2-ancestry mixing, zero discriminant

Percentage Accurate: 76.0% → 98.6%

Time: 5.9s

Alternatives: 7

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: 76.0% 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: 98.6% 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 79.3%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. cbrt-div N/A

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

   4. lower-/.f64 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. lower-cbrt.f64 98.8

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

4. Applied rewrites 98.8%

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

Alternative 2: 91.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -5 \cdot 10^{-302}:\\ \;\;\;\;{\left(-a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(2 \cdot a\right)}^{-0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) -5e-302)
   (* (pow (- a) -0.3333333333333333) (cbrt (* g -0.5)))
   (* (cbrt g) (pow (* 2.0 a) -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -5e-302) {
		tmp = pow(-a, -0.3333333333333333) * cbrt((g * -0.5));
	} else {
		tmp = cbrt(g) * pow((2.0 * a), -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -5e-302) {
		tmp = Math.pow(-a, -0.3333333333333333) * Math.cbrt((g * -0.5));
	} else {
		tmp = Math.cbrt(g) * Math.pow((2.0 * a), -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= -5e-302)
		tmp = Float64((Float64(-a) ^ -0.3333333333333333) * cbrt(Float64(g * -0.5)));
	else
		tmp = Float64(cbrt(g) * (Float64(2.0 * a) ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], -5e-302], N[(N[Power[(-a), -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * -0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[g, 1/3], $MachinePrecision] * N[Power[N[(2.0 * a), $MachinePrecision], -0.3333333333333333], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -5.00000000000000033e-302

   1. Initial program 83.1%

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

      1. lift-cbrt.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. div-inv N/A

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

      6. cbrt-prod N/A

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

      7. pow1/3 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. metadata-eval N/A

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

      14. lower-cbrt.f64 N/A

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

      15. div-inv N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval 0.0

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

   4. Applied rewrites 0.0%

      \[\leadsto \color{blue}{{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

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

      2. metadata-eval N/A

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

      3. pow-pow N/A

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

      4. inv-pow N/A

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

      5. pow1/3 N/A

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

      6. lower-cbrt.f64 N/A

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

      7. lower-/.f64 98.7

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

   6. Applied rewrites 98.7%

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

      1. lift-*.f64 N/A

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

      2. lift-cbrt.f64 N/A

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

      3. lift-cbrt.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. div-inv N/A

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

      7. cbrt-prod N/A

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

      8. clear-num N/A

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

      9. lift-/.f64 N/A

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

      10. div-inv N/A

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

      11. frac-2neg N/A

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

      12. div-inv N/A

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

      13. cbrt-prod N/A

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

      14. pow1/3 N/A

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

      15. distribute-frac-neg2 N/A

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

      16. lift-/.f64 N/A

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

      17. clear-num N/A

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

      18. lower-*.f64 N/A

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

   8. Applied rewrites 92.2%

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

   if -5.00000000000000033e-302 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 75.3%

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

      1. lift-cbrt.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-inv N/A

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

      4. cbrt-prod N/A

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

      5. pow1/3 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. inv-pow N/A

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

      9. pow-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. metadata-eval N/A

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

      12. lower-cbrt.f64 92.0

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

   4. Applied rewrites 92.0%

      \[\leadsto \color{blue}{{\left(2 \cdot a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -5 \cdot 10^{-302}:\\ \;\;\;\;{\left(-a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(2 \cdot a\right)}^{-0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) 1e-305)
   (cbrt (/ g (* 2.0 a)))
   (* (cbrt g) (pow (* 2.0 a) -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 1e-305) {
		tmp = cbrt((g / (2.0 * a)));
	} else {
		tmp = cbrt(g) * pow((2.0 * a), -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 1e-305) {
		tmp = Math.cbrt((g / (2.0 * a)));
	} else {
		tmp = Math.cbrt(g) * Math.pow((2.0 * a), -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= 1e-305)
		tmp = cbrt(Float64(g / Float64(2.0 * a)));
	else
		tmp = Float64(cbrt(g) * (Float64(2.0 * a) ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < 9.99999999999999996e-306

   1. Initial program 83.2%

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

   if 9.99999999999999996e-306 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 75.1%

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

      1. lift-cbrt.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-inv N/A

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

      4. cbrt-prod N/A

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

      5. pow1/3 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. inv-pow N/A

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

      9. pow-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. metadata-eval N/A

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

      12. lower-cbrt.f64 92.1

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

   4. Applied rewrites 92.1%

      \[\leadsto \color{blue}{{\left(2 \cdot a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{-305}:\\ \;\;\;\;\sqrt[3]{\frac{g}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(2 \cdot a\right)}^{-0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) 1e-305)
   (cbrt (/ g (* 2.0 a)))
   (* (pow a -0.3333333333333333) (cbrt (* g 0.5)))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 1e-305) {
		tmp = cbrt((g / (2.0 * a)));
	} 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) <= 1e-305) {
		tmp = Math.cbrt((g / (2.0 * a)));
	} 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) <= 1e-305)
		tmp = cbrt(Float64(g / Float64(2.0 * a)));
	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], 1e-305], N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $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) < 9.99999999999999996e-306

   1. Initial program 83.2%

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

   if 9.99999999999999996e-306 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 75.1%

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

      1. lift-cbrt.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. div-inv N/A

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

      6. cbrt-prod N/A

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

      7. pow1/3 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. metadata-eval N/A

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

      14. lower-cbrt.f64 N/A

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

      15. div-inv N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval 92.0

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

   4. Applied rewrites 92.0%

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

Alternative 5: 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 79.3%

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

   1. lift-cbrt.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. div-inv N/A

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

   4. cbrt-prod N/A

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

   5. pow1/3 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. inv-pow N/A

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

   9. pow-pow N/A

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

   10. lower-pow.f64 N/A

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

   11. metadata-eval N/A

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

   12. lower-cbrt.f64 44.2

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

4. Applied rewrites 44.2%

   \[\leadsto \color{blue}{{\left(2 \cdot a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g}} \]
5. Step-by-step derivation

   1. lift-pow.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. metadata-eval N/A

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

   5. div-inv N/A

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

   6. metadata-eval N/A

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

   7. pow-pow N/A

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

   8. inv-pow N/A

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

   9. clear-num N/A

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

   10. pow1/3 N/A

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

   11. lower-cbrt.f64 N/A

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

   12. lower-/.f64 98.7

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

6. Applied rewrites 98.7%

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

7. Final simplification 98.7%

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

Alternative 6: 76.0% 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 79.3%

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

Alternative 7: 76.0% 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 79.3%

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

   1. lift-/.f64 N/A

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

   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 79.3

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

4. Applied rewrites 79.3%

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

5. Final simplification 79.3%

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

Reproduce

herbie shell --seed 2024232 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))