2-ancestry mixing, zero discriminant

Percentage Accurate: 76.4% → 98.7%

Time: 6.5s

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: 76.4% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 74.3%

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

   1. pow1/3 40.2%

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

   2. clear-num 40.2%

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

   3. associate-/r/ 40.2%

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

   4. unpow-prod-down 27.1%

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

   5. pow1/3 46.4%

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

   6. associate-/r* 46.4%

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

   7. metadata-eval 46.4%

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

   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. Taylor expanded in a around 0 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 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 74.3%

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

   1. pow1/3 40.2%

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

   2. clear-num 40.2%

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

   3. associate-/r/ 40.2%

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

   4. unpow-prod-down 27.1%

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

   5. pow1/3 46.4%

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

   6. associate-/r* 46.4%

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

   7. metadata-eval 46.4%

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

   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 3: 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 74.3%

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

   1. clear-num 74.3%

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

   2. cbrt-div 75.6%

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

   3. metadata-eval 75.6%

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

   4. associate-/l* 75.6%

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

4. Applied egg-rr 75.6%

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

5. Final simplification 75.6%

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

Alternative 4: 76.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 74.3%

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

   1. clear-num 74.3%

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

   2. cbrt-div 75.6%

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

   3. metadata-eval 75.6%

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

   4. associate-/l* 75.6%

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

4. Applied egg-rr 75.6%

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

   1. associate-*r/ 75.6%

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

   2. *-commutative 75.6%

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

   3. associate-/l* 75.7%

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

6. Simplified 75.7%

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

7. Final simplification 75.7%

   \[\leadsto \frac{1}{\sqrt[3]{a \cdot \frac{2}{g}}} \]
8. 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 74.3%

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

   1. add-log-exp 7.3%

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

   2. *-un-lft-identity 7.3%

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

   3. log-prod 7.3%

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

   4. metadata-eval 7.3%

      \[\leadsto \color{blue}{0} + \log \left(e^{\sqrt[3]{\frac{g}{2 \cdot a}}}\right) \]

   5. add-log-exp 74.3%

      \[\leadsto 0 + \color{blue}{\sqrt[3]{\frac{g}{2 \cdot a}}} \]

   6. div-inv 74.3%

      \[\leadsto 0 + \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]

   7. associate-/r* 74.3%

      \[\leadsto 0 + \sqrt[3]{g \cdot \color{blue}{\frac{\frac{1}{2}}{a}}} \]

   8. metadata-eval 74.3%

      \[\leadsto 0 + \sqrt[3]{g \cdot \frac{\color{blue}{0.5}}{a}} \]

4. Applied egg-rr 74.3%

   \[\leadsto \color{blue}{0 + \sqrt[3]{g \cdot \frac{0.5}{a}}} \]
5. Step-by-step derivation

   1. +-lft-identity 74.3%

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

6. Simplified 74.3%

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

7. Final simplification 74.3%

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

Alternative 6: 76.4% 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 74.3%

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

3. Final simplification 74.3%

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

Reproduce

herbie shell --seed 2024115 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))