2-ancestry mixing, zero discriminant

Percentage Accurate: 75.8% → 98.7%

Time: 6.9s

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: 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

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

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 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. cbrt-prod 98.6%

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

   2. clear-num 98.2%

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

   3. cbrt-div 98.2%

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

   4. metadata-eval 98.2%

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

   5. div-inv 98.2%

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

   6. metadata-eval 98.2%

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

   7. *-commutative 98.2%

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

   8. associate-/r/ 98.2%

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

   9. div-inv 98.2%

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

   10. associate-/r* 98.2%

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

   11. metadata-eval 98.2%

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

   12. *-commutative 98.2%

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

   13. metadata-eval 98.2%

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

   14. div-inv 98.2%

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

   15. cbrt-div 98.2%

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

   16. clear-num 98.6%

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

6. Applied egg-rr 98.6%

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

   1. add-cbrt-cube 98.4%

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

   2. pow1/3 44.0%

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

   3. un-div-inv 44.0%

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

   4. frac-times 44.0%

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

   5. metadata-eval 44.0%

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

   6. associate-/r* 44.0%

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

   7. add-cube-cbrt 44.0%

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

8. Applied egg-rr 44.0%

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

   1. unpow1/3 98.7%

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

10. Simplified 98.7%

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

11. Final simplification 98.7%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[g_, a_] := N[(1.0 / N[(N[Power[a, 1/3], $MachinePrecision] / N[Power[N[(0.5 * g), $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. cbrt-div 98.3%

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

   2. clear-num 98.2%

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

4. Applied egg-rr 98.2%

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

   1. clear-num 98.3%

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

   2. div-inv 98.2%

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

   3. metadata-eval 98.2%

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

   4. *-commutative 98.2%

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

   5. metadata-eval 98.2%

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

   6. div-inv 98.2%

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

   7. cbrt-div 98.2%

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

   8. clear-num 98.5%

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

   9. cbrt-prod 73.9%

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

   10. associate-*r/ 74.0%

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

   11. cbrt-undiv 98.6%

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

   12. clear-num 98.6%

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

   13. div-inv 98.6%

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

6. Applied egg-rr 98.6%

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

   1. associate-*r/ 98.6%

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

   2. *-rgt-identity 98.6%

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

   3. *-commutative 98.6%

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

8. Simplified 98.6%

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

9. Final simplification 98.6%

   \[\leadsto \frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}} \]
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 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. clear-num 33.7%

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

   3. associate-/r/ 34.2%

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

   4. unpow-prod-down 22.5%

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

   5. pow1/3 43.6%

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

   6. associate-/r* 44.0%

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

   7. metadata-eval 44.0%

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

   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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[g_, a_] := N[(N[Power[N[(0.5 * g), $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%

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

Alternative 5: 75.8% 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 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%

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

Alternative 6: 75.9% accurate, 1.0× speedup

Math

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

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

3. Taylor expanded in g around 0 74.1%

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

   1. associate-*r/ 74.1%

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

5. Simplified 74.1%

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

6. Final simplification 74.1%

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

Reproduce

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