2-ancestry mixing, zero discriminant

Percentage Accurate: 76.4% → 98.7%

Time: 7.1s

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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

   1. lift-*.f64 N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-cbrt.f64 98.8

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

4. Applied egg-rr 98.8%

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

   1. metadata-eval N/A

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

   2. associate-/r/ N/A

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

   3. div-inv N/A

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

   4. associate-/r* N/A

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

   5. metadata-eval N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 98.8

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

6. Applied egg-rr 98.8%

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

Alternative 2: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -2 \cdot 10^{-305}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{a}{g \cdot 0.5}}}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) -2e-305)
   (/ 1.0 (cbrt (/ a (* g 0.5))))
   (* (pow a -0.3333333333333333) (cbrt (* g 0.5)))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-305) {
		tmp = 1.0 / cbrt((a / (g * 0.5)));
	} else {
		tmp = pow(a, -0.3333333333333333) * cbrt((g * 0.5));
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-305) {
		tmp = 1.0 / Math.cbrt((a / (g * 0.5)));
	} else {
		tmp = Math.pow(a, -0.3333333333333333) * Math.cbrt((g * 0.5));
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= -2e-305)
		tmp = Float64(1.0 / cbrt(Float64(a / Float64(g * 0.5))));
	else
		tmp = Float64((a ^ -0.3333333333333333) * cbrt(Float64(g * 0.5)));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], -2e-305], N[(1.0 / N[Power[N[(a / N[(g * 0.5), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[a, -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -1.99999999999999999e-305

   1. Initial program 81.1%

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

      1. lift-*.f64 N/A

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

      2. clear-num N/A

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

      3. cbrt-div N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. lower-cbrt.f64 N/A

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

      7. clear-num N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/r* N/A

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

      10. clear-num N/A

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

      11. lower-/.f64 N/A

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

      12. div-inv N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 81.2

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

   4. Applied egg-rr 81.2%

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

   if -1.99999999999999999e-305 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 82.3%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. cbrt-prod N/A

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

      4. pow1/3 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. inv-pow N/A

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

      8. pow-pow N/A

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

      9. lower-pow.f64 N/A

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

      10. metadata-eval N/A

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

      11. lower-cbrt.f64 N/A

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

      12. div-inv N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 92.3

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

   4. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

   1. lift-*.f64 N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-cbrt.f64 98.8

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

4. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \]
5. 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 81.7%

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

   1. lift-*.f64 N/A

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

   2. div-inv N/A

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

   3. inv-pow N/A

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

   4. sqr-pow N/A

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

   5. sqr-pow N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval N/A

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

   9. pow-pow N/A

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

   10. pow2 N/A

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

   11. remove-double-neg N/A

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

   12. remove-double-neg N/A

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

   13. sqr-neg N/A

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

   14. pow-prod-down N/A

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

   15. pow-prod-up N/A

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

   16. metadata-eval N/A

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

   17. metadata-eval N/A

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

   18. metadata-eval N/A

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

   19. metadata-eval N/A

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

   20. metadata-eval N/A

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

   21. inv-pow N/A

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

4. Applied egg-rr 44.3%

   \[\leadsto \sqrt[3]{\color{blue}{\frac{g}{\left(a \cdot a\right) \cdot 4} \cdot \left(2 \cdot a\right)}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \sqrt[3]{\frac{g}{\color{blue}{\left(a \cdot a\right)} \cdot 4} \cdot \left(2 \cdot a\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \sqrt[3]{\frac{g}{\color{blue}{\left(a \cdot a\right) \cdot 4}} \cdot \left(2 \cdot a\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \sqrt[3]{\frac{g}{\left(a \cdot a\right) \cdot 4} \cdot \color{blue}{\left(2 \cdot a\right)}} \]

   4. associate-*l/ N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{g \cdot \left(2 \cdot a\right)}{\left(a \cdot a\right) \cdot 4}}} \]

   5. associate-/l* N/A

      \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4}}} \]

   6. *-commutative N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4} \cdot g}} \]

   7. associate-/r/ N/A

      \[\leadsto \sqrt[3]{\color{blue}{\frac{2 \cdot a}{\frac{\left(a \cdot a\right) \cdot 4}{g}}}} \]

   8. un-div-inv N/A

      \[\leadsto \sqrt[3]{\color{blue}{\left(2 \cdot a\right) \cdot \frac{1}{\frac{\left(a \cdot a\right) \cdot 4}{g}}}} \]

   9. clear-num N/A

      \[\leadsto \sqrt[3]{\left(2 \cdot a\right) \cdot \color{blue}{\frac{g}{\left(a \cdot a\right) \cdot 4}}} \]

   10. lift-/.f64 N/A

       \[\leadsto \sqrt[3]{\left(2 \cdot a\right) \cdot \color{blue}{\frac{g}{\left(a \cdot a\right) \cdot 4}}} \]

   11. *-commutative N/A

       \[\leadsto \sqrt[3]{\color{blue}{\frac{g}{\left(a \cdot a\right) \cdot 4} \cdot \left(2 \cdot a\right)}} \]

   12. lift-/.f64 N/A

       \[\leadsto \sqrt[3]{\color{blue}{\frac{g}{\left(a \cdot a\right) \cdot 4}} \cdot \left(2 \cdot a\right)} \]

   13. associate-*l/ N/A

       \[\leadsto \sqrt[3]{\color{blue}{\frac{g \cdot \left(2 \cdot a\right)}{\left(a \cdot a\right) \cdot 4}}} \]

   14. associate-/l* N/A

       \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4}}} \]

   15. cbrt-prod N/A

       \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4}}} \]

   16. lift-cbrt.f64 N/A

       \[\leadsto \color{blue}{\sqrt[3]{g}} \cdot \sqrt[3]{\frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4}} \]

   17. lower-*.f64 N/A

       \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{2 \cdot a}{\left(a \cdot a\right) \cdot 4}}} \]

6. Applied egg-rr 57.4%

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

   1. lift-*.f64 N/A

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

   2. associate-*r/ N/A

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

   3. lift-*.f64 N/A

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

   4. times-frac N/A

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

   5. *-inverses N/A

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

   6. lift-/.f64 N/A

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

   7. *-rgt-identity 98.7

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

8. Applied egg-rr 98.7%

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

Alternative 5: 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]

Derivation

1. Initial program 81.7%

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

Alternative 6: 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 81.7%

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

   1. lift-*.f64 N/A

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

   2. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lower-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. metadata-eval 81.7

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

4. Applied egg-rr 81.7%

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

5. Final simplification 81.7%

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

Reproduce

herbie shell --seed 2024207 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))