2-ancestry mixing, zero discriminant

Percentage Accurate: 76.1% → 98.7%

Time: 7.1s

Alternatives: 11

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: 98.7% 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 78.2%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. 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 98.8

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

4. Applied rewrites 98.8%

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

Alternative 2: 91.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{g}{a \cdot 2}\\ t_1 := \frac{1}{\frac{a}{\sqrt[3]{a \cdot \left(g \cdot \left(0.5 \cdot a\right)\right)}}}\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\sqrt[3]{\frac{\frac{g}{a}}{\frac{0.5}{a} \cdot \left(a \cdot 4\right)}}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-310}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{1}{\sqrt[3]{a \cdot \frac{2}{g}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (let* ((t_0 (/ g (* a 2.0))) (t_1 (/ 1.0 (/ a (cbrt (* a (* g (* 0.5 a))))))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -5e-306)
       (cbrt (/ (/ g a) (* (/ 0.5 a) (* a 4.0))))
       (if (<= t_0 2e-310)
         t_1
         (if (<= t_0 2e+302) (/ 1.0 (cbrt (* a (/ 2.0 g)))) t_1))))))

C

double code(double g, double a) {
	double t_0 = g / (a * 2.0);
	double t_1 = 1.0 / (a / cbrt((a * (g * (0.5 * a)))));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -5e-306) {
		tmp = cbrt(((g / a) / ((0.5 / a) * (a * 4.0))));
	} else if (t_0 <= 2e-310) {
		tmp = t_1;
	} else if (t_0 <= 2e+302) {
		tmp = 1.0 / cbrt((a * (2.0 / g)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double t_0 = g / (a * 2.0);
	double t_1 = 1.0 / (a / Math.cbrt((a * (g * (0.5 * a)))));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -5e-306) {
		tmp = Math.cbrt(((g / a) / ((0.5 / a) * (a * 4.0))));
	} else if (t_0 <= 2e-310) {
		tmp = t_1;
	} else if (t_0 <= 2e+302) {
		tmp = 1.0 / Math.cbrt((a * (2.0 / g)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(g, a)
	t_0 = Float64(g / Float64(a * 2.0))
	t_1 = Float64(1.0 / Float64(a / cbrt(Float64(a * Float64(g * Float64(0.5 * a))))))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -5e-306)
		tmp = cbrt(Float64(Float64(g / a) / Float64(Float64(0.5 / a) * Float64(a * 4.0))));
	elseif (t_0 <= 2e-310)
		tmp = t_1;
	elseif (t_0 <= 2e+302)
		tmp = Float64(1.0 / cbrt(Float64(a * Float64(2.0 / g))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[g_, a_] := Block[{t$95$0 = N[(g / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 / N[(a / N[Power[N[(a * N[(g * N[(0.5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -5e-306], N[Power[N[(N[(g / a), $MachinePrecision] / N[(N[(0.5 / a), $MachinePrecision] * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], If[LessEqual[t$95$0, 2e-310], t$95$1, If[LessEqual[t$95$0, 2e+302], N[(1.0 / N[Power[N[(a * N[(2.0 / g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 g (*.f64 #s(literal 2 binary64) a)) < -inf.0 or -4.99999999999999998e-306 < (/.f64 g (*.f64 #s(literal 2 binary64) a)) < 1.999999999999994e-310 or 2.0000000000000002e302 < (/.f64 g (*.f64 #s(literal 2 binary64) a))

   1. Initial program 7.7%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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. 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 98.6

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

   4. Applied rewrites 98.6%

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

   6. Applied rewrites 98.4%

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

   8. Applied rewrites 27.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{\sqrt[3]{g \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)}}}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 68.5

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

   10. Applied rewrites 68.5%

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

   if -inf.0 < (/.f64 g (*.f64 #s(literal 2 binary64) a)) < -4.99999999999999998e-306

   1. Initial program 99.1%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 99.1

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. *-inverses N/A

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

      8. times-frac N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. times-frac N/A

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

      13. associate-/r* N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. lift-/.f64 N/A

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

      17. associate-*r/ N/A

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

      18. lift-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. associate-/r/ N/A

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

      21. lift-/.f64 N/A

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

      22. frac-times N/A

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

      23. *-lft-identity N/A

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

      24. lower-/.f64 N/A

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

      25. lower-*.f64 N/A

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

      26. lower-*.f64 99.0

          \[\leadsto \sqrt[3]{\frac{\frac{g}{a}}{\frac{0.5}{a} \cdot \color{blue}{\left(a \cdot 4\right)}}} \]

   6. Applied rewrites 99.0%

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{g}{a}}{\frac{0.5}{a} \cdot \left(a \cdot 4\right)}}} \]

   if 1.999999999999994e-310 < (/.f64 g (*.f64 #s(literal 2 binary64) a)) < 2.0000000000000002e302

   1. Initial program 99.1%

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

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

   6. Applied rewrites 98.7%

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

   8. Applied rewrites 42.3%

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

   10. Applied rewrites 98.9%

       \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{\frac{2}{g} \cdot a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{g}{a \cdot 2} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{a}{\sqrt[3]{a \cdot \left(g \cdot \left(0.5 \cdot a\right)\right)}}}\\ \mathbf{elif}\;\frac{g}{a \cdot 2} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\sqrt[3]{\frac{\frac{g}{a}}{\frac{0.5}{a} \cdot \left(a \cdot 4\right)}}\\ \mathbf{elif}\;\frac{g}{a \cdot 2} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;\frac{1}{\frac{a}{\sqrt[3]{a \cdot \left(g \cdot \left(0.5 \cdot a\right)\right)}}}\\ \mathbf{elif}\;\frac{g}{a \cdot 2} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{1}{\sqrt[3]{a \cdot \frac{2}{g}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\sqrt[3]{a \cdot \left(g \cdot \left(0.5 \cdot a\right)\right)}}}\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024226 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))