2-ancestry mixing, zero discriminant

Percentage Accurate: 75.3% → 98.7%

Time: 6.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Initial Program: 75.3% 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 77.8%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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: 92.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (g a)
 :precision binary64
 (if (<= (* a 2.0) -5e-307)
   (* (pow (- a) -0.3333333333333333) (cbrt (* g -0.5)))
   (* (cbrt (* g 0.5)) (pow a -0.3333333333333333))))

C

double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= -5e-307) {
		tmp = pow(-a, -0.3333333333333333) * cbrt((g * -0.5));
	} else {
		tmp = cbrt((g * 0.5)) * pow(a, -0.3333333333333333);
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double tmp;
	if ((a * 2.0) <= -5e-307) {
		tmp = Math.pow(-a, -0.3333333333333333) * Math.cbrt((g * -0.5));
	} else {
		tmp = Math.cbrt((g * 0.5)) * Math.pow(a, -0.3333333333333333);
	}
	return tmp;
}

Julia

function code(g, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -5e-307)
		tmp = Float64((Float64(-a) ^ -0.3333333333333333) * cbrt(Float64(g * -0.5)));
	else
		tmp = Float64(cbrt(Float64(g * 0.5)) * (a ^ -0.3333333333333333));
	end
	return tmp
end

Wolfram

code[g_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -5e-307], N[(N[Power[(-a), -0.3333333333333333], $MachinePrecision] * N[Power[N[(g * -0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[a, -0.3333333333333333], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) a) < -5.00000000000000014e-307

   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. 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. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. associate-/r* N/A

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

      9. lift-*.f64 N/A

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

      10. un-div-inv N/A

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

      11. cbrt-div N/A

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

      12. pow1/3 N/A

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

      13. pow1/3 N/A

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

      14. lower-/.f64 N/A

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

      15. pow1/3 N/A

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

      16. lower-cbrt.f64 N/A

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

      17. pow1/3 N/A

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

      18. lower-cbrt.f64 98.7

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 98.7

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

   6. Applied rewrites 98.7%

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

      1. lift-/.f64 N/A

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

      2. lift-cbrt.f64 N/A

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

      3. lift-cbrt.f64 N/A

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

      4. cbrt-undiv N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l/ N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. lift-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. div-inv N/A

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

      12. distribute-neg-frac2 N/A

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

      13. lift-/.f64 N/A

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

      14. *-commutative N/A

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

      15. cbrt-prod N/A

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

      16. pow1/3 N/A

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

      17. lower-*.f64 N/A

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

   8. Applied rewrites 92.1%

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

   if -5.00000000000000014e-307 < (*.f64 #s(literal 2 binary64) a)

   1. Initial program 74.9%

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

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

      6. cbrt-prod N/A

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

      7. pow1/3 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. metadata-eval N/A

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

      14. lower-cbrt.f64 N/A

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

      15. div-inv N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval 91.9

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

   4. Applied rewrites 91.9%

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

4. Final simplification 92.0%

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

Reproduce

herbie shell --seed 2024228 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))