2-ancestry mixing, zero discriminant

Percentage Accurate: 76.8% → 98.7%

Time: 4.6s

Alternatives: 6

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: 76.8% 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

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(g\_s \cdot \left(\left|\sqrt[3]{0.5 \cdot g\_m}\right| \cdot \sqrt[3]{\left|\frac{1}{a\_m}\right|}\right)\right) \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (* a_s (* g_s (* (fabs (cbrt (* 0.5 g_m))) (cbrt (fabs (/ 1.0 a_m)))))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (fabs(cbrt((0.5 * g_m))) * cbrt(fabs((1.0 / a_m)))));
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (Math.abs(Math.cbrt((0.5 * g_m))) * Math.cbrt(Math.abs((1.0 / a_m)))));
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	return Float64(a_s * Float64(g_s * Float64(abs(cbrt(Float64(0.5 * g_m))) * cbrt(abs(Float64(1.0 / a_m))))))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := N[(a$95$s * N[(g$95$s * N[(N[Abs[N[Power[N[(0.5 * g$95$m), $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision] * N[Power[N[Abs[N[(1.0 / a$95$m), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. 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 98.7

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

   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 98.7

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

3. Applied rewrites 98.7%

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

5. Applied rewrites 98.7%

   \[\leadsto \color{blue}{\left|\sqrt[3]{0.5 \cdot g}\right| \cdot \sqrt[3]{\left|\frac{1}{a}\right|}} \]
6. Add Preprocessing

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(g\_s \cdot \frac{1}{\frac{\sqrt[3]{a\_m + a\_m}}{\sqrt[3]{g\_m}}}\right) \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (* a_s (* g_s (/ 1.0 (/ (cbrt (+ a_m a_m)) (cbrt g_m))))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (1.0 / (cbrt((a_m + a_m)) / cbrt(g_m))));
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (1.0 / (Math.cbrt((a_m + a_m)) / Math.cbrt(g_m))));
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	return Float64(a_s * Float64(g_s * Float64(1.0 / Float64(cbrt(Float64(a_m + a_m)) / cbrt(g_m)))))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := N[(a$95$s * N[(g$95$s * N[(1.0 / N[(N[Power[N[(a$95$m + a$95$m), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[g$95$m, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

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

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

   5. lower-unsound-/.f64 N/A

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

   6. lower-unsound-/.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. count-2-rev N/A

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

   10. lower-+.f64 N/A

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

   11. lower-cbrt.f64 98.7

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

3. Applied rewrites 98.7%

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

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(g\_s \cdot \frac{\sqrt[3]{0.5 \cdot g\_m}}{\sqrt[3]{a\_m}}\right) \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (* a_s (* g_s (/ (cbrt (* 0.5 g_m)) (cbrt a_m)))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (cbrt((0.5 * g_m)) / cbrt(a_m)));
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (Math.cbrt((0.5 * g_m)) / Math.cbrt(a_m)));
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	return Float64(a_s * Float64(g_s * Float64(cbrt(Float64(0.5 * g_m)) / cbrt(a_m))))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := N[(a$95$s * N[(g$95$s * N[(N[Power[N[(0.5 * g$95$m), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[a$95$m, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

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

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. metadata-eval N/A

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

   12. lower-cbrt.f64 98.7

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

3. Applied rewrites 98.7%

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

Alternative 4: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(g\_s \cdot \frac{\sqrt[3]{g\_m}}{\sqrt[3]{a\_m + a\_m}}\right) \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (* a_s (* g_s (/ (cbrt g_m) (cbrt (+ a_m a_m))))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (cbrt(g_m) / cbrt((a_m + a_m))));
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * (Math.cbrt(g_m) / Math.cbrt((a_m + a_m))));
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	return Float64(a_s * Float64(g_s * Float64(cbrt(g_m) / cbrt(Float64(a_m + a_m)))))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := N[(a$95$s * N[(g$95$s * N[(N[Power[g$95$m, 1/3], $MachinePrecision] / N[Power[N[(a$95$m + a$95$m), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. 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 98.7

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

   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 98.7

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

3. Applied rewrites 98.7%

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

Alternative 5: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_0 := e^{\left(\log g\_m - \log \left(a\_m + a\_m\right)\right) \cdot 0.3333333333333333}\\ t_1 := \sqrt[3]{\frac{g\_m}{2 \cdot a\_m}}\\ a\_s \cdot \left(g\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-104}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\sqrt[3]{\frac{g\_m}{a\_m + a\_m}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array}\right) \end{array} \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (let* ((t_0 (exp (* (- (log g_m) (log (+ a_m a_m))) 0.3333333333333333)))
        (t_1 (cbrt (/ g_m (* 2.0 a_m)))))
   (*
    a_s
    (*
     g_s
     (if (<= t_1 2e-104)
       t_0
       (if (<= t_1 5e+96) (cbrt (/ g_m (+ a_m a_m))) t_0))))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	double t_0 = exp(((log(g_m) - log((a_m + a_m))) * 0.3333333333333333));
	double t_1 = cbrt((g_m / (2.0 * a_m)));
	double tmp;
	if (t_1 <= 2e-104) {
		tmp = t_0;
	} else if (t_1 <= 5e+96) {
		tmp = cbrt((g_m / (a_m + a_m)));
	} else {
		tmp = t_0;
	}
	return a_s * (g_s * tmp);
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	double t_0 = Math.exp(((Math.log(g_m) - Math.log((a_m + a_m))) * 0.3333333333333333));
	double t_1 = Math.cbrt((g_m / (2.0 * a_m)));
	double tmp;
	if (t_1 <= 2e-104) {
		tmp = t_0;
	} else if (t_1 <= 5e+96) {
		tmp = Math.cbrt((g_m / (a_m + a_m)));
	} else {
		tmp = t_0;
	}
	return a_s * (g_s * tmp);
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	t_0 = exp(Float64(Float64(log(g_m) - log(Float64(a_m + a_m))) * 0.3333333333333333))
	t_1 = cbrt(Float64(g_m / Float64(2.0 * a_m)))
	tmp = 0.0
	if (t_1 <= 2e-104)
		tmp = t_0;
	elseif (t_1 <= 5e+96)
		tmp = cbrt(Float64(g_m / Float64(a_m + a_m)));
	else
		tmp = t_0;
	end
	return Float64(a_s * Float64(g_s * tmp))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := Block[{t$95$0 = N[Exp[N[(N[(N[Log[g$95$m], $MachinePrecision] - N[Log[N[(a$95$m + a$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(g$95$m / N[(2.0 * a$95$m), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, N[(a$95$s * N[(g$95$s * If[LessEqual[t$95$1, 2e-104], t$95$0, If[LessEqual[t$95$1, 5e+96], N[Power[N[(g$95$m / N[(a$95$m + a$95$m), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], t$95$0]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a))) < 1.99999999999999985e-104 or 5.0000000000000004e96 < (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a)))

   1. Initial program 76.8%

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

      1. lift-cbrt.f64 N/A

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

      2. pow1/3 N/A

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

      3. pow-to-exp N/A

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

      4. lower-unsound-exp.f64 N/A

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

      5. lower-unsound-*.f64 N/A

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

      6. lower-unsound-log.f64 72.0

         \[\leadsto e^{\color{blue}{\log \left(\frac{g}{2 \cdot a}\right)} \cdot 0.3333333333333333} \]

      7. lift-*.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 72.0

         \[\leadsto e^{\log \left(\frac{g}{\color{blue}{a + a}}\right) \cdot 0.3333333333333333} \]

   3. Applied rewrites 72.0%

      \[\leadsto \color{blue}{e^{\log \left(\frac{g}{a + a}\right) \cdot 0.3333333333333333}} \]
   4. Step-by-step derivation

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower-unsound--.f64 N/A

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

      5. lower-unsound-log.f64 N/A

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

      6. lower-unsound-log.f64 91.0

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

   5. Applied rewrites 91.0%

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

   if 1.99999999999999985e-104 < (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a))) < 5.0000000000000004e96

   1. Initial program 76.8%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   2. 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 76.8

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

   3. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{a + a}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} g\_m = \left|g\right| \\ g\_s = \mathsf{copysign}\left(1, g\right) \\ a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ a\_s \cdot \left(g\_s \cdot \sqrt[3]{\frac{g\_m}{a\_m + a\_m}}\right) \end{array} \]

FPCore

g\_m = (fabs.f64 g)
g\_s = (copysign.f64 #s(literal 1 binary64) g)
a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
(FPCore (a_s g_s g_m a_m)
 :precision binary64
 (* a_s (* g_s (cbrt (/ g_m (+ a_m a_m))))))

C

g\_m = fabs(g);
g\_s = copysign(1.0, g);
a\_m = fabs(a);
a\_s = copysign(1.0, a);
double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * cbrt((g_m / (a_m + a_m))));
}

Java

g\_m = Math.abs(g);
g\_s = Math.copySign(1.0, g);
a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
public static double code(double a_s, double g_s, double g_m, double a_m) {
	return a_s * (g_s * Math.cbrt((g_m / (a_m + a_m))));
}

Julia

g\_m = abs(g)
g\_s = copysign(1.0, g)
a\_m = abs(a)
a\_s = copysign(1.0, a)
function code(a_s, g_s, g_m, a_m)
	return Float64(a_s * Float64(g_s * cbrt(Float64(g_m / Float64(a_m + a_m)))))
end

Wolfram

g\_m = N[Abs[g], $MachinePrecision]
g\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[g]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, g$95$s_, g$95$m_, a$95$m_] := N[(a$95$s * N[(g$95$s * N[Power[N[(g$95$m / N[(a$95$m + a$95$m), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
2. 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 76.8

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

3. Applied rewrites 76.8%

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

Reproduce

herbie shell --seed 2025154 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))