2-ancestry mixing, zero discriminant

Percentage Accurate: 75.8% → 98.6%

Time: 6.9s

Alternatives: 6

Speedup: 0.5×

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: 75.8% 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: 98.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

   1. clear-num 72.6%

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

   2. associate-/r/ 73.7%

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

   3. associate-/r* 74.1%

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

   4. metadata-eval 74.1%

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

4. Applied egg-rr 74.1%

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

   1. associate-*l/ 74.1%

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

   2. *-commutative 74.1%

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

   3. cbrt-undiv 98.6%

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

   4. cbrt-prod 98.7%

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

   5. associate-/l* 98.7%

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

6. Applied egg-rr 98.7%

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

7. Final simplification 98.7%

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

Alternative 2: 98.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

   1. pow1/3 34.2%

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

   2. *-un-lft-identity 34.2%

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

   3. times-frac 34.6%

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

   4. metadata-eval 34.6%

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

   5. unpow-prod-down 34.6%

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

4. Applied egg-rr 34.6%

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

   1. unpow1/3 34.6%

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

   2. unpow1/3 74.1%

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

6. Simplified 74.1%

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

   1. cbrt-div 98.7%

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

   2. div-inv 98.7%

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

8. Applied egg-rr 98.7%

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

   1. associate-*r/ 98.7%

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

   2. *-rgt-identity 98.7%

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

10. Simplified 98.7%

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

11. Final simplification 98.7%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

   1. clear-num 72.6%

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

   2. associate-/r/ 73.7%

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

   3. associate-/r* 74.1%

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

   4. metadata-eval 74.1%

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

4. Applied egg-rr 74.1%

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

   1. associate-*l/ 74.1%

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

   2. *-commutative 74.1%

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

   3. cbrt-undiv 98.6%

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

   4. cbrt-prod 98.7%

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

   5. associate-/l* 98.7%

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

6. Applied egg-rr 98.7%

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

   1. add-sqr-sqrt 47.0%

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

   2. div-inv 46.9%

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

   3. times-frac 46.9%

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

   4. pow1/3 44.7%

      \[\leadsto \frac{\sqrt{\color{blue}{{g}^{0.3333333333333333}}}}{\sqrt[3]{a}} \cdot \frac{\sqrt{\sqrt[3]{g}}}{\frac{1}{\sqrt[3]{0.5}}} \]

   5. sqrt-pow1 44.7%

      \[\leadsto \frac{\color{blue}{{g}^{\left(\frac{0.3333333333333333}{2}\right)}}}{\sqrt[3]{a}} \cdot \frac{\sqrt{\sqrt[3]{g}}}{\frac{1}{\sqrt[3]{0.5}}} \]

   6. metadata-eval 44.7%

      \[\leadsto \frac{{g}^{\color{blue}{0.16666666666666666}}}{\sqrt[3]{a}} \cdot \frac{\sqrt{\sqrt[3]{g}}}{\frac{1}{\sqrt[3]{0.5}}} \]

   7. pow1/3 44.0%

      \[\leadsto \frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \frac{\sqrt{\color{blue}{{g}^{0.3333333333333333}}}}{\frac{1}{\sqrt[3]{0.5}}} \]

   8. sqrt-pow1 44.0%

      \[\leadsto \frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \frac{\color{blue}{{g}^{\left(\frac{0.3333333333333333}{2}\right)}}}{\frac{1}{\sqrt[3]{0.5}}} \]

   9. metadata-eval 44.0%

      \[\leadsto \frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \frac{{g}^{\color{blue}{0.16666666666666666}}}{\frac{1}{\sqrt[3]{0.5}}} \]

8. Applied egg-rr 44.0%

   \[\leadsto \color{blue}{\frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \frac{{g}^{0.16666666666666666}}{\frac{1}{\sqrt[3]{0.5}}}} \]
9. Step-by-step derivation

   1. associate-/r/ 44.0%

      \[\leadsto \frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \color{blue}{\left(\frac{{g}^{0.16666666666666666}}{1} \cdot \sqrt[3]{0.5}\right)} \]

   2. /-rgt-identity 44.0%

      \[\leadsto \frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot \left(\color{blue}{{g}^{0.16666666666666666}} \cdot \sqrt[3]{0.5}\right) \]

   3. associate-*r* 44.0%

      \[\leadsto \color{blue}{\left(\frac{{g}^{0.16666666666666666}}{\sqrt[3]{a}} \cdot {g}^{0.16666666666666666}\right) \cdot \sqrt[3]{0.5}} \]

   4. associate-*l/ 44.0%

      \[\leadsto \color{blue}{\frac{{g}^{0.16666666666666666} \cdot {g}^{0.16666666666666666}}{\sqrt[3]{a}}} \cdot \sqrt[3]{0.5} \]

   5. pow-sqr 44.0%

      \[\leadsto \frac{\color{blue}{{g}^{\left(2 \cdot 0.16666666666666666\right)}}}{\sqrt[3]{a}} \cdot \sqrt[3]{0.5} \]

   6. metadata-eval 44.0%

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

   7. unpow1/3 98.7%

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

10. Simplified 98.7%

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

    1. associate-*l/ 98.7%

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

    2. clear-num 98.6%

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

    3. cbrt-unprod 98.6%

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

12. Applied egg-rr 98.6%

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

13. Final simplification 98.6%

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

Alternative 4: 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 73.7%

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

   1. clear-num 72.6%

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

   2. associate-/r/ 73.7%

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

   3. cbrt-prod 98.2%

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

   4. associate-/r* 98.6%

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

   5. metadata-eval 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

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

Alternative 5: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

   1. associate-/r* 74.1%

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

   2. cbrt-div 98.6%

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

   3. div-inv 98.6%

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

   4. metadata-eval 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

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

Alternative 6: 75.8% 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 73.7%

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

   1. clear-num 72.6%

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

   2. associate-/r/ 73.7%

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

   3. associate-/r* 74.1%

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

   4. metadata-eval 74.1%

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

4. Applied egg-rr 74.1%

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

5. Final simplification 74.1%

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

Reproduce

herbie shell --seed 2024026 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))