2-ancestry mixing, zero discriminant

Percentage Accurate: 76.9% → 98.7%

Time: 2.0s

Alternatives: 4

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: 76.9% 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, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

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

   3. lift-/.f64 N/A

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

   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. lower-/.f64 N/A

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

   9. lower-cbrt.f64 98.7

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

3. Applied rewrites 98.7%

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

4. Taylor expanded in g around 0

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

   1. lower-*.f64 98.7

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

6. Applied rewrites 98.7%

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

Alternative 2: 98.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

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

   3. lift-/.f64 N/A

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

   4. cbrt-div N/A

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

   5. lower-/.f64 N/A

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

   6. lower-cbrt.f64 N/A

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

   7. lower-cbrt.f64 N/A

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

   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 3: 80.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\left(\left(-\log \left(\frac{-1}{g}\right)\right) + \log \left(\frac{-0.5}{a}\right)\right) \cdot 0.3333333333333333}\\ t_1 := \sqrt[3]{\frac{g}{2 \cdot a}}\\ t_2 := \sqrt[3]{\frac{g}{a + a}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (g a)
 :precision binary64
 (let* ((t_0
         (exp
          (* (+ (- (log (/ -1.0 g))) (log (/ -0.5 a))) 0.3333333333333333)))
        (t_1 (cbrt (/ g (* 2.0 a))))
        (t_2 (cbrt (/ g (+ a a)))))
   (if (<= t_1 -1e-106)
     t_2
     (if (<= t_1 0.0) t_0 (if (<= t_1 1e+97) t_2 t_0)))))

C

double code(double g, double a) {
	double t_0 = exp(((-log((-1.0 / g)) + log((-0.5 / a))) * 0.3333333333333333));
	double t_1 = cbrt((g / (2.0 * a)));
	double t_2 = cbrt((g / (a + a)));
	double tmp;
	if (t_1 <= -1e-106) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = t_0;
	} else if (t_1 <= 1e+97) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double g, double a) {
	double t_0 = Math.exp(((-Math.log((-1.0 / g)) + Math.log((-0.5 / a))) * 0.3333333333333333));
	double t_1 = Math.cbrt((g / (2.0 * a)));
	double t_2 = Math.cbrt((g / (a + a)));
	double tmp;
	if (t_1 <= -1e-106) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = t_0;
	} else if (t_1 <= 1e+97) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(g, a)
	t_0 = exp(Float64(Float64(Float64(-log(Float64(-1.0 / g))) + log(Float64(-0.5 / a))) * 0.3333333333333333))
	t_1 = cbrt(Float64(g / Float64(2.0 * a)))
	t_2 = cbrt(Float64(g / Float64(a + a)))
	tmp = 0.0
	if (t_1 <= -1e-106)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = t_0;
	elseif (t_1 <= 1e+97)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[g_, a_] := Block[{t$95$0 = N[Exp[N[(N[((-N[Log[N[(-1.0 / g), $MachinePrecision]], $MachinePrecision]) + N[Log[N[(-0.5 / a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(g / N[(a + a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[t$95$1, -1e-106], t$95$2, If[LessEqual[t$95$1, 0.0], t$95$0, If[LessEqual[t$95$1, 1e+97], t$95$2, t$95$0]]]]]]

Derivation

1. Split input into 2 regimes

2. if (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a))) < -9.99999999999999941e-107 or -0.0 < (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a))) < 1.0000000000000001e97

   1. Initial program 76.9%

      \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
   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 76.9

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

   3. Applied rewrites 76.9%

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

   if -9.99999999999999941e-107 < (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a))) < -0.0 or 1.0000000000000001e97 < (cbrt.f64 (/.f64 g (*.f64 #s(literal 2 binary64) a)))

   1. Initial program 76.9%

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

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

      3. lift-/.f64 N/A

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

      4. pow1/3 N/A

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

      5. pow-to-exp N/A

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

      6. lower-exp.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. count-2-rev N/A

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

      11. lower-+.f64 36.5

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

   3. Applied rewrites 36.5%

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

   4. Taylor expanded in g around -inf

      \[\leadsto e^{\color{blue}{\left(\log \left(\frac{\frac{-1}{2}}{a}\right) + -1 \cdot \log \left(\frac{-1}{g}\right)\right)} \cdot \frac{1}{3}} \]
   5. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower-/.f64 22.3

         \[\leadsto e^{\left(\left(-\log \left(\frac{-1}{g}\right)\right) + \log \left(\frac{-0.5}{a}\right)\right) \cdot 0.3333333333333333} \]

   6. Applied rewrites 22.3%

      \[\leadsto e^{\color{blue}{\left(\left(-\log \left(\frac{-1}{g}\right)\right) + \log \left(\frac{-0.5}{a}\right)\right)} \cdot 0.3333333333333333} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.9%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 76.9

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

3. Applied rewrites 76.9%

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

Reproduce

herbie shell --seed 2025134 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))