2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.6%

Time: 7.4s

Alternatives: 10

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: 76.1% 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

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.0%

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

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

   6. lower-/.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. div-inv N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. 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. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. div-inv N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. metadata-eval N/A

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

   9. div-inv N/A

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

   10. associate-/r/ N/A

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

   11. lift-/.f64 N/A

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

   12. frac-2neg N/A

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

   13. cbrt-div N/A

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

   14. div-inv N/A

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

   15. lower-*.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lower-neg.f64 N/A

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

   18. lower-/.f64 N/A

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

   19. lower-cbrt.f64 N/A

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

   20. lift-/.f64 N/A

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

   21. lift-/.f64 N/A

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

   22. associate-/r/ N/A

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

   23. metadata-eval N/A

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

   24. distribute-lft-neg-in N/A

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

6. Applied rewrites 98.8%

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

Alternative 2: 91.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\sqrt[3]{-g} \cdot {\left(a \cdot -2\right)}^{-0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(a \cdot 2\right)}^{-0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* a 2.0) -2e-301)
   (* (cbrt (- g)) (pow (* a -2.0) -0.3333333333333333))
   (* (cbrt g) (pow (* a 2.0) -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= -2e-301) {
		tmp = cbrt(-g) * pow((a * -2.0), -0.3333333333333333);
	} else {
		tmp = cbrt(g) * pow((a * 2.0), -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= -2e-301) {
		tmp = Math.cbrt(-g) * Math.pow((a * -2.0), -0.3333333333333333);
	} else {
		tmp = Math.cbrt(g) * Math.pow((a * 2.0), -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -2e-301)
		tmp = Float64(cbrt(Float64(-g)) * (Float64(a * -2.0) ^ -0.3333333333333333));
	else
		tmp = Float64(cbrt(g) * (Float64(a * 2.0) ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -2e-301], N[(N[Power[(-g), 1/3], $MachinePrecision] * N[Power[N[(a * -2.0), $MachinePrecision], -0.3333333333333333], $MachinePrecision]), $MachinePrecision], N[(N[Power[g, 1/3], $MachinePrecision] * N[Power[N[(a * 2.0), $MachinePrecision], -0.3333333333333333], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -2.00000000000000013e-301

   1. Initial program 76.5%

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

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

      6. lower-/.f64 N/A

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

      7. lower-cbrt.f64 N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. 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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-cbrt.f64 N/A

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

      3. lift-cbrt.f64 N/A

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

      4. cbrt-undiv N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. div-inv N/A

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

      10. associate-/r/ N/A

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

      11. lift-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. cbrt-div N/A

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

      14. div-inv N/A

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

      15. lower-*.f64 N/A

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

      16. lower-cbrt.f64 N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-/.f64 N/A

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

      19. lower-cbrt.f64 N/A

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

      20. lift-/.f64 N/A

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

      21. lift-/.f64 N/A

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

      22. associate-/r/ N/A

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

      23. metadata-eval N/A

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

      24. distribute-lft-neg-in N/A

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

   6. Applied rewrites 98.6%

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

      1. lift-/.f64 N/A

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

      2. lift-cbrt.f64 N/A

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

      3. pow1/3 N/A

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

      4. pow-flip N/A

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

      5. metadata-eval N/A

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

      6. lower-pow.f64 92.1

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

   8. Applied rewrites 92.1%

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

   if -2.00000000000000013e-301 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 75.7%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 90.9

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

   4. Applied rewrites 90.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\sqrt[3]{-g} \cdot {\left(a \cdot -2\right)}^{-0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{g} \cdot {\left(a \cdot 2\right)}^{-0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024229 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))