(- 20670851120203963/500000000000000 (* (* z0 z0) 816052492761019/10000000000000))

Percentage Accurate: 99.9% → 99.9%

Time: 1.2s

Alternatives: 4

Speedup: N/A×

• 75.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]

FPCore

(FPCore (z0)
  :precision binary64
  (- 41.341702240407926 (* (* z0 z0) 81.6052492761019)))

C

double code(double z0) {
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    code = 41.341702240407926d0 - ((z0 * z0) * 81.6052492761019d0)
end function

Java

public static double code(double z0) {
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
}

Python

def code(z0):
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019)

Julia

function code(z0)
	return Float64(41.341702240407926 - Float64(Float64(z0 * z0) * 81.6052492761019))
end

MATLAB

function tmp = code(z0)
	tmp = 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
end

Wolfram

code[z0_] := N[(41.341702240407926 - N[(N[(z0 * z0), $MachinePrecision] * 81.6052492761019), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]

FPCore

(FPCore (z0)
  :precision binary64
  (- 41.341702240407926 (* (* z0 z0) 81.6052492761019)))

C

double code(double z0) {
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    code = 41.341702240407926d0 - ((z0 * z0) * 81.6052492761019d0)
end function

Java

public static double code(double z0) {
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
}

Python

def code(z0):
	return 41.341702240407926 - ((z0 * z0) * 81.6052492761019)

Julia

function code(z0)
	return Float64(41.341702240407926 - Float64(Float64(z0 * z0) * 81.6052492761019))
end

MATLAB

function tmp = code(z0)
	tmp = 41.341702240407926 - ((z0 * z0) * 81.6052492761019);
end

Wolfram

code[z0_] := N[(41.341702240407926 - N[(N[(z0 * z0), $MachinePrecision] * 81.6052492761019), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\left(z0 \cdot z0 - 0.5066059182116223\right) \cdot -81.6052492761019 \]

FPCore

(FPCore (z0)
  :precision binary64
  (* (- (* z0 z0) 0.5066059182116223) -81.6052492761019))

C

double code(double z0) {
	return ((z0 * z0) - 0.5066059182116223) * -81.6052492761019;
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    code = ((z0 * z0) - 0.5066059182116223d0) * (-81.6052492761019d0)
end function

Java

public static double code(double z0) {
	return ((z0 * z0) - 0.5066059182116223) * -81.6052492761019;
}

Python

def code(z0):
	return ((z0 * z0) - 0.5066059182116223) * -81.6052492761019

Julia

function code(z0)
	return Float64(Float64(Float64(z0 * z0) - 0.5066059182116223) * -81.6052492761019)
end

MATLAB

function tmp = code(z0)
	tmp = ((z0 * z0) - 0.5066059182116223) * -81.6052492761019;
end

Wolfram

code[z0_] := N[(N[(N[(z0 * z0), $MachinePrecision] - 0.5066059182116223), $MachinePrecision] * -81.6052492761019), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(z0 \cdot z0\right) \cdot \frac{816052492761019}{10000000000000}} \]

   2. *-commutative N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\frac{816052492761019}{10000000000000} \cdot \left(z0 \cdot z0\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

   4. sqr-neg-rev N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(z0\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)} \]

   5. associate-*r* N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)} \]

   6. distribute-rgt-neg-out N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot z0\right)\right)} \]

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

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

   9. distribute-rgt-neg-out N/A

      \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z0\right)\right)\right)\right)\right)} \cdot z0 \]

   10. remove-double-neg N/A

       \[\leadsto \frac{20670851120203963}{500000000000000} - \left(\frac{816052492761019}{10000000000000} \cdot \color{blue}{z0}\right) \cdot z0 \]

   11. lower-*.f64 99.9%

       \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right)} \cdot z0 \]

3. Applied rewrites 99.9%

   \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right) \cdot z0} \]

5. Applied rewrites 74.6%

   \[\leadsto \color{blue}{\left(\frac{41.341702240407926}{z0 \cdot z0} - 81.6052492761019\right) \cdot \left(z0 \cdot z0\right)} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\frac{\frac{20670851120203963}{500000000000000}}{z0 \cdot z0} - \frac{816052492761019}{10000000000000}\right) \cdot \left(z0 \cdot z0\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000}}{z0 \cdot z0} - \frac{816052492761019}{10000000000000}\right) \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

   3. associate-*r* N/A

      \[\leadsto \color{blue}{\left(\left(\frac{\frac{20670851120203963}{500000000000000}}{z0 \cdot z0} - \frac{816052492761019}{10000000000000}\right) \cdot z0\right) \cdot z0} \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{z0 \cdot \left(\left(\frac{\frac{20670851120203963}{500000000000000}}{z0 \cdot z0} - \frac{816052492761019}{10000000000000}\right) \cdot z0\right)} \]

   5. associate-*l* N/A

      \[\leadsto \color{blue}{\left(z0 \cdot \left(\frac{\frac{20670851120203963}{500000000000000}}{z0 \cdot z0} - \frac{816052492761019}{10000000000000}\right)\right) \cdot z0} \]

7. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\left(\frac{41.341702240407926}{z0} - 81.6052492761019 \cdot z0\right) \cdot z0} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\frac{\frac{20670851120203963}{500000000000000}}{z0} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0} \]

   2. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(\frac{\frac{20670851120203963}{500000000000000}}{z0} - \frac{816052492761019}{10000000000000} \cdot z0\right)} \cdot z0 \]

   3. lift-/.f64 N/A

      \[\leadsto \left(\color{blue}{\frac{\frac{20670851120203963}{500000000000000}}{z0}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   4. mult-flip N/A

      \[\leadsto \left(\color{blue}{\frac{20670851120203963}{500000000000000} \cdot \frac{1}{z0}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   5. metadata-eval N/A

      \[\leadsto \left(\color{blue}{\frac{\frac{20670851120203963}{40802624638050950}}{\frac{10000000000000}{816052492761019}}} \cdot \frac{1}{z0} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   6. associate-*l/ N/A

      \[\leadsto \left(\color{blue}{\frac{\frac{20670851120203963}{40802624638050950} \cdot \frac{1}{z0}}{\frac{10000000000000}{816052492761019}}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   7. metadata-eval N/A

      \[\leadsto \left(\frac{\color{blue}{\left(\frac{20670851120203963}{500000000000000} \cdot \frac{10000000000000}{816052492761019}\right)} \cdot \frac{1}{z0}}{\frac{10000000000000}{816052492761019}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   8. associate-*r* N/A

      \[\leadsto \left(\frac{\color{blue}{\frac{20670851120203963}{500000000000000} \cdot \left(\frac{10000000000000}{816052492761019} \cdot \frac{1}{z0}\right)}}{\frac{10000000000000}{816052492761019}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   9. mult-flip N/A

      \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \color{blue}{\frac{\frac{10000000000000}{816052492761019}}{z0}}}{\frac{10000000000000}{816052492761019}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   10. lift-/.f64 N/A

       \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \color{blue}{\frac{\frac{10000000000000}{816052492761019}}{z0}}}{\frac{10000000000000}{816052492761019}} - \frac{816052492761019}{10000000000000} \cdot z0\right) \cdot z0 \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0}}{\frac{10000000000000}{816052492761019}} - \color{blue}{\frac{816052492761019}{10000000000000} \cdot z0}\right) \cdot z0 \]

   12. *-commutative N/A

       \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0}}{\frac{10000000000000}{816052492761019}} - \color{blue}{z0 \cdot \frac{816052492761019}{10000000000000}}\right) \cdot z0 \]

   13. metadata-eval N/A

       \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0}}{\frac{10000000000000}{816052492761019}} - z0 \cdot \color{blue}{\frac{1}{\frac{10000000000000}{816052492761019}}}\right) \cdot z0 \]

   14. mult-flip-rev N/A

       \[\leadsto \left(\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0}}{\frac{10000000000000}{816052492761019}} - \color{blue}{\frac{z0}{\frac{10000000000000}{816052492761019}}}\right) \cdot z0 \]

   15. sub-div N/A

       \[\leadsto \color{blue}{\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0} - z0}{\frac{10000000000000}{816052492761019}}} \cdot z0 \]

   16. associate-/r/ N/A

       \[\leadsto \color{blue}{\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0} - z0}{\frac{\frac{10000000000000}{816052492761019}}{z0}}} \]

   17. lift-/.f64 N/A

       \[\leadsto \frac{\frac{20670851120203963}{500000000000000} \cdot \frac{\frac{10000000000000}{816052492761019}}{z0} - z0}{\color{blue}{\frac{\frac{10000000000000}{816052492761019}}{z0}}} \]

   18. sub-to-fraction N/A

       \[\leadsto \color{blue}{\frac{20670851120203963}{500000000000000} - \frac{z0}{\frac{\frac{10000000000000}{816052492761019}}{z0}}} \]

   19. lift-/.f64 N/A

       \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{z0}{\color{blue}{\frac{\frac{10000000000000}{816052492761019}}{z0}}} \]

   20. associate-/r/ N/A

       \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\frac{z0}{\frac{10000000000000}{816052492761019}} \cdot z0} \]

   21. associate-*l/ N/A

       \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\frac{z0 \cdot z0}{\frac{10000000000000}{816052492761019}}} \]

   22. lift-*.f64 N/A

       \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{\color{blue}{z0 \cdot z0}}{\frac{10000000000000}{816052492761019}} \]

   23. sub-to-fraction N/A

       \[\leadsto \color{blue}{\frac{\frac{20670851120203963}{500000000000000} \cdot \frac{10000000000000}{816052492761019} - z0 \cdot z0}{\frac{10000000000000}{816052492761019}}} \]

   24. metadata-eval N/A

       \[\leadsto \frac{\color{blue}{\frac{20670851120203963}{40802624638050950}} - z0 \cdot z0}{\frac{10000000000000}{816052492761019}} \]

9. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\left(z0 \cdot z0 - 0.5066059182116223\right) \cdot -81.6052492761019} \]
10. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \leq -200000:\\ \;\;\;\;\left(-81.6052492761019 \cdot z0\right) \cdot z0\\ \mathbf{else}:\\ \;\;\;\;41.341702240407926\\ \end{array} \]

FPCore

(FPCore (z0)
  :precision binary64
  (if (<=
     (- 41.341702240407926 (* (* z0 z0) 81.6052492761019))
     -200000.0)
  (* (* -81.6052492761019 z0) z0)
  41.341702240407926))

C

double code(double z0) {
	double tmp;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0) {
		tmp = (-81.6052492761019 * z0) * z0;
	} else {
		tmp = 41.341702240407926;
	}
	return tmp;
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8) :: tmp
    if ((41.341702240407926d0 - ((z0 * z0) * 81.6052492761019d0)) <= (-200000.0d0)) then
        tmp = ((-81.6052492761019d0) * z0) * z0
    else
        tmp = 41.341702240407926d0
    end if
    code = tmp
end function

Java

public static double code(double z0) {
	double tmp;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0) {
		tmp = (-81.6052492761019 * z0) * z0;
	} else {
		tmp = 41.341702240407926;
	}
	return tmp;
}

Python

def code(z0):
	tmp = 0
	if (41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0:
		tmp = (-81.6052492761019 * z0) * z0
	else:
		tmp = 41.341702240407926
	return tmp

Julia

function code(z0)
	tmp = 0.0
	if (Float64(41.341702240407926 - Float64(Float64(z0 * z0) * 81.6052492761019)) <= -200000.0)
		tmp = Float64(Float64(-81.6052492761019 * z0) * z0);
	else
		tmp = 41.341702240407926;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0)
	tmp = 0.0;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0)
		tmp = (-81.6052492761019 * z0) * z0;
	else
		tmp = 41.341702240407926;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_] := If[LessEqual[N[(41.341702240407926 - N[(N[(z0 * z0), $MachinePrecision] * 81.6052492761019), $MachinePrecision]), $MachinePrecision], -200000.0], N[(N[(-81.6052492761019 * z0), $MachinePrecision] * z0), $MachinePrecision], 41.341702240407926]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 20670851120203963/500000000000000 binary64) (*.f64 (*.f64 z0 z0) #s(literal 816052492761019/10000000000000 binary64))) < -2e5

   1. Initial program 99.9%

      \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(z0 \cdot z0\right) \cdot \frac{816052492761019}{10000000000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\frac{816052492761019}{10000000000000} \cdot \left(z0 \cdot z0\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

      4. sqr-neg-rev N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(z0\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)} \]

      5. associate-*r* N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)} \]

      6. distribute-rgt-neg-out N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot z0\right)\right)} \]

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

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

      9. distribute-rgt-neg-out N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z0\right)\right)\right)\right)\right)} \cdot z0 \]

      10. remove-double-neg N/A

          \[\leadsto \frac{20670851120203963}{500000000000000} - \left(\frac{816052492761019}{10000000000000} \cdot \color{blue}{z0}\right) \cdot z0 \]

      11. lower-*.f64 99.9%

          \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right)} \cdot z0 \]

   3. Applied rewrites 99.9%

      \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right) \cdot z0} \]

   5. Applied rewrites 74.6%

      \[\leadsto \color{blue}{\left(\frac{41.341702240407926}{z0 \cdot z0} - 81.6052492761019\right) \cdot \left(z0 \cdot z0\right)} \]

   6. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{-816052492761019}{10000000000000}} \cdot \left(z0 \cdot z0\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.0%

      \[\leadsto \color{blue}{-81.6052492761019} \cdot \left(z0 \cdot z0\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-816052492761019}{10000000000000} \cdot \left(z0 \cdot z0\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{-816052492761019}{10000000000000} \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{-816052492761019}{10000000000000} \cdot z0\right) \cdot z0} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{-816052492761019}{10000000000000} \cdot z0\right) \cdot z0} \]

      5. lower-*.f64 50.0%

         \[\leadsto \color{blue}{\left(-81.6052492761019 \cdot z0\right)} \cdot z0 \]

   10. Applied rewrites 50.0%

       \[\leadsto \color{blue}{\left(-81.6052492761019 \cdot z0\right) \cdot z0} \]

   if -2e5 < (-.f64 #s(literal 20670851120203963/500000000000000 binary64) (*.f64 (*.f64 z0 z0) #s(literal 816052492761019/10000000000000 binary64)))

   1. Initial program 99.9%

      \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\frac{20670851120203963}{500000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto \color{blue}{41.341702240407926} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \leq -200000:\\ \;\;\;\;-81.6052492761019 \cdot \left(z0 \cdot z0\right)\\ \mathbf{else}:\\ \;\;\;\;41.341702240407926\\ \end{array} \]

FPCore

(FPCore (z0)
  :precision binary64
  (if (<=
     (- 41.341702240407926 (* (* z0 z0) 81.6052492761019))
     -200000.0)
  (* -81.6052492761019 (* z0 z0))
  41.341702240407926))

C

double code(double z0) {
	double tmp;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0) {
		tmp = -81.6052492761019 * (z0 * z0);
	} else {
		tmp = 41.341702240407926;
	}
	return tmp;
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8) :: tmp
    if ((41.341702240407926d0 - ((z0 * z0) * 81.6052492761019d0)) <= (-200000.0d0)) then
        tmp = (-81.6052492761019d0) * (z0 * z0)
    else
        tmp = 41.341702240407926d0
    end if
    code = tmp
end function

Java

public static double code(double z0) {
	double tmp;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0) {
		tmp = -81.6052492761019 * (z0 * z0);
	} else {
		tmp = 41.341702240407926;
	}
	return tmp;
}

Python

def code(z0):
	tmp = 0
	if (41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0:
		tmp = -81.6052492761019 * (z0 * z0)
	else:
		tmp = 41.341702240407926
	return tmp

Julia

function code(z0)
	tmp = 0.0
	if (Float64(41.341702240407926 - Float64(Float64(z0 * z0) * 81.6052492761019)) <= -200000.0)
		tmp = Float64(-81.6052492761019 * Float64(z0 * z0));
	else
		tmp = 41.341702240407926;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0)
	tmp = 0.0;
	if ((41.341702240407926 - ((z0 * z0) * 81.6052492761019)) <= -200000.0)
		tmp = -81.6052492761019 * (z0 * z0);
	else
		tmp = 41.341702240407926;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_] := If[LessEqual[N[(41.341702240407926 - N[(N[(z0 * z0), $MachinePrecision] * 81.6052492761019), $MachinePrecision]), $MachinePrecision], -200000.0], N[(-81.6052492761019 * N[(z0 * z0), $MachinePrecision]), $MachinePrecision], 41.341702240407926]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 20670851120203963/500000000000000 binary64) (*.f64 (*.f64 z0 z0) #s(literal 816052492761019/10000000000000 binary64))) < -2e5

   1. Initial program 99.9%

      \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(z0 \cdot z0\right) \cdot \frac{816052492761019}{10000000000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\frac{816052492761019}{10000000000000} \cdot \left(z0 \cdot z0\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(z0 \cdot z0\right)} \]

      4. sqr-neg-rev N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \frac{816052492761019}{10000000000000} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(z0\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)} \]

      5. associate-*r* N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)} \]

      6. distribute-rgt-neg-out N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right) \cdot z0\right)\right)} \]

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

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\mathsf{neg}\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(z0\right)\right)\right)\right) \cdot z0} \]

      9. distribute-rgt-neg-out N/A

         \[\leadsto \frac{20670851120203963}{500000000000000} - \color{blue}{\left(\frac{816052492761019}{10000000000000} \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z0\right)\right)\right)\right)\right)} \cdot z0 \]

      10. remove-double-neg N/A

          \[\leadsto \frac{20670851120203963}{500000000000000} - \left(\frac{816052492761019}{10000000000000} \cdot \color{blue}{z0}\right) \cdot z0 \]

      11. lower-*.f64 99.9%

          \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right)} \cdot z0 \]

   3. Applied rewrites 99.9%

      \[\leadsto 41.341702240407926 - \color{blue}{\left(81.6052492761019 \cdot z0\right) \cdot z0} \]

   5. Applied rewrites 74.6%

      \[\leadsto \color{blue}{\left(\frac{41.341702240407926}{z0 \cdot z0} - 81.6052492761019\right) \cdot \left(z0 \cdot z0\right)} \]

   6. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{-816052492761019}{10000000000000}} \cdot \left(z0 \cdot z0\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.0%

      \[\leadsto \color{blue}{-81.6052492761019} \cdot \left(z0 \cdot z0\right) \]

   if -2e5 < (-.f64 #s(literal 20670851120203963/500000000000000 binary64) (*.f64 (*.f64 z0 z0) #s(literal 816052492761019/10000000000000 binary64)))

   1. Initial program 99.9%

      \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\frac{20670851120203963}{500000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto \color{blue}{41.341702240407926} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.6% accurate, 14.0× speedup

Math

\[41.341702240407926 \]

FPCore

(FPCore (z0)
  :precision binary64
  41.341702240407926)

C

double code(double z0) {
	return 41.341702240407926;
}

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(z0)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    code = 41.341702240407926d0
end function

Java

public static double code(double z0) {
	return 41.341702240407926;
}

Python

def code(z0):
	return 41.341702240407926

Julia

function code(z0)
	return 41.341702240407926
end

MATLAB

function tmp = code(z0)
	tmp = 41.341702240407926;
end

Wolfram

code[z0_] := 41.341702240407926

Derivation

1. Initial program 99.9%

   \[41.341702240407926 - \left(z0 \cdot z0\right) \cdot 81.6052492761019 \]

2. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\frac{20670851120203963}{500000000000000}} \]
3. Step-by-step derivation

4. Applied rewrites 50.6%

   \[\leadsto \color{blue}{41.341702240407926} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0)
  :name "(- 20670851120203963/500000000000000 (* (* z0 z0) 816052492761019/10000000000000))"
  :precision binary64
  (- 41.341702240407926 (* (* z0 z0) 81.6052492761019)))