2-ancestry mixing, zero discriminant

Percentage Accurate: 75.7% → 98.7%

Time: 46.0s

Alternatives: 8

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: 75.7% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g}}{{2}^{0.3333333333333333} \cdot \sqrt[3]{a}} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (/ (cbrt g) (* (pow 2.0 0.3333333333333333) (cbrt a))))

C

double code(double g, double a) {
	return cbrt(g) / (pow(2.0, 0.3333333333333333) * cbrt(a));
}

Java

public static double code(double g, double a) {
	return Math.cbrt(g) / (Math.pow(2.0, 0.3333333333333333) * Math.cbrt(a));
}

Julia

function code(g, a)
	return Float64(cbrt(g) / Float64((2.0 ^ 0.3333333333333333) * cbrt(a)))
end

Wolfram

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

Derivation

1. Initial program 77.2%

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

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.8

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

4. Applied rewrites 98.8%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. lift-+.f64 N/A

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

   4. count-2 N/A

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

   5. unpow-prod-down N/A

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

   6. pow1/3 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-pow.f64 N/A

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

   9. lower-cbrt.f64 98.9

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

6. Applied rewrites 98.9%

   \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{{2}^{0.3333333333333333} \cdot \sqrt[3]{a}}} \]
7. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.2%

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

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.8

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

4. Applied rewrites 98.8%

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

   1. lift-cbrt.f64 N/A

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

   2. pow1/3 N/A

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

   3. lift-+.f64 N/A

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

   4. count-2 N/A

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

   5. unpow-prod-down N/A

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

   6. pow1/3 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-pow.f64 N/A

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

   9. lower-cbrt.f64 98.9

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

6. Applied rewrites 98.9%

   \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{{2}^{0.3333333333333333} \cdot \sqrt[3]{a}}} \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. lift-pow.f64 N/A

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

   7. unpow1/3 N/A

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

   8. lift-cbrt.f64 N/A

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

   9. cbrt-div N/A

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

   10. lift-/.f64 N/A

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

   11. associate-/l/ N/A

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

   12. metadata-eval N/A

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

   13. lift-cbrt.f64 N/A

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

   14. cbrt-div N/A

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

   15. lift-/.f64 N/A

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

   16. cbrt-div N/A

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

   17. frac-2neg N/A

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

   18. cbrt-div N/A

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

   19. lower-/.f64 N/A

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

8. Applied rewrites 98.8%

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

Alternative 3: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{-298}:\\ \;\;\;\;\sqrt[3]{g \cdot \frac{0.5}{a}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(a + a\right)}^{-0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) 1e-298)
   (cbrt (* g (/ 0.5 a)))
   (* (cbrt g) (pow (+ a a) -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 1e-298) {
		tmp = cbrt((g * (0.5 / a)));
	} else {
		tmp = cbrt(g) * pow((a + a), -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 1e-298) {
		tmp = Math.cbrt((g * (0.5 / a)));
	} else {
		tmp = Math.cbrt(g) * Math.pow((a + a), -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= 1e-298)
		tmp = cbrt(Float64(g * Float64(0.5 / a)));
	else
		tmp = Float64(cbrt(g) * (Float64(a + a) ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], 1e-298], N[Power[N[(g * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], N[(N[Power[g, 1/3], $MachinePrecision] * N[Power[N[(a + a), $MachinePrecision], -0.3333333333333333], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < 9.99999999999999912e-299

   1. Initial program 78.2%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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. lift-*.f64 N/A

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

      5. count-2-rev N/A

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

      6. flip-+ N/A

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

      7. clear-num-rev N/A

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

      8. +-inverses N/A

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

      9. +-inverses N/A

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

      10. +-inverses N/A

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

      11. +-inverses N/A

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

      12. flip-+ N/A

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

      13. count-2-rev N/A

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

      14. lift-*.f64 N/A

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

      15. lower-*.f64 5.6

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

      16. lift-*.f64 N/A

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

      17. count-2-rev N/A

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

      18. lower-+.f64 5.6

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

   4. Applied rewrites 5.6%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. +-inverses N/A

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

      5. +-inverses N/A

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

      6. +-inverses N/A

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

      7. +-inverses N/A

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

      8. flip-+ N/A

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

      9. count-2 N/A

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

      10. metadata-eval N/A

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

      11. associate-/r/ N/A

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

      12. clear-num-rev N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 78.2

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

   6. Applied rewrites 78.2%

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

   if 9.99999999999999912e-299 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 76.2%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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. clear-num N/A

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

      4. associate-/r/ N/A

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

      5. cbrt-prod N/A

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

      6. lift-*.f64 N/A

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

      7. count-2-rev N/A

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

      8. flip-+ N/A

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

      9. clear-num-rev N/A

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

      10. +-inverses N/A

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

      11. +-inverses N/A

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

      12. +-inverses N/A

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

      13. +-inverses N/A

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

      14. flip-+ N/A

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

      15. count-2-rev N/A

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

      16. lift-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-cbrt.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. count-2-rev N/A

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

      21. lower-+.f64 N/A

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

      22. lower-cbrt.f64 6.3

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

   4. Applied rewrites 6.3%

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

      1. lift-cbrt.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. clear-num N/A

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

      5. +-inverses N/A

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

      6. +-inverses N/A

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

      7. +-inverses N/A

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

      8. +-inverses N/A

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

      9. flip-+ N/A

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

      10. count-2 N/A

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

      11. metadata-eval N/A

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

      12. associate-/r/ N/A

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

      13. clear-num-rev N/A

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

      14. cbrt-div N/A

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

      15. metadata-eval N/A

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

      16. clear-num-rev N/A

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

      17. associate-/r/ N/A

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

      18. metadata-eval N/A

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

      19. count-2 N/A

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

      20. lift-+.f64 N/A

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

      21. pow1/3 N/A

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

      22. pow-flip N/A

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

      23. metadata-eval N/A

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

      24. metadata-eval N/A

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

      25. lower-pow.f64 N/A

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

      26. metadata-eval 92.1

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

   6. Applied rewrites 92.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{-298}:\\ \;\;\;\;\sqrt[3]{g \cdot \frac{0.5}{a}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(a + a\right)}^{-0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (g a) :precision binary64 (/ (cbrt g) (cbrt (+ a a))))

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.2%

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

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

   7. lift-*.f64 N/A

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

   8. count-2-rev N/A

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

   9. lower-+.f64 98.8

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

4. Applied rewrites 98.8%

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

Alternative 5: 75.7% 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 77.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower-/.f64 77.2

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

4. Applied rewrites 77.2%

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

Alternative 6: 75.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. lift-*.f64 N/A

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

   5. count-2-rev N/A

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

   6. flip-+ N/A

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

   7. clear-num-rev N/A

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

   8. +-inverses N/A

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

   9. +-inverses N/A

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

   10. +-inverses N/A

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

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-*.f64 5.7

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

   16. lift-*.f64 N/A

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

   17. count-2-rev N/A

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

   18. lower-+.f64 5.7

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

4. Applied rewrites 5.7%

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

   1. lift-+.f64 N/A

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

   2. flip-+ N/A

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

   3. clear-num N/A

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

   4. +-inverses N/A

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

   5. +-inverses N/A

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

   6. +-inverses N/A

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

   7. +-inverses N/A

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

   8. flip-+ N/A

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

   9. count-2 N/A

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

   10. metadata-eval N/A

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

   11. associate-/r/ N/A

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

   12. clear-num-rev N/A

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

   13. clear-num N/A

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

   14. lift-/.f64 77.2

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

6. Applied rewrites 77.2%

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

7. Final simplification 77.2%

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

Alternative 7: 75.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (+ a a))))

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.2%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 77.2

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

4. Applied rewrites 77.2%

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

Alternative 8: 5.9% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (g a) :precision binary64 (cbrt (* g (+ a a))))

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. lift-*.f64 N/A

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

   5. count-2-rev N/A

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

   6. flip-+ N/A

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

   7. clear-num-rev N/A

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

   8. +-inverses N/A

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

   9. +-inverses N/A

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

   10. +-inverses N/A

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

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-*.f64 5.7

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

   16. lift-*.f64 N/A

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

   17. count-2-rev N/A

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

   18. lower-+.f64 5.7

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

4. Applied rewrites 5.7%

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

5. Final simplification 5.7%

   \[\leadsto \sqrt[3]{g \cdot \left(a + a\right)} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024278 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))