2-ancestry mixing, zero discriminant

Percentage Accurate: 75.6% → 98.7%

Time: 7.3s

Alternatives: 7

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: 75.6% 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 72.2%

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

   1. associate-/r* 72.2%

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

   2. cbrt-div 98.8%

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

   3. div-inv 98.8%

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

   4. metadata-eval 98.8%

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

4. Applied egg-rr 98.8%

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

   1. metadata-eval 98.8%

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

   2. div-inv 98.8%

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

   3. clear-num 98.7%

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

6. Applied egg-rr 98.7%

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

   1. cbrt-div 98.7%

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

   2. metadata-eval 98.7%

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

   3. associate-/r* 98.7%

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

   4. associate-/l/ 98.7%

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

   5. frac-2neg 98.7%

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

   6. distribute-frac-neg 98.7%

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

   7. add-cbrt-cube 98.6%

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

   8. un-div-inv 98.6%

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

   9. frac-times 98.6%

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

   10. metadata-eval 98.6%

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

   11. associate-/r* 98.5%

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

   12. add-cube-cbrt 98.8%

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

8. Applied egg-rr 98.8%

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

   1. distribute-frac-neg2 98.8%

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

   2. remove-double-neg 98.8%

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

10. Simplified 98.8%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

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(Float64(1.0 / cbrt(a)) * cbrt(Float64(g * 0.5)))
end

Wolfram

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

Derivation

1. Initial program 72.2%

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

   1. associate-/r* 72.2%

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

   2. cbrt-div 98.8%

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

   3. div-inv 98.8%

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

   4. metadata-eval 98.8%

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

4. Applied egg-rr 98.8%

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

   1. clear-num 98.7%

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

   2. associate-/r/ 98.8%

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

6. Applied egg-rr 98.8%

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

Alternative 3: 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 72.2%

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

   1. associate-/r* 72.2%

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

   2. cbrt-div 98.8%

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

   3. div-inv 98.8%

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

   4. metadata-eval 98.8%

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

4. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}}} \]
5. 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 72.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 98.7%

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

4. Applied egg-rr 98.7%

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

Alternative 5: 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 72.2%

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

   1. pow1/3 31.3%

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

   2. clear-num 30.8%

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

   3. associate-/r/ 31.3%

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

   4. unpow-prod-down 23.6%

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

   5. pow1/3 50.2%

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

   6. associate-/r* 50.2%

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

   7. metadata-eval 50.2%

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

   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%

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

Alternative 6: 75.6% 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 72.2%

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

   1. clear-num 70.7%

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

   2. associate-/r/ 72.2%

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

   3. associate-/r* 72.2%

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

   4. metadata-eval 72.2%

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

4. Applied egg-rr 72.2%

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

   1. associate-*l/ 72.2%

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

   2. *-commutative 72.2%

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

   3. clear-num 70.7%

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

   4. div-inv 70.6%

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

   5. *-commutative 70.6%

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

   6. associate-/r* 70.6%

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

   7. metadata-eval 70.6%

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

   8. associate-/r* 72.3%

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

6. Applied egg-rr 72.3%

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

Alternative 7: 75.6% 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 72.2%

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

   1. clear-num 70.7%

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

   2. associate-/r/ 72.2%

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

   3. associate-/r* 72.2%

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

   4. metadata-eval 72.2%

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

4. Applied egg-rr 72.2%

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

5. Final simplification 72.2%

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

Reproduce

herbie shell --seed 2024136 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))