2-ancestry mixing, zero discriminant

Percentage Accurate: 74.8% → 98.7%

Time: 7.3s

Alternatives: 6

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: 74.8% 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: 98.7% 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 74.5%

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

   1. pow1/3 35.9%

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

   2. associate-/r* 35.9%

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

   3. div-inv 35.9%

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

   4. unpow-prod-down 24.4%

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

   5. pow1/3 49.3%

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

   6. div-inv 49.3%

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

   7. metadata-eval 49.3%

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

4. Applied egg-rr 49.3%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333}} \]
5. Step-by-step derivation

   1. unpow1/3 98.7%

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

6. Simplified 98.7%

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

   1. cbrt-prod 98.6%

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

   2. associate-*l* 98.6%

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

   3. cbrt-prod 98.6%

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

   4. div-inv 98.6%

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

   5. clear-num 98.6%

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

   6. cbrt-div 98.7%

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

   7. metadata-eval 98.7%

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

   8. div-inv 98.7%

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

   9. metadata-eval 98.7%

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

   10. div-inv 98.7%

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

   11. clear-num 98.6%

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

   12. div-inv 98.6%

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

   13. associate-/r* 98.7%

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

   14. metadata-eval 98.7%

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

   15. metadata-eval 98.7%

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

   16. div-inv 98.7%

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

   17. cbrt-div 98.7%

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

   18. clear-num 98.7%

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

8. Applied egg-rr 98.7%

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

9. Taylor expanded in g around 0 98.8%

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

10. Final simplification 98.8%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 74.5%

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

   1. pow1/3 35.9%

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

   2. associate-/r* 35.9%

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

   3. div-inv 35.9%

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

   4. unpow-prod-down 24.4%

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

   5. pow1/3 49.3%

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

   6. div-inv 49.3%

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

   7. metadata-eval 49.3%

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

4. Applied egg-rr 49.3%

   \[\leadsto \color{blue}{\sqrt[3]{g \cdot 0.5} \cdot {\left(\frac{1}{a}\right)}^{0.3333333333333333}} \]
5. Step-by-step derivation

   1. unpow1/3 98.7%

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

6. Simplified 98.7%

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

7. Final simplification 98.7%

   \[\leadsto \sqrt[3]{0.5 \cdot g} \cdot \sqrt[3]{\frac{1}{a}} \]
8. 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 74.5%

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

   1. pow1/3 35.9%

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

   2. clear-num 36.0%

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

   3. associate-/r/ 35.9%

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

   4. unpow-prod-down 24.4%

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

   5. pow1/3 46.5%

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

   6. associate-/r* 46.5%

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

   7. metadata-eval 46.5%

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

   8. pow1/3 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

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

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 74.5%

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

   1. cbrt-div 98.7%

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

   2. clear-num 98.6%

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

4. Applied egg-rr 98.6%

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

   1. associate-/r/ 98.7%

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

   2. associate-*l/ 98.7%

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

   3. *-lft-identity 98.7%

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

   4. *-commutative 98.7%

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

6. Simplified 98.7%

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

7. Final simplification 98.7%

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

Alternative 5: 74.8% 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 74.5%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 74.5%

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

   6. div-inv 74.4%

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

   7. associate-/r* 74.4%

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

   8. metadata-eval 74.4%

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

4. Applied egg-rr 74.4%

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

   1. +-lft-identity 74.4%

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

6. Simplified 74.4%

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

7. Final simplification 74.4%

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

Alternative 6: 74.8% 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 74.5%

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

3. Final simplification 74.5%

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

Reproduce

herbie shell --seed 2024071 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))