

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

6. Simplified 77.5%

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

   1. inv-pow 77.5%

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

   2. cbrt-prod 98.7%

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

   3. unpow-prod-down 98.7%

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

8. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{a}\right)}^{-1} \cdot {\left(\sqrt[3]{\frac{2}{g}}\right)}^{-1}} \]
9. Step-by-step derivation

   1. unpow-1 98.7%

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

   2. associate-*r/ 98.7%

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

   3. *-rgt-identity 98.7%

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

   4. unpow-1 98.7%

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

10. Simplified 98.7%

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

11. Taylor expanded in a around 0 98.7%

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

12. Final simplification 98.7%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

   1. clear-num 76.9%

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

   2. cbrt-div 77.5%

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

   3. metadata-eval 77.5%

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

   4. associate-/l* 77.5%

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

4. Applied egg-rr 77.5%

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

   1. associate-*r/ 77.5%

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

   2. *-commutative 77.5%

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

   3. associate-/l* 77.5%

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

6. Simplified 77.5%

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

   1. *-commutative 77.5%

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

   2. cbrt-prod 98.7%

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

8. Applied egg-rr 98.7%

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

9. Final simplification 98.7%

   \[\leadsto \frac{1}{\sqrt[3]{\frac{2}{g}} \cdot \sqrt[3]{a}} \]
10. Add Preprocessing

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 78.1%

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

   1. pow1/3 32.4%

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

   2. clear-num 31.8%

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

   3. associate-/r/ 32.4%

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

   4. unpow-prod-down 17.9%

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

   5. pow1/3 44.9%

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

   6. associate-/r* 44.9%

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

   7. metadata-eval 44.9%

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

   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%

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

Alternative 4: 76.5% 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 78.1%

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

   1. add-log-exp 8.0%

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

   2. *-un-lft-identity 8.0%

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

   3. log-prod 8.0%

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

   4. metadata-eval 8.0%

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

   5. add-log-exp 78.1%

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

   6. div-inv 78.1%

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

   7. associate-/r* 78.1%

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

   8. metadata-eval 78.1%

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

4. Applied egg-rr 78.1%

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

   1. +-lft-identity 78.1%

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

6. Simplified 78.1%

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

7. Final simplification 78.1%

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

Alternative 5: 76.5% 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 78.1%

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

3. Final simplification 78.1%

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

Reproduce

herbie shell --seed 2024072 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))