2-ancestry mixing, zero discriminant

Percentage Accurate: 76.8% → 98.6%

Time: 3.4s

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: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{g} \cdot \left(\sqrt[3]{{a}^{-1}} \cdot \sqrt[3]{0.5}\right) \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 74.0%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]
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 74.0

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

5. Applied rewrites 74.0%

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

7. Applied rewrites 98.6%

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

9. Applied rewrites 98.6%

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

10. Taylor expanded in a around 0

    \[\leadsto \sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \color{blue}{\sqrt[3]{\frac{1}{2}}}\right) \]
11. Step-by-step derivation

12. Applied rewrites 98.8%

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

13. Final simplification 98.8%

    \[\leadsto \sqrt[3]{g} \cdot \left(\sqrt[3]{{a}^{-1}} \cdot \sqrt[3]{0.5}\right) \]
14. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× 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 74.0%

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

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

   4. cbrt-div N/A

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

   5. lift-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. flip-+ N/A

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

   8. distribute-neg-frac N/A

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

   9. +-inverses N/A

      \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\mathsf{neg}\left(\color{blue}{0}\right)}{a - a}}} \]

   10. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lower-neg.f64 N/A

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

   18. lower-cbrt.f64 1.7

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

   19. lift-*.f64 N/A

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

   20. count-2-rev N/A

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

   21. flip-+ N/A

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

   22. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   23. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   24. +-inverses N/A

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

   25. distribute-neg-frac N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. lift-neg.f64 N/A

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

   8. metadata-eval N/A

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

   9. frac-2neg N/A

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

   10. lift-/.f64 N/A

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

   11. lift-/.f64 N/A

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

   12. associate-/r* N/A

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

   13. cbrt-div N/A

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

   14. count-2-rev N/A

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

   15. lift-+.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lift-+.f64 N/A

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

   18. flip-+ N/A

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

   19. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   20. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   21. +-inverses N/A

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

   22. distribute-neg-frac N/A

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

   23. flip-+ N/A

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

   24. count-2-rev N/A

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

   25. distribute-lft-neg-in N/A

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

   26. metadata-eval N/A

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

6. Applied rewrites 98.8%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 98.8

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

8. Applied rewrites 98.8%

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

Alternative 3: 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 74.0%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 74.0

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

4. Applied rewrites 74.0%

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

Alternative 4: 1.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{g}{0}\right)}^{0.3333333333333333} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (pow (/ g 0.0) 0.3333333333333333))

C

double code(double g, double a) {
	return pow((g / 0.0), 0.3333333333333333);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(g, a)
use fmin_fmax_functions
    real(8), intent (in) :: g
    real(8), intent (in) :: a
    code = (g / 0.0d0) ** 0.3333333333333333d0
end function

Java

public static double code(double g, double a) {
	return Math.pow((g / 0.0), 0.3333333333333333);
}

Python

def code(g, a):
	return math.pow((g / 0.0), 0.3333333333333333)

Julia

function code(g, a)
	return Float64(g / 0.0) ^ 0.3333333333333333
end

MATLAB

function tmp = code(g, a)
	tmp = (g / 0.0) ^ 0.3333333333333333;
end

Wolfram

code[g_, a_] := N[Power[N[(g / 0.0), $MachinePrecision], 0.3333333333333333], $MachinePrecision]

Derivation

1. Initial program 74.0%

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

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

   4. cbrt-div N/A

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

   5. lift-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. flip-+ N/A

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

   8. distribute-neg-frac N/A

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

   9. +-inverses N/A

      \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\mathsf{neg}\left(\color{blue}{0}\right)}{a - a}}} \]

   10. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lower-neg.f64 N/A

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

   18. lower-cbrt.f64 1.7

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

   19. lift-*.f64 N/A

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

   20. count-2-rev N/A

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

   21. flip-+ N/A

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

   22. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   23. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   24. +-inverses N/A

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

   25. distribute-neg-frac N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. lift-neg.f64 N/A

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

   8. metadata-eval N/A

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

   9. frac-2neg N/A

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

   10. lift-/.f64 N/A

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

   11. lift-/.f64 N/A

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

   12. associate-/r* N/A

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

   13. cbrt-div N/A

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

   14. count-2-rev N/A

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

   15. lift-+.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lift-+.f64 N/A

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

   18. flip-+ N/A

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

   19. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   20. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   21. +-inverses N/A

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

   22. distribute-neg-frac N/A

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

   23. flip-+ N/A

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

   24. count-2-rev N/A

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

   25. distribute-lft-neg-in N/A

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

   26. metadata-eval N/A

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

6. Applied rewrites 98.8%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 98.8

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

8. Applied rewrites 98.8%

   \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\color{blue}{a + a}}} \]
9. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. lift-/.f64 N/A

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

   6. unpow1/3 N/A

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

   7. lift-pow.f64 35.0

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

   8. lift-+.f64 N/A

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

   9. flip-+ N/A

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

   10. +-inverses N/A

       \[\leadsto {\left(\frac{g}{\frac{\color{blue}{0}}{a - a}}\right)}^{\frac{1}{3}} \]

   11. metadata-eval N/A

       \[\leadsto {\left(\frac{g}{\frac{\color{blue}{0 - 0}}{a - a}}\right)}^{\frac{1}{3}} \]

   12. metadata-eval N/A

       \[\leadsto {\left(\frac{g}{\frac{\color{blue}{0 \cdot 0} - 0}{a - a}}\right)}^{\frac{1}{3}} \]

   13. metadata-eval N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - \color{blue}{0 \cdot 0}}{a - a}}\right)}^{\frac{1}{3}} \]

   14. mul0-rgt N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - 0 \cdot \color{blue}{\left(\left(a \cdot a\right) \cdot 0\right)}}{a - a}}\right)}^{\frac{1}{3}} \]

   15. mul0-rgt N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - \color{blue}{\left(\left(a \cdot a\right) \cdot 0\right)} \cdot \left(\left(a \cdot a\right) \cdot 0\right)}{a - a}}\right)}^{\frac{1}{3}} \]

   16. +-inverses N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - \left(\left(a \cdot a\right) \cdot 0\right) \cdot \left(\left(a \cdot a\right) \cdot 0\right)}{\color{blue}{0}}}\right)}^{\frac{1}{3}} \]

   17. metadata-eval N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - \left(\left(a \cdot a\right) \cdot 0\right) \cdot \left(\left(a \cdot a\right) \cdot 0\right)}{\color{blue}{0 + 0}}}\right)}^{\frac{1}{3}} \]

   18. mul0-rgt N/A

       \[\leadsto {\left(\frac{g}{\frac{0 \cdot 0 - \left(\left(a \cdot a\right) \cdot 0\right) \cdot \left(\left(a \cdot a\right) \cdot 0\right)}{0 + \color{blue}{\left(a \cdot a\right) \cdot 0}}}\right)}^{\frac{1}{3}} \]

   19. flip-- N/A

       \[\leadsto {\left(\frac{g}{\color{blue}{0 - \left(a \cdot a\right) \cdot 0}}\right)}^{\frac{1}{3}} \]

   20. mul0-rgt N/A

       \[\leadsto {\left(\frac{g}{0 - \color{blue}{0}}\right)}^{\frac{1}{3}} \]

   21. metadata-eval 1.9

       \[\leadsto {\left(\frac{g}{\color{blue}{0}}\right)}^{0.3333333333333333} \]

10. Applied rewrites 1.9%

    \[\leadsto \color{blue}{{\left(\frac{g}{0}\right)}^{0.3333333333333333}} \]
11. Add Preprocessing

Alternative 5: 1.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\sqrt[3]{g}}{0} \end{array} \]

FPCore

(FPCore (g a) :precision binary64 (/ (cbrt g) 0.0))

C

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

Java

public static double code(double g, double a) {
	return Math.cbrt(g) / 0.0;
}

Julia

function code(g, a)
	return Float64(cbrt(g) / 0.0)
end

Wolfram

code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] / 0.0), $MachinePrecision]

Derivation

1. Initial program 74.0%

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

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

   4. cbrt-div N/A

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

   5. lift-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. flip-+ N/A

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

   8. distribute-neg-frac N/A

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

   9. +-inverses N/A

      \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\mathsf{neg}\left(\color{blue}{0}\right)}{a - a}}} \]

   10. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{\mathsf{neg}\left(g\right)}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   11. +-inverses N/A

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

   12. flip-+ N/A

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

   13. count-2-rev N/A

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

   14. lift-*.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lower-neg.f64 N/A

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

   18. lower-cbrt.f64 1.7

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

   19. lift-*.f64 N/A

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

   20. count-2-rev N/A

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

   21. flip-+ N/A

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

   22. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   23. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{-g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   24. +-inverses N/A

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

   25. distribute-neg-frac N/A

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

4. Applied rewrites 98.8%

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

   1. lift-/.f64 N/A

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

   2. lift-cbrt.f64 N/A

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

   3. lift-cbrt.f64 N/A

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

   4. cbrt-undiv N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/r* N/A

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

   7. lift-neg.f64 N/A

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

   8. metadata-eval N/A

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

   9. frac-2neg N/A

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

   10. lift-/.f64 N/A

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

   11. lift-/.f64 N/A

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

   12. associate-/r* N/A

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

   13. cbrt-div N/A

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

   14. count-2-rev N/A

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

   15. lift-+.f64 N/A

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

   16. lower-cbrt.f64 N/A

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

   17. lift-+.f64 N/A

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

   18. flip-+ N/A

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

   19. +-inverses N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{0}}{a - a}}} \]

   20. metadata-eval N/A

       \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{a - a}}} \]

   21. +-inverses N/A

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

   22. distribute-neg-frac N/A

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

   23. flip-+ N/A

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

   24. count-2-rev N/A

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

   25. distribute-lft-neg-in N/A

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

   26. metadata-eval N/A

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

6. Applied rewrites 98.8%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

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

   3. lower-+.f64 98.8

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

8. Applied rewrites 98.8%

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

10. Applied rewrites 2.1%

    \[\leadsto \color{blue}{\frac{-\sqrt[3]{g}}{0}} \]

11. Final simplification 1.8%

    \[\leadsto \frac{\sqrt[3]{g}}{0} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024358 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))