2-ancestry mixing, zero discriminant

Percentage Accurate: 75.8% → 98.7%

Time: 7.6s

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: 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: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

   1. pow1/3 33.0%

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

   2. associate-/r* 33.0%

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

   3. div-inv 33.0%

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

   4. unpow-prod-down 22.9%

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

   5. pow1/3 47.6%

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

   6. div-inv 47.6%

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

   7. metadata-eval 47.6%

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

4. Applied egg-rr 47.6%

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

Alternative 2: 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 73.0%

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

   1. pow1/3 33.0%

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

   2. clear-num 32.8%

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

   3. associate-/r/ 33.0%

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

   4. unpow-prod-down 22.9%

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

   5. pow1/3 45.8%

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

   6. associate-/r* 45.8%

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

   7. metadata-eval 45.8%

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

   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. Add Preprocessing

Alternative 3: 75.8% 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 73.0%

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

3. Final simplification 73.0%

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

Alternative 4: 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 73.0%

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

   1. clear-num 71.3%

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

   2. associate-/r/ 73.0%

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

   3. associate-/r* 73.0%

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

   4. metadata-eval 73.0%

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

4. Applied egg-rr 73.0%

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

5. Final simplification 73.0%

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

Alternative 5: 5.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{0.5 \cdot \left(g \cdot a\right)} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

   1. clear-num 71.3%

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

   2. associate-/r/ 73.0%

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

   3. associate-/r* 73.0%

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

   4. metadata-eval 73.0%

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

4. Applied egg-rr 73.0%

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

   1. associate-*l/ 73.0%

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

   2. *-commutative 73.0%

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

   3. div-inv 73.0%

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

   4. cbrt-unprod 98.7%

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

   5. *-commutative 98.7%

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

   6. cbrt-prod 98.6%

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

   7. associate-*r* 98.6%

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

   8. cbrt-div 98.6%

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

   9. metadata-eval 98.6%

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

6. Applied egg-rr 98.6%

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

   1. *-commutative 98.6%

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

   2. associate-*l/ 98.7%

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

   3. *-lft-identity 98.7%

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

8. Simplified 98.7%

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

   1. *-commutative 98.7%

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

   2. cbrt-undiv 73.0%

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

   3. cbrt-unprod 73.0%

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

   4. div-inv 73.0%

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

   5. add-exp-log 34.9%

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

   6. neg-log 34.9%

      \[\leadsto \sqrt[3]{\left(g \cdot e^{\color{blue}{-\log a}}\right) \cdot 0.5} \]

   7. add-sqr-sqrt 13.7%

      \[\leadsto \sqrt[3]{\left(g \cdot e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}}\right) \cdot 0.5} \]

   8. sqrt-unprod 15.6%

      \[\leadsto \sqrt[3]{\left(g \cdot e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}}\right) \cdot 0.5} \]

   9. sqr-neg 15.6%

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

   10. sqrt-unprod 1.7%

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

   11. add-sqr-sqrt 3.2%

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

   12. add-exp-log 5.8%

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

10. Applied egg-rr 5.8%

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

11. Final simplification 5.8%

    \[\leadsto \sqrt[3]{0.5 \cdot \left(g \cdot a\right)} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024132 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))