2-ancestry mixing, zero discriminant

Percentage Accurate: 76.5% → 98.6%

Time: 7.3s

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: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g \cdot 2}}{\sqrt[3]{a \cdot 4}} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ (cbrt (* g 2.0)) (cbrt (* a 4.0))))

C

double code(double g, double a) {
	return cbrt((g * 2.0)) / cbrt((a * 4.0));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g * 2.0)) / Math.cbrt((a * 4.0));
}

Julia

function code(g, a)
	return Float64(cbrt(Float64(g * 2.0)) / cbrt(Float64(a * 4.0)))
end

Wolfram

code[g_, a_] := N[(N[Power[N[(g * 2.0), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[N[(a * 4.0), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.0%

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

   1. lift-*.f64 N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-cbrt.f64 98.7

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

4. Applied egg-rr 98.7%

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

6. Applied egg-rr 98.8%

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

Alternative 2: 92.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\sqrt[3]{-g} \cdot {\left(a \cdot -2\right)}^{-0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) -2e-307)
   (* (cbrt (- g)) (pow (* a -2.0) -0.3333333333333333))
   (* (pow a -0.3333333333333333) (cbrt (* g 0.5)))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-307) {
		tmp = cbrt(-g) * pow((a * -2.0), -0.3333333333333333);
	} else {
		tmp = pow(a, -0.3333333333333333) * cbrt((g * 0.5));
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-307) {
		tmp = Math.cbrt(-g) * Math.pow((a * -2.0), -0.3333333333333333);
	} else {
		tmp = Math.pow(a, -0.3333333333333333) * Math.cbrt((g * 0.5));
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= -2e-307)
		tmp = Float64(cbrt(Float64(-g)) * (Float64(a * -2.0) ^ -0.3333333333333333));
	else
		tmp = Float64((a ^ -0.3333333333333333) * cbrt(Float64(g * 0.5)));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], -2e-307], N[(N[Power[(-g), 1/3], $MachinePrecision] * N[Power[N[(a * -2.0), $MachinePrecision], -0.3333333333333333], $MachinePrecision]), $MachinePrecision], N[(N[Power[a, -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -1.99999999999999982e-307

   1. Initial program 72.8%

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

      1. lift-*.f64 N/A

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

      2. cbrt-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower-cbrt.f64 N/A

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

      5. lower-cbrt.f64 98.8

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

   4. Applied egg-rr 98.8%

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

   6. Applied egg-rr 98.7%

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

      1. lift-neg.f64 N/A

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

      2. lift-cbrt.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-cbrt.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 98.7

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

      7. lift-cbrt.f64 N/A

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

      8. pow1/3 N/A

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

      9. lift-/.f64 N/A

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

      10. clear-num N/A

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

      11. inv-pow N/A

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

      12. pow-pow N/A

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

      13. metadata-eval N/A

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

      14. lower-pow.f64 N/A

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

      15. div-inv N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 92.3

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

   8. Applied egg-rr 92.3%

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

   if -1.99999999999999982e-307 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 77.0%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 92.2

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

   4. Applied egg-rr 92.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\sqrt[3]{-g} \cdot {\left(a \cdot -2\right)}^{-0.3333333333333333}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq -2 \cdot 10^{-307}:\\ \;\;\;\;{\left(-a\right)}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) -2e-307)
   (* (pow (- a) -0.3333333333333333) (cbrt (* g -0.5)))
   (* (pow a -0.3333333333333333) (cbrt (* g 0.5)))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-307) {
		tmp = pow(-a, -0.3333333333333333) * cbrt((g * -0.5));
	} else {
		tmp = pow(a, -0.3333333333333333) * cbrt((g * 0.5));
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= -2e-307) {
		tmp = Math.pow(-a, -0.3333333333333333) * Math.cbrt((g * -0.5));
	} else {
		tmp = Math.pow(a, -0.3333333333333333) * Math.cbrt((g * 0.5));
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= -2e-307)
		tmp = Float64((Float64(-a) ^ -0.3333333333333333) * cbrt(Float64(g * -0.5)));
	else
		tmp = Float64((a ^ -0.3333333333333333) * cbrt(Float64(g * 0.5)));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], -2e-307], N[(N[Power[(-a), -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * -0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[a, -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -1.99999999999999982e-307

   1. Initial program 72.8%

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

      1. lift-*.f64 N/A

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

      2. cbrt-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower-cbrt.f64 N/A

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

      5. lower-cbrt.f64 98.8

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

   4. Applied egg-rr 98.8%

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

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{g \cdot 2}}{\sqrt[3]{a \cdot 4}}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. cbrt-undiv N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*l/ N/A

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

      9. lift-*.f64 N/A

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

      10. div-inv N/A

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

      11. cbrt-prod N/A

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

      12. pow1/3 N/A

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

      13. metadata-eval N/A

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

      14. pow-pow N/A

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

      15. inv-pow N/A

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

      16. pow1/3 N/A

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

      17. inv-pow N/A

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

      18. pow-pow N/A

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

      19. metadata-eval N/A

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

      20. unpow-prod-down N/A

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

      21. associate-/r/ N/A

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

      22. clear-num N/A

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

      23. frac-2neg N/A

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

      24. div-inv N/A

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

   8. Applied egg-rr 92.3%

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

   if -1.99999999999999982e-307 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 77.0%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 92.2

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

   4. Applied egg-rr 92.2%

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

Alternative 4: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 3 \cdot 10^{-292}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{a}{g \cdot 0.5}}}\\ \mathbf{else}:\\ \;\;\;\;{a}^{-0.3333333333333333} \cdot \sqrt[3]{g \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* 2.0 a) 3e-292)
   (/ 1.0 (cbrt (/ a (* g 0.5))))
   (* (pow a -0.3333333333333333) (cbrt (* g 0.5)))))

C

double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 3e-292) {
		tmp = 1.0 / cbrt((a / (g * 0.5)));
	} else {
		tmp = pow(a, -0.3333333333333333) * cbrt((g * 0.5));
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((2.0 * a) <= 3e-292) {
		tmp = 1.0 / Math.cbrt((a / (g * 0.5)));
	} else {
		tmp = Math.pow(a, -0.3333333333333333) * Math.cbrt((g * 0.5));
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= 3e-292)
		tmp = Float64(1.0 / cbrt(Float64(a / Float64(g * 0.5))));
	else
		tmp = Float64((a ^ -0.3333333333333333) * cbrt(Float64(g * 0.5)));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(2.0 * a), $MachinePrecision], 3e-292], N[(1.0 / N[Power[N[(a / N[(g * 0.5), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[a, -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < 3.00000000000000015e-292

   1. Initial program 73.7%

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

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. lower-cbrt.f64 N/A

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

      7. clear-num N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/r* N/A

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

      10. clear-num N/A

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

      11. lower-/.f64 N/A

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

      12. div-inv N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 74.7

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

   4. Applied egg-rr 74.7%

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

   if 3.00000000000000015e-292 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 76.3%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 92.3

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

   4. Applied egg-rr 92.3%

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

Alternative 5: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.0%

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

   1. lift-*.f64 N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-cbrt.f64 98.7

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

4. Applied egg-rr 98.7%

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

6. Applied egg-rr 98.8%

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

Alternative 6: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.0%

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

   1. lift-*.f64 N/A

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

   2. cbrt-div N/A

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

   3. lower-/.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-cbrt.f64 98.7

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

4. Applied egg-rr 98.7%

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

Alternative 7: 76.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.0%

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

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

   4. metadata-eval N/A

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

   5. lower-/.f64 N/A

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

   6. lower-cbrt.f64 N/A

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

   7. clear-num N/A

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

   8. lift-*.f64 N/A

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

   9. associate-/r* N/A

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

   10. clear-num N/A

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

   11. lower-/.f64 N/A

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

   12. div-inv N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval 75.7

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

4. Applied egg-rr 75.7%

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

Alternative 8: 75.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.0%

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

   1. associate-/l/ N/A

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

   2. clear-num N/A

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

   3. associate-/l/ N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. metadata-eval N/A

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

   7. lower-/.f64 75.0

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

4. Applied egg-rr 75.0%

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

Alternative 9: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.0%

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

Alternative 10: 76.5% 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 75.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 75.0

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

4. Applied egg-rr 75.0%

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

5. Final simplification 75.0%

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

Reproduce

herbie shell --seed 2024212 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))