(/ (- (- (+ z0 z0) -2) (/ -13333333333333333/10000000000000000 z0)) (* z0 z0))

Percentage Accurate: 76.1% → 99.9%

Time: 1.6s

Alternatives: 8

Speedup: 1.2×

• 66.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ (- (- (+ z0 z0) -2.0) (/ -1.3333333333333333 z0)) (* z0 z0)))

C

double code(double z0) {
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
}

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) - (-2.0d0)) - ((-1.3333333333333333d0) / z0)) / (z0 * z0)
end function

Java

public static double code(double z0) {
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
}

Python

def code(z0):
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0)

Julia

function code(z0)
	return Float64(Float64(Float64(Float64(z0 + z0) - -2.0) - Float64(-1.3333333333333333 / z0)) / Float64(z0 * z0))
end

MATLAB

function tmp = code(z0)
	tmp = (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
end

Wolfram

code[z0_] := N[(N[(N[(N[(z0 + z0), $MachinePrecision] - -2.0), $MachinePrecision] - N[(-1.3333333333333333 / z0), $MachinePrecision]), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.1% accurate, 1.0× speedup

Math

\[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ (- (- (+ z0 z0) -2.0) (/ -1.3333333333333333 z0)) (* z0 z0)))

C

double code(double z0) {
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
}

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) - (-2.0d0)) - ((-1.3333333333333333d0) / z0)) / (z0 * z0)
end function

Java

public static double code(double z0) {
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
}

Python

def code(z0):
	return (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0)

Julia

function code(z0)
	return Float64(Float64(Float64(Float64(z0 + z0) - -2.0) - Float64(-1.3333333333333333 / z0)) / Float64(z0 * z0))
end

MATLAB

function tmp = code(z0)
	tmp = (((z0 + z0) - -2.0) - (-1.3333333333333333 / z0)) / (z0 * z0);
end

Wolfram

code[z0_] := N[(N[(N[(N[(z0 + z0), $MachinePrecision] - -2.0), $MachinePrecision] - N[(-1.3333333333333333 / z0), $MachinePrecision]), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.8× speedup

Math

\[\frac{2}{z0} - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(\left(-z0\right) \cdot z0\right) \cdot z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (-
 (/ 2.0 z0)
 (/ (- (+ z0 z0) -1.3333333333333333) (* (* (- z0) z0) z0))))

C

double code(double z0) {
	return (2.0 / z0) - (((z0 + z0) - -1.3333333333333333) / ((-z0 * z0) * z0));
}

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 = (2.0d0 / z0) - (((z0 + z0) - (-1.3333333333333333d0)) / ((-z0 * z0) * z0))
end function

Java

public static double code(double z0) {
	return (2.0 / z0) - (((z0 + z0) - -1.3333333333333333) / ((-z0 * z0) * z0));
}

Python

def code(z0):
	return (2.0 / z0) - (((z0 + z0) - -1.3333333333333333) / ((-z0 * z0) * z0))

Julia

function code(z0)
	return Float64(Float64(2.0 / z0) - Float64(Float64(Float64(z0 + z0) - -1.3333333333333333) / Float64(Float64(Float64(-z0) * z0) * z0)))
end

MATLAB

function tmp = code(z0)
	tmp = (2.0 / z0) - (((z0 + z0) - -1.3333333333333333) / ((-z0 * z0) * z0));
end

Wolfram

code[z0_] := N[(N[(2.0 / z0), $MachinePrecision] - N[(N[(N[(z0 + z0), $MachinePrecision] - -1.3333333333333333), $MachinePrecision] / N[(N[((-z0) * z0), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

   3. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   4. lift--.f64 N/A

      \[\leadsto \frac{\frac{\color{blue}{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}}{z0}}{z0} \]

   5. lift--.f64 N/A

      \[\leadsto \frac{\frac{\color{blue}{\left(\left(z0 + z0\right) - -2\right)} - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0} \]

   6. associate--l- N/A

      \[\leadsto \frac{\frac{\color{blue}{\left(z0 + z0\right) - \left(-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}\right)}}{z0}}{z0} \]

   7. lift-+.f64 N/A

      \[\leadsto \frac{\frac{\color{blue}{\left(z0 + z0\right)} - \left(-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}\right)}{z0}}{z0} \]

   8. count-2 N/A

      \[\leadsto \frac{\frac{\color{blue}{2 \cdot z0} - \left(-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}\right)}{z0}}{z0} \]

   9. sub-to-fraction-rev N/A

      \[\leadsto \frac{\color{blue}{2 - \frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}}{z0} \]

   10. div-sub N/A

       \[\leadsto \color{blue}{\frac{2}{z0} - \frac{\frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   11. associate-/r* N/A

       \[\leadsto \frac{2}{z0} - \color{blue}{\frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   12. lift-*.f64 N/A

       \[\leadsto \frac{2}{z0} - \frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

   13. lower--.f64 N/A

       \[\leadsto \color{blue}{\frac{2}{z0} - \frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   14. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{2}{z0}} - \frac{-2 + \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0} \]

   15. lift-/.f64 N/A

       \[\leadsto \frac{2}{z0} - \frac{-2 + \color{blue}{\frac{\frac{-13333333333333333}{10000000000000000}}{z0}}}{z0 \cdot z0} \]

   16. frac-2neg N/A

       \[\leadsto \frac{2}{z0} - \frac{-2 + \color{blue}{\frac{\mathsf{neg}\left(\frac{-13333333333333333}{10000000000000000}\right)}{\mathsf{neg}\left(z0\right)}}}{z0 \cdot z0} \]

   17. add-to-fraction N/A

       \[\leadsto \frac{2}{z0} - \frac{\color{blue}{\frac{-2 \cdot \left(\mathsf{neg}\left(z0\right)\right) + \left(\mathsf{neg}\left(\frac{-13333333333333333}{10000000000000000}\right)\right)}{\mathsf{neg}\left(z0\right)}}}{z0 \cdot z0} \]

   18. associate-/l/ N/A

       \[\leadsto \frac{2}{z0} - \color{blue}{\frac{-2 \cdot \left(\mathsf{neg}\left(z0\right)\right) + \left(\mathsf{neg}\left(\frac{-13333333333333333}{10000000000000000}\right)\right)}{\left(\mathsf{neg}\left(z0\right)\right) \cdot \left(z0 \cdot z0\right)}} \]

   19. lower-/.f64 N/A

       \[\leadsto \frac{2}{z0} - \color{blue}{\frac{-2 \cdot \left(\mathsf{neg}\left(z0\right)\right) + \left(\mathsf{neg}\left(\frac{-13333333333333333}{10000000000000000}\right)\right)}{\left(\mathsf{neg}\left(z0\right)\right) \cdot \left(z0 \cdot z0\right)}} \]

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\frac{2}{z0} - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(\left(-z0\right) \cdot z0\right) \cdot z0}} \]
4. Add Preprocessing

Alternative 2: 99.9% accurate, 0.9× speedup

Math

\[\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ (- 2.0 (/ (- (+ z0 z0) -1.3333333333333333) (* (- z0) z0))) z0))

C

double code(double z0) {
	return (2.0 - (((z0 + z0) - -1.3333333333333333) / (-z0 * z0))) / z0;
}

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 = (2.0d0 - (((z0 + z0) - (-1.3333333333333333d0)) / (-z0 * z0))) / z0
end function

Java

public static double code(double z0) {
	return (2.0 - (((z0 + z0) - -1.3333333333333333) / (-z0 * z0))) / z0;
}

Python

def code(z0):
	return (2.0 - (((z0 + z0) - -1.3333333333333333) / (-z0 * z0))) / z0

Julia

function code(z0)
	return Float64(Float64(2.0 - Float64(Float64(Float64(z0 + z0) - -1.3333333333333333) / Float64(Float64(-z0) * z0))) / z0)
end

MATLAB

function tmp = code(z0)
	tmp = (2.0 - (((z0 + z0) - -1.3333333333333333) / (-z0 * z0))) / z0;
end

Wolfram

code[z0_] := N[(N[(2.0 - N[(N[(N[(z0 + z0), $MachinePrecision] - -1.3333333333333333), $MachinePrecision] / N[((-z0) * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

   3. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0}} \]
4. Add Preprocessing

Alternative 3: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \frac{2 - \frac{-2}{z0}}{z0}\\ \mathbf{if}\;z0 \leq -540:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq 115000000:\\ \;\;\;\;\frac{2 \cdot z0 - -1.3333333333333333}{\left(z0 \cdot z0\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0)
  :precision binary64
  (let* ((t_0 (/ (- 2.0 (/ -2.0 z0)) z0)))
  (if (<= z0 -540.0)
    t_0
    (if (<= z0 115000000.0)
      (/ (- (* 2.0 z0) -1.3333333333333333) (* (* z0 z0) z0))
      t_0))))

C

double code(double z0) {
	double t_0 = (2.0 - (-2.0 / z0)) / z0;
	double tmp;
	if (z0 <= -540.0) {
		tmp = t_0;
	} else if (z0 <= 115000000.0) {
		tmp = ((2.0 * z0) - -1.3333333333333333) / ((z0 * z0) * z0);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 - ((-2.0d0) / z0)) / z0
    if (z0 <= (-540.0d0)) then
        tmp = t_0
    else if (z0 <= 115000000.0d0) then
        tmp = ((2.0d0 * z0) - (-1.3333333333333333d0)) / ((z0 * z0) * z0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0) {
	double t_0 = (2.0 - (-2.0 / z0)) / z0;
	double tmp;
	if (z0 <= -540.0) {
		tmp = t_0;
	} else if (z0 <= 115000000.0) {
		tmp = ((2.0 * z0) - -1.3333333333333333) / ((z0 * z0) * z0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0):
	t_0 = (2.0 - (-2.0 / z0)) / z0
	tmp = 0
	if z0 <= -540.0:
		tmp = t_0
	elif z0 <= 115000000.0:
		tmp = ((2.0 * z0) - -1.3333333333333333) / ((z0 * z0) * z0)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0)
	t_0 = Float64(Float64(2.0 - Float64(-2.0 / z0)) / z0)
	tmp = 0.0
	if (z0 <= -540.0)
		tmp = t_0;
	elseif (z0 <= 115000000.0)
		tmp = Float64(Float64(Float64(2.0 * z0) - -1.3333333333333333) / Float64(Float64(z0 * z0) * z0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0)
	t_0 = (2.0 - (-2.0 / z0)) / z0;
	tmp = 0.0;
	if (z0 <= -540.0)
		tmp = t_0;
	elseif (z0 <= 115000000.0)
		tmp = ((2.0 * z0) - -1.3333333333333333) / ((z0 * z0) * z0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_] := Block[{t$95$0 = N[(N[(2.0 - N[(-2.0 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]}, If[LessEqual[z0, -540.0], t$95$0, If[LessEqual[z0, 115000000.0], N[(N[(N[(2.0 * z0), $MachinePrecision] - -1.3333333333333333), $MachinePrecision] / N[(N[(z0 * z0), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -540 or 1.15e8 < z0

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \frac{2 - \frac{\color{blue}{\frac{13333333333333333}{10000000000000000}}}{\left(-z0\right) \cdot z0}}{z0} \]
   5. Step-by-step derivation

   6. Applied rewrites 97.9%

      \[\leadsto \frac{2 - \frac{\color{blue}{1.3333333333333333}}{\left(-z0\right) \cdot z0}}{z0} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 63.9%

         \[\leadsto \frac{2 - \frac{-2}{\color{blue}{z0}}}{z0} \]

   9. Applied rewrites 63.9%

      \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]

   if -540 < z0 < 1.15e8

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}}{z0 \cdot z0} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \color{blue}{\frac{\frac{-13333333333333333}{10000000000000000}}{z0}}}{z0 \cdot z0} \]

      4. sub-to-fraction N/A

         \[\leadsto \frac{\color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - \frac{-13333333333333333}{10000000000000000}}{z0}}}{z0 \cdot z0} \]

      5. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - \frac{-13333333333333333}{10000000000000000}}{z0 \cdot \left(z0 \cdot z0\right)}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - \frac{-13333333333333333}{10000000000000000}}{z0 \cdot \left(z0 \cdot z0\right)}} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - \frac{-13333333333333333}{10000000000000000}}}{z0 \cdot \left(z0 \cdot z0\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(z0 + z0\right) - -2\right) \cdot z0} - \frac{-13333333333333333}{10000000000000000}}{z0 \cdot \left(z0 \cdot z0\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - \frac{-13333333333333333}{10000000000000000}}{\color{blue}{\left(z0 \cdot z0\right) \cdot z0}} \]

      10. lower-*.f64 66.2%

          \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - -1.3333333333333333}{\color{blue}{\left(z0 \cdot z0\right) \cdot z0}} \]

   3. Applied rewrites 66.2%

      \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) \cdot z0 - -1.3333333333333333}{\left(z0 \cdot z0\right) \cdot z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{2} \cdot z0 - -1.3333333333333333}{\left(z0 \cdot z0\right) \cdot z0} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.8%

      \[\leadsto \frac{\color{blue}{2} \cdot z0 - -1.3333333333333333}{\left(z0 \cdot z0\right) \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \frac{2 - \frac{-2}{z0}}{z0}\\ \mathbf{if}\;z0 \leq -3800:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z0 \leq 115000000:\\ \;\;\;\;\frac{\frac{1.3333333333333333}{z0}}{z0 \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0)
  :precision binary64
  (let* ((t_0 (/ (- 2.0 (/ -2.0 z0)) z0)))
  (if (<= z0 -3800.0)
    t_0
    (if (<= z0 115000000.0)
      (/ (/ 1.3333333333333333 z0) (* z0 z0))
      t_0))))

C

double code(double z0) {
	double t_0 = (2.0 - (-2.0 / z0)) / z0;
	double tmp;
	if (z0 <= -3800.0) {
		tmp = t_0;
	} else if (z0 <= 115000000.0) {
		tmp = (1.3333333333333333 / z0) / (z0 * z0);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 - ((-2.0d0) / z0)) / z0
    if (z0 <= (-3800.0d0)) then
        tmp = t_0
    else if (z0 <= 115000000.0d0) then
        tmp = (1.3333333333333333d0 / z0) / (z0 * z0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0) {
	double t_0 = (2.0 - (-2.0 / z0)) / z0;
	double tmp;
	if (z0 <= -3800.0) {
		tmp = t_0;
	} else if (z0 <= 115000000.0) {
		tmp = (1.3333333333333333 / z0) / (z0 * z0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0):
	t_0 = (2.0 - (-2.0 / z0)) / z0
	tmp = 0
	if z0 <= -3800.0:
		tmp = t_0
	elif z0 <= 115000000.0:
		tmp = (1.3333333333333333 / z0) / (z0 * z0)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0)
	t_0 = Float64(Float64(2.0 - Float64(-2.0 / z0)) / z0)
	tmp = 0.0
	if (z0 <= -3800.0)
		tmp = t_0;
	elseif (z0 <= 115000000.0)
		tmp = Float64(Float64(1.3333333333333333 / z0) / Float64(z0 * z0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0)
	t_0 = (2.0 - (-2.0 / z0)) / z0;
	tmp = 0.0;
	if (z0 <= -3800.0)
		tmp = t_0;
	elseif (z0 <= 115000000.0)
		tmp = (1.3333333333333333 / z0) / (z0 * z0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_] := Block[{t$95$0 = N[(N[(2.0 - N[(-2.0 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]}, If[LessEqual[z0, -3800.0], t$95$0, If[LessEqual[z0, 115000000.0], N[(N[(1.3333333333333333 / z0), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -3800 or 1.15e8 < z0

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \frac{2 - \frac{\color{blue}{\frac{13333333333333333}{10000000000000000}}}{\left(-z0\right) \cdot z0}}{z0} \]
   5. Step-by-step derivation

   6. Applied rewrites 97.9%

      \[\leadsto \frac{2 - \frac{\color{blue}{1.3333333333333333}}{\left(-z0\right) \cdot z0}}{z0} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 63.9%

         \[\leadsto \frac{2 - \frac{-2}{\color{blue}{z0}}}{z0} \]

   9. Applied rewrites 63.9%

      \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]

   if -3800 < z0 < 1.15e8

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{\frac{13333333333333333}{10000000000000000}}{z0}}}{z0 \cdot z0} \]
   3. Step-by-step derivation

      1. lower-/.f64 51.5%

         \[\leadsto \frac{\frac{1.3333333333333333}{\color{blue}{z0}}}{z0 \cdot z0} \]

   4. Applied rewrites 51.5%

      \[\leadsto \frac{\color{blue}{\frac{1.3333333333333333}{z0}}}{z0 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.9% accurate, 1.2× speedup

Math

\[\frac{\frac{1.3333333333333333}{z0 \cdot z0} + 2}{z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ (+ (/ 1.3333333333333333 (* z0 z0)) 2.0) z0))

C

double code(double z0) {
	return ((1.3333333333333333 / (z0 * z0)) + 2.0) / z0;
}

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 = ((1.3333333333333333d0 / (z0 * z0)) + 2.0d0) / z0
end function

Java

public static double code(double z0) {
	return ((1.3333333333333333 / (z0 * z0)) + 2.0) / z0;
}

Python

def code(z0):
	return ((1.3333333333333333 / (z0 * z0)) + 2.0) / z0

Julia

function code(z0)
	return Float64(Float64(Float64(1.3333333333333333 / Float64(z0 * z0)) + 2.0) / z0)
end

MATLAB

function tmp = code(z0)
	tmp = ((1.3333333333333333 / (z0 * z0)) + 2.0) / z0;
end

Wolfram

code[z0_] := N[(N[(N[(1.3333333333333333 / N[(z0 * z0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / z0), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

   3. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0}} \]

4. Taylor expanded in z0 around 0

   \[\leadsto \frac{2 - \frac{\color{blue}{\frac{13333333333333333}{10000000000000000}}}{\left(-z0\right) \cdot z0}}{z0} \]
5. Step-by-step derivation

6. Applied rewrites 97.9%

   \[\leadsto \frac{2 - \frac{\color{blue}{1.3333333333333333}}{\left(-z0\right) \cdot z0}}{z0} \]
7. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \frac{\color{blue}{2 - \frac{\frac{13333333333333333}{10000000000000000}}{\left(-z0\right) \cdot z0}}}{z0} \]

   2. sub-flip N/A

      \[\leadsto \frac{\color{blue}{2 + \left(\mathsf{neg}\left(\frac{\frac{13333333333333333}{10000000000000000}}{\left(-z0\right) \cdot z0}\right)\right)}}{z0} \]

   3. +-commutative N/A

      \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{\frac{13333333333333333}{10000000000000000}}{\left(-z0\right) \cdot z0}\right)\right) + 2}}{z0} \]

   4. lower-+.f64 N/A

      \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{\frac{13333333333333333}{10000000000000000}}{\left(-z0\right) \cdot z0}\right)\right) + 2}}{z0} \]

   5. lift-/.f64 N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\frac{\frac{13333333333333333}{10000000000000000}}{\left(-z0\right) \cdot z0}}\right)\right) + 2}{z0} \]

   6. distribute-neg-frac2 N/A

      \[\leadsto \frac{\color{blue}{\frac{\frac{13333333333333333}{10000000000000000}}{\mathsf{neg}\left(\left(-z0\right) \cdot z0\right)}} + 2}{z0} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\frac{\frac{13333333333333333}{10000000000000000}}{\mathsf{neg}\left(\color{blue}{\left(-z0\right) \cdot z0}\right)} + 2}{z0} \]

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

      \[\leadsto \frac{\frac{\frac{13333333333333333}{10000000000000000}}{\color{blue}{\left(-z0\right) \cdot \left(\mathsf{neg}\left(z0\right)\right)}} + 2}{z0} \]

   9. lift-neg.f64 N/A

      \[\leadsto \frac{\frac{\frac{13333333333333333}{10000000000000000}}{\color{blue}{\left(\mathsf{neg}\left(z0\right)\right)} \cdot \left(\mathsf{neg}\left(z0\right)\right)} + 2}{z0} \]

   10. sqr-neg-rev N/A

       \[\leadsto \frac{\frac{\frac{13333333333333333}{10000000000000000}}{\color{blue}{z0 \cdot z0}} + 2}{z0} \]

   11. lift-*.f64 N/A

       \[\leadsto \frac{\frac{\frac{13333333333333333}{10000000000000000}}{\color{blue}{z0 \cdot z0}} + 2}{z0} \]

   12. lower-/.f64 97.9%

       \[\leadsto \frac{\color{blue}{\frac{1.3333333333333333}{z0 \cdot z0}} + 2}{z0} \]

8. Applied rewrites 97.9%

   \[\leadsto \frac{\color{blue}{\frac{1.3333333333333333}{z0 \cdot z0} + 2}}{z0} \]
9. Add Preprocessing

Alternative 6: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \left(z0 + z0\right) - -2\\ \mathbf{if}\;\frac{t\_0 - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\frac{2}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{z0 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0)
  :precision binary64
  (let* ((t_0 (- (+ z0 z0) -2.0)))
  (if (<= (/ (- t_0 (/ -1.3333333333333333 z0)) (* z0 z0)) 5e-40)
    (/ 2.0 z0)
    (/ t_0 (* z0 z0)))))

C

double code(double z0) {
	double t_0 = (z0 + z0) - -2.0;
	double tmp;
	if (((t_0 - (-1.3333333333333333 / z0)) / (z0 * z0)) <= 5e-40) {
		tmp = 2.0 / z0;
	} else {
		tmp = t_0 / (z0 * z0);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z0 + z0) - (-2.0d0)
    if (((t_0 - ((-1.3333333333333333d0) / z0)) / (z0 * z0)) <= 5d-40) then
        tmp = 2.0d0 / z0
    else
        tmp = t_0 / (z0 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0) {
	double t_0 = (z0 + z0) - -2.0;
	double tmp;
	if (((t_0 - (-1.3333333333333333 / z0)) / (z0 * z0)) <= 5e-40) {
		tmp = 2.0 / z0;
	} else {
		tmp = t_0 / (z0 * z0);
	}
	return tmp;
}

Python

def code(z0):
	t_0 = (z0 + z0) - -2.0
	tmp = 0
	if ((t_0 - (-1.3333333333333333 / z0)) / (z0 * z0)) <= 5e-40:
		tmp = 2.0 / z0
	else:
		tmp = t_0 / (z0 * z0)
	return tmp

Julia

function code(z0)
	t_0 = Float64(Float64(z0 + z0) - -2.0)
	tmp = 0.0
	if (Float64(Float64(t_0 - Float64(-1.3333333333333333 / z0)) / Float64(z0 * z0)) <= 5e-40)
		tmp = Float64(2.0 / z0);
	else
		tmp = Float64(t_0 / Float64(z0 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0)
	t_0 = (z0 + z0) - -2.0;
	tmp = 0.0;
	if (((t_0 - (-1.3333333333333333 / z0)) / (z0 * z0)) <= 5e-40)
		tmp = 2.0 / z0;
	else
		tmp = t_0 / (z0 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_] := Block[{t$95$0 = N[(N[(z0 + z0), $MachinePrecision] - -2.0), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$0 - N[(-1.3333333333333333 / z0), $MachinePrecision]), $MachinePrecision] / N[(z0 * z0), $MachinePrecision]), $MachinePrecision], 5e-40], N[(2.0 / z0), $MachinePrecision], N[(t$95$0 / N[(z0 * z0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (-.f64 (+.f64 z0 z0) #s(literal -2 binary64)) (/.f64 #s(literal -13333333333333333/10000000000000000 binary64) z0)) (*.f64 z0 z0)) < 4.9999999999999996e-40

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{2}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 52.7%

         \[\leadsto \frac{2}{\color{blue}{z0}} \]

   4. Applied rewrites 52.7%

      \[\leadsto \color{blue}{\frac{2}{z0}} \]

   if 4.9999999999999996e-40 < (/.f64 (-.f64 (-.f64 (+.f64 z0 z0) #s(literal -2 binary64)) (/.f64 #s(literal -13333333333333333/10000000000000000 binary64) z0)) (*.f64 z0 z0))

   1. Initial program 76.1%

      \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z0}}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{\color{blue}{z0}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

      4. lower-/.f64 63.9%

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

   4. Applied rewrites 63.9%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z0}}{z0}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{\color{blue}{z0}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{2 + 2 \cdot \frac{1}{z0}}{z0} \]

      5. mult-flip-rev N/A

         \[\leadsto \frac{2 + \frac{2}{z0}}{z0} \]

      6. add-to-fraction N/A

         \[\leadsto \frac{\frac{2 \cdot z0 + 2}{z0}}{z0} \]

      7. count-2 N/A

         \[\leadsto \frac{\frac{\left(z0 + z0\right) + 2}{z0}}{z0} \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\frac{\left(z0 + z0\right) + 2}{z0}}{z0} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\left(z0 + z0\right) + \left(\mathsf{neg}\left(-2\right)\right)}{z0}}{z0} \]

      10. sub-flip N/A

          \[\leadsto \frac{\frac{\left(z0 + z0\right) - -2}{z0}}{z0} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{\frac{\left(z0 + z0\right) - -2}{z0}}{z0} \]

      12. associate-/r* N/A

          \[\leadsto \frac{\left(z0 + z0\right) - -2}{\color{blue}{z0 \cdot z0}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\left(z0 + z0\right) - -2}{z0 \cdot \color{blue}{z0}} \]

      14. lower-/.f64 40.1%

          \[\leadsto \frac{\left(z0 + z0\right) - -2}{\color{blue}{z0 \cdot z0}} \]

   6. Applied rewrites 40.1%

      \[\leadsto \frac{\left(z0 + z0\right) - -2}{\color{blue}{z0 \cdot z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.9% accurate, 1.4× speedup

Math

\[\frac{2 - \frac{-2}{z0}}{z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ (- 2.0 (/ -2.0 z0)) z0))

C

double code(double z0) {
	return (2.0 - (-2.0 / z0)) / z0;
}

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 = (2.0d0 - ((-2.0d0) / z0)) / z0
end function

Java

public static double code(double z0) {
	return (2.0 - (-2.0 / z0)) / z0;
}

Python

def code(z0):
	return (2.0 - (-2.0 / z0)) / z0

Julia

function code(z0)
	return Float64(Float64(2.0 - Float64(-2.0 / z0)) / z0)
end

MATLAB

function tmp = code(z0)
	tmp = (2.0 - (-2.0 / z0)) / z0;
end

Wolfram

code[z0_] := N[(N[(2.0 - N[(-2.0 / z0), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0 \cdot z0}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{\color{blue}{z0 \cdot z0}} \]

   3. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{\frac{-13333333333333333}{10000000000000000}}{z0}}{z0}}{z0}} \]

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\frac{2 - \frac{\left(z0 + z0\right) - -1.3333333333333333}{\left(-z0\right) \cdot z0}}{z0}} \]

4. Taylor expanded in z0 around 0

   \[\leadsto \frac{2 - \frac{\color{blue}{\frac{13333333333333333}{10000000000000000}}}{\left(-z0\right) \cdot z0}}{z0} \]
5. Step-by-step derivation

6. Applied rewrites 97.9%

   \[\leadsto \frac{2 - \frac{\color{blue}{1.3333333333333333}}{\left(-z0\right) \cdot z0}}{z0} \]

7. Taylor expanded in z0 around inf

   \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]
8. Step-by-step derivation

   1. lower-/.f64 63.9%

      \[\leadsto \frac{2 - \frac{-2}{\color{blue}{z0}}}{z0} \]

9. Applied rewrites 63.9%

   \[\leadsto \frac{2 - \color{blue}{\frac{-2}{z0}}}{z0} \]
10. Add Preprocessing

Alternative 8: 52.7% accurate, 3.1× speedup

Math

\[\frac{2}{z0} \]

FPCore

(FPCore (z0)
  :precision binary64
  (/ 2.0 z0))

C

double code(double z0) {
	return 2.0 / z0;
}

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 = 2.0d0 / z0
end function

Java

public static double code(double z0) {
	return 2.0 / z0;
}

Python

def code(z0):
	return 2.0 / z0

Julia

function code(z0)
	return Float64(2.0 / z0)
end

MATLAB

function tmp = code(z0)
	tmp = 2.0 / z0;
end

Wolfram

code[z0_] := N[(2.0 / z0), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{\left(\left(z0 + z0\right) - -2\right) - \frac{-1.3333333333333333}{z0}}{z0 \cdot z0} \]

2. Taylor expanded in z0 around inf

   \[\leadsto \color{blue}{\frac{2}{z0}} \]
3. Step-by-step derivation

   1. lower-/.f64 52.7%

      \[\leadsto \frac{2}{\color{blue}{z0}} \]

4. Applied rewrites 52.7%

   \[\leadsto \color{blue}{\frac{2}{z0}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0)
  :name "(/ (- (- (+ z0 z0) -2) (/ -13333333333333333/10000000000000000 z0)) (* z0 z0))"
  :precision binary64
  (/ (- (- (+ z0 z0) -2.0) (/ -1.3333333333333333 z0)) (* z0 z0)))