2-ancestry mixing, zero discriminant

Percentage Accurate: 76.0% → 98.6%

Time: 6.9s

Alternatives: 9

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, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 40.3

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

4. Applied rewrites 40.3%

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

   1. metadata-eval N/A

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

   2. pow-pow N/A

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

   3. inv-pow N/A

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

   4. pow1/3 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. 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 98.7

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

   2. /-rgt-identity N/A

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

   3. clear-num N/A

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

   4. lower-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-/r* N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 98.7

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

8. Applied rewrites 98.7%

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

10. Applied rewrites 98.8%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 40.3

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

4. Applied rewrites 40.3%

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

   1. metadata-eval N/A

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

   2. pow-pow N/A

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

   3. inv-pow N/A

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

   4. pow1/3 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. 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 98.7

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

   2. /-rgt-identity N/A

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

   3. clear-num N/A

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

   4. lower-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-/r* N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 98.7

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

8. Applied rewrites 98.7%

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

Alternative 3: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-308}:\\ \;\;\;\;\sqrt[3]{\frac{1}{a} \cdot \left(g \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g \cdot 0.5} \cdot {a}^{-0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* a 2.0) 4e-308)
   (cbrt (* (/ 1.0 a) (* g 0.5)))
   (* (cbrt (* g 0.5)) (pow a -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= 4e-308) {
		tmp = cbrt(((1.0 / a) * (g * 0.5)));
	} else {
		tmp = cbrt((g * 0.5)) * pow(a, -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= 4e-308) {
		tmp = Math.cbrt(((1.0 / a) * (g * 0.5)));
	} else {
		tmp = Math.cbrt((g * 0.5)) * Math.pow(a, -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 4e-308)
		tmp = cbrt(Float64(Float64(1.0 / a) * Float64(g * 0.5)));
	else
		tmp = Float64(cbrt(Float64(g * 0.5)) * (a ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 4e-308], N[Power[N[(N[(1.0 / a), $MachinePrecision] * N[(g * 0.5), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], N[(N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[a, -0.3333333333333333], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < 4.00000000000000013e-308

   1. Initial program 72.6%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 73.3

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

   4. Applied rewrites 73.3%

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

   if 4.00000000000000013e-308 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 73.5%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 92.1

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

   4. Applied rewrites 92.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-308}:\\ \;\;\;\;\sqrt[3]{\frac{1}{a} \cdot \left(g \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g \cdot 0.5} \cdot {a}^{-0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 40.3

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

4. Applied rewrites 40.3%

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

   1. metadata-eval N/A

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

   2. pow-pow N/A

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

   3. inv-pow N/A

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

   4. pow1/3 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. 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. Add Preprocessing

Alternative 5: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

   1. associate-/r* N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. div-inv N/A

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

   6. lower-*.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower-cbrt.f64 98.7

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

4. Applied rewrites 98.7%

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

Alternative 6: 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 73.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 40.3

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

4. Applied rewrites 40.3%

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

   1. metadata-eval N/A

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

   2. pow-pow N/A

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

   3. inv-pow N/A

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

   4. pow1/3 N/A

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

   5. lower-cbrt.f64 N/A

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

   6. 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 98.7

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

   2. /-rgt-identity N/A

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

   3. clear-num N/A

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

   4. lower-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-/r* N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 98.7

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

8. Applied rewrites 98.7%

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

   1. lift-/.f64 N/A

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

   2. associate-/r/ N/A

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

   3. metadata-eval N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. cbrt-prod N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. metadata-eval N/A

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

   10. associate-/r/ N/A

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

   11. lift-/.f64 N/A

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

   12. lift-/.f64 N/A

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

   13. lift-/.f64 N/A

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

   14. lift-/.f64 N/A

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

   15. associate-/r/ N/A

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

   16. metadata-eval N/A

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

   17. associate-*r* N/A

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

   18. cbrt-prod N/A

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

   19. lift-/.f64 N/A

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

   20. associate-*l/ N/A

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

   21. metadata-eval N/A

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

   22. pow1/3 N/A

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

10. Applied rewrites 98.7%

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

Alternative 7: 76.0% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

   1. associate-/r* N/A

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

   2. clear-num N/A

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

   3. associate-/r* N/A

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

   4. associate-/l/ N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 73.4

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

4. Applied rewrites 73.4%

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

Alternative 8: 76.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.0%

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

   1. associate-/r* N/A

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

   2. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lower-*.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. div-inv N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 73.4

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

4. Applied rewrites 73.4%

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

Alternative 9: 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 73.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 73.4

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

4. Applied rewrites 73.4%

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

5. Final simplification 73.4%

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

Reproduce

herbie shell --seed 2024216 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))