2-ancestry mixing, zero discriminant

Percentage Accurate: 76.3% → 98.7%

Time: 6.8s

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: 76.3% 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, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.4%

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

3. Taylor expanded in g around 0 73.4%

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

   1. pow1/3 39.4%

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

   2. div-inv 39.4%

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

   3. unpow-prod-down 26.6%

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

   4. pow1/3 48.3%

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

5. Applied egg-rr 48.3%

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

   1. unpow1/3 98.7%

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

   2. *-commutative 98.7%

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

7. Simplified 98.7%

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

Alternative 2: 98.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.4%

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

   1. pow1/3 39.8%

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

   2. clear-num 39.0%

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

   3. associate-/r/ 39.8%

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

   4. unpow-prod-down 26.6%

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

   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 98.7%

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

4. Applied egg-rr 98.7%

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

   1. *-commutative 98.7%

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

   2. cbrt-div 98.7%

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

   3. associate-*r/ 98.7%

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

6. Applied egg-rr 98.7%

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

Alternative 3: 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 73.4%

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

   1. cbrt-div 98.4%

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

   2. clear-num 98.4%

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

4. Applied egg-rr 98.4%

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

   1. associate-/r/ 98.3%

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

   2. associate-*l/ 98.4%

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

   3. *-lft-identity 98.4%

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

   4. *-commutative 98.4%

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

6. Simplified 98.4%

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

   1. cbrt-undiv 73.4%

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

   2. metadata-eval 73.4%

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

   3. div-inv 73.4%

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

   4. add-cube-cbrt 73.3%

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

   5. cbrt-undiv 73.2%

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

   6. cbrt-undiv 73.2%

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

   7. cbrt-undiv 73.0%

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

   8. cbrt-undiv 98.1%

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

   9. *-un-lft-identity 98.1%

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

   10. add-cbrt-cube 98.7%

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

   11. div-inv 98.4%

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

   12. times-frac 98.5%

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

8. Applied egg-rr 98.5%

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

   1. associate-*r/ 98.5%

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

   2. associate-*l/ 98.5%

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

   3. *-lft-identity 98.5%

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

   4. associate-/l/ 98.4%

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

   5. associate-*l/ 98.7%

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

   6. *-lft-identity 98.7%

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

10. Simplified 98.7%

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5}}}} \]
11. 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 73.4%

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

   1. pow1/3 39.8%

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

   2. clear-num 39.0%

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

   3. associate-/r/ 39.8%

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

   4. unpow-prod-down 26.6%

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

   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 98.7%

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

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 5: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt[3]{2 \cdot \frac{a}{g}}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ 1.0 (cbrt (* 2.0 (/ a g)))))

C

double code(double g, double a) {
	return 1.0 / cbrt((2.0 * (a / g)));
}

Java

public static double code(double g, double a) {
	return 1.0 / Math.cbrt((2.0 * (a / g)));
}

Julia

function code(g, a)
	return Float64(1.0 / cbrt(Float64(2.0 * Float64(a / g))))
end

Wolfram

code[g_, a_] := N[(1.0 / N[Power[N[(2.0 * N[(a / g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.4%

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

   1. clear-num 72.4%

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

   2. cbrt-div 73.5%

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

   3. metadata-eval 73.5%

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

   4. associate-/l* 73.9%

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

4. Applied egg-rr 73.9%

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

Alternative 6: 76.3% 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 73.4%

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

   1. clear-num 72.4%

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

   2. associate-/r/ 73.5%

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

   3. associate-/r* 73.8%

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

   4. metadata-eval 73.8%

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

4. Applied egg-rr 73.8%

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

5. Final simplification 73.8%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))