2-ancestry mixing, zero discriminant

Percentage Accurate: 76.8% → 98.7%

Time: 3.7s

Alternatives: 5

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

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

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 75.4%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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. lower-/.f64 N/A

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

   9. lower-cbrt.f64 98.7

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

4. Applied rewrites 98.7%

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

5. Taylor expanded in g around 0

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

   1. lower-*.f64 98.7

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

7. Applied rewrites 98.7%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 75.4%

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

3. Taylor expanded in g around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-cbrt.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-/.f64 75.4

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

5. Applied rewrites 75.4%

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

7. Applied rewrites 98.5%

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

9. Applied rewrites 98.7%

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

Alternative 3: 76.8% accurate, 1.0× speedup

Math

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

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(Float64(0.5 / a) * g))
end

Wolfram

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

Derivation

1. Initial program 75.4%

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

3. Taylor expanded in g around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-cbrt.f64 N/A

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

   4. lower-cbrt.f64 N/A

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

   5. lower-/.f64 75.4

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

5. Applied rewrites 75.4%

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

7. Applied rewrites 98.5%

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

9. Applied rewrites 98.7%

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

11. Applied rewrites 75.4%

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

Alternative 4: 76.8% 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 75.4%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 75.4

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

4. Applied rewrites 75.4%

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

Alternative 5: 3.2% accurate, 117.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (g a) :precision binary64 0.0)

C

double code(double g, double a) {
	return 0.0;
}

Fortran

real(8) function code(g, a)
    real(8), intent (in) :: g
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double g, double a) {
	return 0.0;
}

Python

def code(g, a):
	return 0.0

Julia

function code(g, a)
	return 0.0
end

MATLAB

function tmp = code(g, a)
	tmp = 0.0;
end

Wolfram

code[g_, a_] := 0.0

Derivation

1. Initial program 75.4%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. count-2-rev N/A

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

   4. flip3-+ N/A

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

   5. associate-/r/ N/A

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

   6. lower-*.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. count-2 N/A

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

   9. lower-*.f64 N/A

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

   10. lower-pow.f64 N/A

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

   11. lower-fma.f64 N/A

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

   12. +-inverses 24.4

       \[\leadsto \sqrt[3]{\frac{g}{2 \cdot {a}^{3}} \cdot \mathsf{fma}\left(a, a, \color{blue}{0}\right)} \]

4. Applied rewrites 24.4%

   \[\leadsto \sqrt[3]{\color{blue}{\frac{g}{2 \cdot {a}^{3}} \cdot \mathsf{fma}\left(a, a, 0\right)}} \]

6. Applied rewrites 3.2%

   \[\leadsto \sqrt[3]{\color{blue}{0}} \]
7. Step-by-step derivation

   1. lift-cbrt.f64 N/A

      \[\leadsto \color{blue}{\sqrt[3]{0}} \]

   2. pow1/3 N/A

      \[\leadsto \color{blue}{{0}^{\frac{1}{3}}} \]

   3. metadata-eval 3.2

      \[\leadsto \color{blue}{0} \]

8. Applied rewrites 3.2%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024333 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))