2-ancestry mixing, zero discriminant

Percentage Accurate: 76.3% → 98.7%

Time: 6.4s

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, 0.5× 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 77.0%

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

   1. clear-num 76.6%

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

   2. associate-/r/ 77.0%

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

   3. associate-/r* 77.4%

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

   4. metadata-eval 77.4%

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

4. Applied egg-rr 77.4%

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

   1. associate-*l/ 77.4%

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

   2. cbrt-div 98.7%

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

   3. *-un-lft-identity 98.7%

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

   4. associate-*l/ 98.7%

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

6. Applied egg-rr 98.7%

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

   1. associate-*l/ 98.7%

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

   2. associate-/l* 98.8%

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

8. Applied egg-rr 98.8%

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

9. Final simplification 98.8%

   \[\leadsto \frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}} \]
10. 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 77.0%

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

   1. pow1/3 41.2%

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

   2. associate-/r* 41.2%

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

   3. div-inv 41.2%

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

   4. unpow-prod-down 27.9%

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

   5. pow1/3 45.0%

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

   6. div-inv 45.0%

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

   7. metadata-eval 45.0%

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

4. Applied egg-rr 45.0%

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

   1. *-commutative 45.0%

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

   2. unpow1/3 98.7%

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

6. Simplified 98.7%

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

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 77.0%

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

   1. pow1/3 41.2%

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

   2. clear-num 40.7%

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

   3. associate-/r/ 41.2%

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

   4. unpow-prod-down 28.0%

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

   5. pow1/3 51.8%

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

   6. associate-/r* 52.2%

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

   7. metadata-eval 52.2%

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

   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%

   \[\leadsto \sqrt[3]{\frac{0.5}{a}} \cdot \sqrt[3]{g} \]
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 77.0%

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

   1. associate-/r* 77.4%

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

   2. cbrt-div 98.7%

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

   3. div-inv 98.7%

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

   4. metadata-eval 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 5: 76.4% 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 77.0%

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

   1. clear-num 76.6%

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

   2. associate-/r/ 77.0%

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

   3. associate-/r* 77.4%

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

   4. metadata-eval 77.4%

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

4. Applied egg-rr 77.4%

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

5. Final simplification 77.4%

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

Alternative 6: 76.4% 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 77.0%

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

3. Taylor expanded in g around 0 77.4%

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

   1. associate-*r/ 77.4%

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

5. Simplified 77.4%

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

6. Final simplification 77.4%

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

Reproduce

herbie shell --seed 2024027 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))