(/ (- (* (- (/ (* -552621316200069/25000000000000000 z0) z1) -2122065862260549/40000000000000000) z0) (* 3978873516901917/50000000000000000 z1)) (* (* z1 z0) z1))

Percentage Accurate: 77.7% → 99.6%

Time: 2.5s

Alternatives: 16

Speedup: 1.0×

• 63.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (-
  (* (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725) z0)
  (* 0.07957747033803834 z1))
 (* (* z1 z0) z1)))

C

double code(double z0, double z1) {
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = ((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)
end function

Java

public static double code(double z0, double z1) {
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
}

Python

def code(z0, z1):
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)

Julia

function code(z0, z1)
	return Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1))
end

MATLAB

function tmp = code(z0, z1)
	tmp = (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
end

Wolfram

code[z0_, z1_] := N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]

Initial Program: 77.7% accurate, 1.0× speedup

Math

\[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (-
  (* (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725) z0)
  (* 0.07957747033803834 z1))
 (* (* z1 z0) z1)))

C

double code(double z0, double z1) {
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = ((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)
end function

Java

public static double code(double z0, double z1) {
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
}

Python

def code(z0, z1):
	return (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)

Julia

function code(z0, z1)
	return Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1))
end

MATLAB

function tmp = code(z0, z1)
	tmp = (((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1);
end

Wolfram

code[z0_, z1_] := N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.9× speedup

Math

\[\frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (+
  (/ -0.07957747033803834 z0)
  (/
   (- 0.053051646556513725 (* (- z0) (/ -0.02210485264800276 z1)))
   z1))
 z1))

C

double code(double z0, double z1) {
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (-z0 * (-0.02210485264800276 / z1))) / z1)) / z1;
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = (((-0.07957747033803834d0) / z0) + ((0.053051646556513725d0 - (-z0 * ((-0.02210485264800276d0) / z1))) / z1)) / z1
end function

Java

public static double code(double z0, double z1) {
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (-z0 * (-0.02210485264800276 / z1))) / z1)) / z1;
}

Python

def code(z0, z1):
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (-z0 * (-0.02210485264800276 / z1))) / z1)) / z1

Julia

function code(z0, z1)
	return Float64(Float64(Float64(-0.07957747033803834 / z0) + Float64(Float64(0.053051646556513725 - Float64(Float64(-z0) * Float64(-0.02210485264800276 / z1))) / z1)) / z1)
end

MATLAB

function tmp = code(z0, z1)
	tmp = ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (-z0 * (-0.02210485264800276 / z1))) / z1)) / z1;
end

Wolfram

code[z0_, z1_] := N[(N[(N[(-0.07957747033803834 / z0), $MachinePrecision] + N[(N[(0.053051646556513725 - N[((-z0) * N[(-0.02210485264800276 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

   2. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

   3. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   6. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   7. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   8. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   10. lower-/.f64 99.6%

       \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

6. Applied rewrites 99.6%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{\color{blue}{z1}} \]
7. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \left(\mathsf{neg}\left(\frac{552621316200069}{25000000000000000}\right)\right) \cdot \frac{z0}{z1}}{z1}}{z1} \]

   4. metadata-eval N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   5. lift-/.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   6. associate-/l* N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}}{z1}}{z1} \]

   7. *-commutative N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   8. associate-/l* N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + z0 \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   9. fp-cancel-sign-sub-inv N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   10. lower--.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   11. lower-*.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   12. lower-neg.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   13. lower-/.f64 99.6%

       \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]

8. Applied rewrites 99.6%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]
9. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (+
  (/ -0.07957747033803834 z0)
  (/ (- 0.053051646556513725 (* 0.02210485264800276 (/ z0 z1))) z1))
 z1))

C

double code(double z0, double z1) {
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (0.02210485264800276 * (z0 / z1))) / z1)) / z1;
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = (((-0.07957747033803834d0) / z0) + ((0.053051646556513725d0 - (0.02210485264800276d0 * (z0 / z1))) / z1)) / z1
end function

Java

public static double code(double z0, double z1) {
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (0.02210485264800276 * (z0 / z1))) / z1)) / z1;
}

Python

def code(z0, z1):
	return ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (0.02210485264800276 * (z0 / z1))) / z1)) / z1

Julia

function code(z0, z1)
	return Float64(Float64(Float64(-0.07957747033803834 / z0) + Float64(Float64(0.053051646556513725 - Float64(0.02210485264800276 * Float64(z0 / z1))) / z1)) / z1)
end

MATLAB

function tmp = code(z0, z1)
	tmp = ((-0.07957747033803834 / z0) + ((0.053051646556513725 - (0.02210485264800276 * (z0 / z1))) / z1)) / z1;
end

Wolfram

code[z0_, z1_] := N[(N[(N[(-0.07957747033803834 / z0), $MachinePrecision] + N[(N[(0.053051646556513725 - N[(0.02210485264800276 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

   2. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

   3. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   6. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   7. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   8. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   10. lower-/.f64 99.6%

       \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

6. Applied rewrites 99.6%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{\color{blue}{z1}} \]
7. Add Preprocessing

Alternative 3: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -\infty:\\ \;\;\;\;\frac{\left(\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725\right) - \frac{0.07957747033803834 \cdot z1}{z0}}{z1 \cdot z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z0}{z1} \cdot -0.02210485264800276 - -0.053051646556513725}{z1 \cdot z1} + \frac{-0.07957747033803834}{z1 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     (- INFINITY))
  (/
   (-
    (- (/ (* z0 -0.02210485264800276) z1) -0.053051646556513725)
    (/ (* 0.07957747033803834 z1) z0))
   (* z1 z1))
  (+
   (/
    (- (* (/ z0 z1) -0.02210485264800276) -0.053051646556513725)
    (* z1 z1))
   (/ -0.07957747033803834 (* z1 z0)))))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -((double) INFINITY)) {
		tmp = ((((z0 * -0.02210485264800276) / z1) - -0.053051646556513725) - ((0.07957747033803834 * z1) / z0)) / (z1 * z1);
	} else {
		tmp = ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0));
	}
	return tmp;
}

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -Double.POSITIVE_INFINITY) {
		tmp = ((((z0 * -0.02210485264800276) / z1) - -0.053051646556513725) - ((0.07957747033803834 * z1) / z0)) / (z1 * z1);
	} else {
		tmp = ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0));
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -math.inf:
		tmp = ((((z0 * -0.02210485264800276) / z1) - -0.053051646556513725) - ((0.07957747033803834 * z1) / z0)) / (z1 * z1)
	else:
		tmp = ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0))
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(z0 * -0.02210485264800276) / z1) - -0.053051646556513725) - Float64(Float64(0.07957747033803834 * z1) / z0)) / Float64(z1 * z1));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / Float64(z1 * z1)) + Float64(-0.07957747033803834 / Float64(z1 * z0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -Inf)
		tmp = ((((z0 * -0.02210485264800276) / z1) - -0.053051646556513725) - ((0.07957747033803834 * z1) / z0)) / (z1 * z1);
	else
		tmp = ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(N[(N[(N[(N[(z0 * -0.02210485264800276), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] - N[(N[(0.07957747033803834 * z1), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(z0 / z1), $MachinePrecision] * -0.02210485264800276), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision] + N[(-0.07957747033803834 / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -inf.0

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot z0}}{z1}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot z0}}}{z1} \]

      5. *-commutative N/A

         \[\leadsto \frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z0 \cdot z1}}}{z1} \]

      6. associate-/r* N/A

         \[\leadsto \frac{\color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z0}}{z1}}}{z1} \]

      7. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z0}}{z1 \cdot z1}} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z0}}{z1 \cdot z1}} \]

   3. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\frac{\left(\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725\right) - \frac{0.07957747033803834 \cdot z1}{z0}}{z1 \cdot z1}} \]

   if -inf.0 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      3. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      8. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. lower-/.f64 99.6%

          \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

   6. Applied rewrites 99.6%

      \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{\color{blue}{z1}} \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \left(\mathsf{neg}\left(\frac{552621316200069}{25000000000000000}\right)\right) \cdot \frac{z0}{z1}}{z1}}{z1} \]

      4. metadata-eval N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}}{z1}}{z1} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      8. associate-/l* N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + z0 \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      9. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      12. lower-neg.f64 N/A

          \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      13. lower-/.f64 99.6%

          \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]

   8. Applied rewrites 99.6%

      \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{\color{blue}{z1}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

      3. +-commutative N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1} + \frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1} \]

      4. div-add N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} + \color{blue}{\frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} + \color{blue}{\frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1}} \]

   10. Applied rewrites 97.1%

       \[\leadsto \frac{\frac{z0}{z1} \cdot -0.02210485264800276 - -0.053051646556513725}{z1 \cdot z1} + \color{blue}{\frac{-0.07957747033803834}{z1 \cdot z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.1% accurate, 1.0× speedup

Math

\[\frac{\frac{z0}{z1} \cdot -0.02210485264800276 - -0.053051646556513725}{z1 \cdot z1} + \frac{-0.07957747033803834}{z1 \cdot z0} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (+
 (/
  (- (* (/ z0 z1) -0.02210485264800276) -0.053051646556513725)
  (* z1 z1))
 (/ -0.07957747033803834 (* z1 z0))))

C

double code(double z0, double z1) {
	return ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = ((((z0 / z1) * (-0.02210485264800276d0)) - (-0.053051646556513725d0)) / (z1 * z1)) + ((-0.07957747033803834d0) / (z1 * z0))
end function

Java

public static double code(double z0, double z1) {
	return ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0));
}

Python

def code(z0, z1):
	return ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0))

Julia

function code(z0, z1)
	return Float64(Float64(Float64(Float64(Float64(z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / Float64(z1 * z1)) + Float64(-0.07957747033803834 / Float64(z1 * z0)))
end

MATLAB

function tmp = code(z0, z1)
	tmp = ((((z0 / z1) * -0.02210485264800276) - -0.053051646556513725) / (z1 * z1)) + (-0.07957747033803834 / (z1 * z0));
end

Wolfram

code[z0_, z1_] := N[(N[(N[(N[(N[(z0 / z1), $MachinePrecision] * -0.02210485264800276), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision] + N[(-0.07957747033803834 / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

   2. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

   3. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   6. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   7. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   8. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   10. lower-/.f64 99.6%

       \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

6. Applied rewrites 99.6%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{\color{blue}{z1}} \]
7. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \left(\mathsf{neg}\left(\frac{552621316200069}{25000000000000000}\right)\right) \cdot \frac{z0}{z1}}{z1}}{z1} \]

   4. metadata-eval N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   5. lift-/.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1}}{z1} \]

   6. associate-/l* N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}}{z1}}{z1} \]

   7. *-commutative N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + \frac{z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   8. associate-/l* N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} + z0 \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   9. fp-cancel-sign-sub-inv N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   10. lower--.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   11. lower-*.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(\mathsf{neg}\left(z0\right)\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   12. lower-neg.f64 N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   13. lower-/.f64 99.6%

       \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]

8. Applied rewrites 99.6%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - \left(-z0\right) \cdot \frac{-0.02210485264800276}{z1}}{z1}}{z1} \]
9. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{\color{blue}{z1}} \]

   2. lift-+.f64 N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0} + \frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} \]

   3. +-commutative N/A

      \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1} + \frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1} \]

   4. div-add N/A

      \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} + \color{blue}{\frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1}} \]

   5. lower-+.f64 N/A

      \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} - \left(-z0\right) \cdot \frac{\frac{-552621316200069}{25000000000000000}}{z1}}{z1}}{z1} + \color{blue}{\frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1}} \]

10. Applied rewrites 97.1%

    \[\leadsto \frac{\frac{z0}{z1} \cdot -0.02210485264800276 - -0.053051646556513725}{z1 \cdot z1} + \color{blue}{\frac{-0.07957747033803834}{z1 \cdot z0}} \]
11. Add Preprocessing

Alternative 5: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -1e+131)
  (/
   (-
    (*
     (- (* (/ -0.02210485264800276 z1) z0) -0.053051646556513725)
     z0)
    (* 0.07957747033803834 z1))
   (* (* z1 z1) z0))
  (/
   (-
    (*
     z0
     (/
      (- (* z0 -0.02210485264800276) (* -0.053051646556513725 z1))
      (* z1 z1)))
    0.07957747033803834)
   (* z1 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -1e+131) {
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z1) * z0);
	} else {
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-1d+131)) then
        tmp = ((((((-0.02210485264800276d0) / z1) * z0) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z1) * z0)
    else
        tmp = ((z0 * (((z0 * (-0.02210485264800276d0)) - ((-0.053051646556513725d0) * z1)) / (z1 * z1))) - 0.07957747033803834d0) / (z1 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -1e+131) {
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z1) * z0);
	} else {
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -1e+131:
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z1) * z0)
	else:
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0)
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -1e+131)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(Float64(z0 * Float64(Float64(Float64(z0 * -0.02210485264800276) - Float64(-0.053051646556513725 * z1)) / Float64(z1 * z1))) - 0.07957747033803834) / Float64(z1 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -1e+131)
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z1) * z0);
	else
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -1e+131], N[(N[(N[(N[(N[(N[(-0.02210485264800276 / z1), $MachinePrecision] * z0), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z0 * N[(N[(N[(z0 * -0.02210485264800276), $MachinePrecision] - N[(-0.053051646556513725 * z1), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -9.9999999999999991e130

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   if -9.9999999999999991e130 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      3. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      8. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. lower-/.f64 99.6%

          \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

   6. Applied rewrites 77.1%

      \[\leadsto \frac{\frac{\left(0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276\right) \cdot z0}{z1 \cdot z1} - 0.07957747033803834}{\color{blue}{z1 \cdot z0}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{z0 \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right)}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      4. associate-/l* N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      6. lower-/.f64 91.0%

         \[\leadsto \frac{z0 \cdot \frac{0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      8. +-commutative N/A

         \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      10. fp-cancel-sign-sub-inv N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \left(\mathsf{neg}\left(\frac{2122065862260549}{40000000000000000}\right)\right) \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      11. metadata-eval N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      12. lower--.f64 N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      13. lower-*.f64 91.0%

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

   8. Applied rewrites 91.0%

      \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(z1 \cdot z0\right) \cdot z1\\ \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{t\_0} \leq -4 \cdot 10^{+195}:\\ \;\;\;\;\frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (* (* z1 z0) z1)))
  (if (<=
       (/
        (-
         (*
          (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
          z0)
         (* 0.07957747033803834 z1))
        t_0)
       -4e+195)
    (/
     (-
      (*
       (- (* (/ -0.02210485264800276 z1) z0) -0.053051646556513725)
       z0)
      (* 0.07957747033803834 z1))
     t_0)
    (/
     (-
      (*
       z0
       (/
        (- (* z0 -0.02210485264800276) (* -0.053051646556513725 z1))
        (* z1 z1)))
      0.07957747033803834)
     (* z1 z0)))))

C

double code(double z0, double z1) {
	double t_0 = (z1 * z0) * z1;
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0) <= -4e+195) {
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0;
	} else {
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z1 * z0) * z1
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / t_0) <= (-4d+195)) then
        tmp = ((((((-0.02210485264800276d0) / z1) * z0) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / t_0
    else
        tmp = ((z0 * (((z0 * (-0.02210485264800276d0)) - ((-0.053051646556513725d0) * z1)) / (z1 * z1))) - 0.07957747033803834d0) / (z1 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = (z1 * z0) * z1;
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0) <= -4e+195) {
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0;
	} else {
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (z1 * z0) * z1
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0) <= -4e+195:
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0
	else:
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0)
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(z1 * z0) * z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / t_0) <= -4e+195)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / t_0);
	else
		tmp = Float64(Float64(Float64(z0 * Float64(Float64(Float64(z0 * -0.02210485264800276) - Float64(-0.053051646556513725 * z1)) / Float64(z1 * z1))) - 0.07957747033803834) / Float64(z1 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (z1 * z0) * z1;
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0) <= -4e+195)
		tmp = (((((-0.02210485264800276 / z1) * z0) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / t_0;
	else
		tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], -4e+195], N[(N[(N[(N[(N[(N[(-0.02210485264800276 / z1), $MachinePrecision] * z0), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(N[(z0 * N[(N[(N[(z0 * -0.02210485264800276), $MachinePrecision] - N[(-0.053051646556513725 * z1), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -3.9999999999999999e195

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   if -3.9999999999999999e195 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      3. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      8. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. lower-/.f64 99.6%

          \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

   6. Applied rewrites 77.1%

      \[\leadsto \frac{\frac{\left(0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276\right) \cdot z0}{z1 \cdot z1} - 0.07957747033803834}{\color{blue}{z1 \cdot z0}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{z0 \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right)}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      4. associate-/l* N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      6. lower-/.f64 91.0%

         \[\leadsto \frac{z0 \cdot \frac{0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      8. +-commutative N/A

         \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      10. fp-cancel-sign-sub-inv N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \left(\mathsf{neg}\left(\frac{2122065862260549}{40000000000000000}\right)\right) \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      11. metadata-eval N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      12. lower--.f64 N/A

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      13. lower-*.f64 91.0%

          \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

   8. Applied rewrites 91.0%

      \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 91.0% accurate, 1.0× speedup

Math

\[\frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 (-
  (*
   z0
   (/
    (- (* z0 -0.02210485264800276) (* -0.053051646556513725 z1))
    (* z1 z1)))
  0.07957747033803834)
 (* z1 z0)))

C

double code(double z0, double z1) {
	return ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = ((z0 * (((z0 * (-0.02210485264800276d0)) - ((-0.053051646556513725d0) * z1)) / (z1 * z1))) - 0.07957747033803834d0) / (z1 * z0)
end function

Java

public static double code(double z0, double z1) {
	return ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
}

Python

def code(z0, z1):
	return ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0)

Julia

function code(z0, z1)
	return Float64(Float64(Float64(z0 * Float64(Float64(Float64(z0 * -0.02210485264800276) - Float64(-0.053051646556513725 * z1)) / Float64(z1 * z1))) - 0.07957747033803834) / Float64(z1 * z0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = ((z0 * (((z0 * -0.02210485264800276) - (-0.053051646556513725 * z1)) / (z1 * z1))) - 0.07957747033803834) / (z1 * z0);
end

Wolfram

code[z0_, z1_] := N[(N[(N[(z0 * N[(N[(N[(z0 * -0.02210485264800276), $MachinePrecision] - N[(-0.053051646556513725 * z1), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z1 around -inf

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

   2. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

   3. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   6. lower-+.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   7. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   8. lower-/.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   10. lower-/.f64 99.6%

       \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

6. Applied rewrites 77.1%

   \[\leadsto \frac{\frac{\left(0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276\right) \cdot z0}{z1 \cdot z1} - 0.07957747033803834}{\color{blue}{z1 \cdot z0}} \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\frac{\left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right) \cdot z0}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   3. *-commutative N/A

      \[\leadsto \frac{\frac{z0 \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}\right)}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   4. associate-/l* N/A

      \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   6. lower-/.f64 91.0%

      \[\leadsto \frac{z0 \cdot \frac{0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

   7. lift-+.f64 N/A

      \[\leadsto \frac{z0 \cdot \frac{\frac{2122065862260549}{40000000000000000} \cdot z1 + z0 \cdot \frac{-552621316200069}{25000000000000000}}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   8. +-commutative N/A

      \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   9. lift-*.f64 N/A

      \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} + \frac{2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   10. fp-cancel-sign-sub-inv N/A

       \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \left(\mathsf{neg}\left(\frac{2122065862260549}{40000000000000000}\right)\right) \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   11. metadata-eval N/A

       \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   12. lower--.f64 N/A

       \[\leadsto \frac{z0 \cdot \frac{z0 \cdot \frac{-552621316200069}{25000000000000000} - \frac{-2122065862260549}{40000000000000000} \cdot z1}{z1 \cdot z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

   13. lower-*.f64 91.0%

       \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]

8. Applied rewrites 91.0%

   \[\leadsto \frac{z0 \cdot \frac{z0 \cdot -0.02210485264800276 - -0.053051646556513725 \cdot z1}{z1 \cdot z1} - 0.07957747033803834}{z1 \cdot z0} \]
9. Add Preprocessing

Alternative 8: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\frac{z0}{z1} \cdot 0.053051646556513725 - 0.07957747033803834}{z1}}{2 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -5e+31)
  (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
  (/
   (*
    2.0
    (/ (- (* (/ z0 z1) 0.053051646556513725) 0.07957747033803834) z1))
   (* 2.0 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (2.0 * ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1)) / (2.0 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-5d+31)) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = (2.0d0 * ((((z0 / z1) * 0.053051646556513725d0) - 0.07957747033803834d0) / z1)) / (2.0d0 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (2.0 * ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1)) / (2.0 * z0);
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = (2.0 * ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1)) / (2.0 * z0)
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -5e+31)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(2.0 * Float64(Float64(Float64(Float64(z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1)) / Float64(2.0 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = (2.0 * ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1)) / (2.0 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -5e+31], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(N[(N[(N[(z0 / z1), $MachinePrecision] * 0.053051646556513725), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / N[(2.0 * z0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -5.0000000000000003e31

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if -5.0000000000000003e31 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z1 \cdot z0\right)}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1}}{z1 \cdot z0}} \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

   3. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\left(z0 \cdot \frac{\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725}{z1} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \left(\color{blue}{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \color{blue}{\frac{z0}{z1}} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1}{z1 \cdot z0} \]

      2. lower-/.f64 64.5%

         \[\leadsto \left(0.053051646556513725 \cdot \frac{z0}{\color{blue}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]

   6. Applied rewrites 64.5%

      \[\leadsto \left(\color{blue}{0.053051646556513725 \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1}{z1 \cdot z0}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \color{blue}{\frac{1}{z1 \cdot z0}} \]

      3. metadata-eval N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{\color{blue}{1 \cdot 1}}{z1 \cdot z0} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1 \cdot 1}{\color{blue}{z1 \cdot z0}} \]

      5. frac-times N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \color{blue}{\left(\frac{1}{z1} \cdot \frac{1}{z0}\right)} \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \left(\color{blue}{\frac{1}{z1}} \cdot \frac{1}{z0}\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \left(\frac{1}{z1} \cdot \color{blue}{\frac{1}{z0}}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \color{blue}{\left(\frac{1}{z1} \cdot \frac{1}{z0}\right)} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{1}{z1} \cdot \frac{1}{z0}\right) \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right)} \]

      10. *-lft-identity N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(\frac{1}{z1} \cdot \frac{1}{z0}\right)\right)} \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{1 \cdot \left(\left(\frac{1}{z1} \cdot \frac{1}{z0}\right) \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right)\right)} \]

      12. metadata-eval N/A

          \[\leadsto \color{blue}{\frac{2}{2}} \cdot \left(\left(\frac{1}{z1} \cdot \frac{1}{z0}\right) \cdot \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{2}{2} \cdot \color{blue}{\left(\left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \left(\frac{1}{z1} \cdot \frac{1}{z0}\right)\right)} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{2}{2} \cdot \left(\left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \color{blue}{\left(\frac{1}{z1} \cdot \frac{1}{z0}\right)}\right) \]

   8. Applied rewrites 66.3%

      \[\leadsto \color{blue}{\frac{2 \cdot \frac{\frac{z0}{z1} \cdot 0.053051646556513725 - 0.07957747033803834}{z1}}{2 \cdot z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{z0}{z1} \cdot 0.053051646556513725 - 0.07957747033803834}{z1}}{z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -5e+31)
  (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
  (/
   (/ (- (* (/ z0 z1) 0.053051646556513725) 0.07957747033803834) z1)
   z0)))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1) / 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-5d+31)) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = ((((z0 / z1) * 0.053051646556513725d0) - 0.07957747033803834d0) / z1) / z0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1) / z0;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1) / z0
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -5e+31)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1) / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = ((((z0 / z1) * 0.053051646556513725) - 0.07957747033803834) / z1) / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -5e+31], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(z0 / z1), $MachinePrecision] * 0.053051646556513725), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / z1), $MachinePrecision] / z0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -5.0000000000000003e31

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if -5.0000000000000003e31 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z1 \cdot z0\right)}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1}}{z1 \cdot z0}} \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

   3. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\left(z0 \cdot \frac{\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725}{z1} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \left(\color{blue}{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \color{blue}{\frac{z0}{z1}} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1}{z1 \cdot z0} \]

      2. lower-/.f64 64.5%

         \[\leadsto \left(0.053051646556513725 \cdot \frac{z0}{\color{blue}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]

   6. Applied rewrites 64.5%

      \[\leadsto \left(\color{blue}{0.053051646556513725 \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1}{z1 \cdot z0}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}\right) \cdot \color{blue}{\frac{1}{z1 \cdot z0}} \]

      3. mult-flip-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{\color{blue}{z1 \cdot z0}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z1}}{z0}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z1}}{z0}} \]

      7. lower-/.f64 66.3%

         \[\leadsto \frac{\color{blue}{\frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z1}}}{z0} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \color{blue}{\frac{z0}{z1}} - \frac{3978873516901917}{50000000000000000}}{z1}}{z0} \]

      9. *-commutative N/A

         \[\leadsto \frac{\frac{\frac{z0}{z1} \cdot \color{blue}{\frac{2122065862260549}{40000000000000000}} - \frac{3978873516901917}{50000000000000000}}{z1}}{z0} \]

      10. lower-*.f64 66.3%

          \[\leadsto \frac{\frac{\frac{z0}{z1} \cdot \color{blue}{0.053051646556513725} - 0.07957747033803834}{z1}}{z0} \]

   8. Applied rewrites 66.3%

      \[\leadsto \color{blue}{\frac{\frac{\frac{z0}{z1} \cdot 0.053051646556513725 - 0.07957747033803834}{z1}}{z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z0}}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -5e+31)
  (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
  (/
   (/ (- (* 0.053051646556513725 (/ z0 z1)) 0.07957747033803834) z0)
   z1)))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / z0) / z1;
	}
	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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-5d+31)) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = (((0.053051646556513725d0 * (z0 / z1)) - 0.07957747033803834d0) / z0) / z1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / z0) / z1;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = (((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / z0) / z1
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -5e+31)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(Float64(Float64(0.053051646556513725 * Float64(z0 / z1)) - 0.07957747033803834) / z0) / z1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = (((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / z0) / z1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -5e+31], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.053051646556513725 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / z0), $MachinePrecision] / z1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -5.0000000000000003e31

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if -5.0000000000000003e31 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      3. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      8. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. lower-/.f64 99.6%

          \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

   6. Applied rewrites 99.6%

      \[\leadsto \frac{\frac{-0.07957747033803834}{z0} + \frac{0.053051646556513725 - 0.02210485264800276 \cdot \frac{z0}{z1}}{z1}}{\color{blue}{z1}} \]

   7. Taylor expanded in z0 around 0

      \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z0}}{z1} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z0}}{z1} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z0}}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z0}}{z1} \]

      4. lower-/.f64 64.7%

         \[\leadsto \frac{\frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z0}}{z1} \]

   9. Applied rewrites 64.7%

      \[\leadsto \frac{\frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z0}}{z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\left(0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -5e+31)
  (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
  (*
   (- (* 0.053051646556513725 (/ z0 z1)) 0.07957747033803834)
   (/ 1.0 (* z1 z0)))))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) * (1.0 / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-5d+31)) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = ((0.053051646556513725d0 * (z0 / z1)) - 0.07957747033803834d0) * (1.0d0 / (z1 * z0))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) * (1.0 / (z1 * z0));
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) * (1.0 / (z1 * z0))
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -5e+31)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(Float64(0.053051646556513725 * Float64(z0 / z1)) - 0.07957747033803834) * Float64(1.0 / Float64(z1 * z0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) * (1.0 / (z1 * z0));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -5e+31], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.053051646556513725 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] * N[(1.0 / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -5.0000000000000003e31

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if -5.0000000000000003e31 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z1 \cdot z0\right)}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1}}{z1 \cdot z0}} \]

      5. mult-flip N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

   3. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\left(z0 \cdot \frac{\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725}{z1} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0}} \]

   4. Taylor expanded in z0 around 0

      \[\leadsto \left(\color{blue}{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\frac{2122065862260549}{40000000000000000} \cdot \color{blue}{\frac{z0}{z1}} - \frac{3978873516901917}{50000000000000000}\right) \cdot \frac{1}{z1 \cdot z0} \]

      2. lower-/.f64 64.5%

         \[\leadsto \left(0.053051646556513725 \cdot \frac{z0}{\color{blue}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]

   6. Applied rewrites 64.5%

      \[\leadsto \left(\color{blue}{0.053051646556513725 \cdot \frac{z0}{z1}} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z1 \cdot z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<=
     (/
      (-
       (*
        (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725)
        z0)
       (* 0.07957747033803834 z1))
      (* (* z1 z0) z1))
     -5e+31)
  (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
  (/
   (- (* 0.053051646556513725 (/ z0 z1)) 0.07957747033803834)
   (* z1 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((((((((-0.02210485264800276d0) * z0) / z1) - (-0.053051646556513725d0)) * z0) - (0.07957747033803834d0 * z1)) / ((z1 * z0) * z1)) <= (-5d+31)) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = ((0.053051646556513725d0 * (z0 / z1)) - 0.07957747033803834d0) / (z1 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / (z1 * z0);
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if ((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / (z1 * z0)
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - Float64(0.07957747033803834 * z1)) / Float64(Float64(z1 * z0) * z1)) <= -5e+31)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(Float64(0.053051646556513725 * Float64(z0 / z1)) - 0.07957747033803834) / Float64(z1 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (((((((-0.02210485264800276 * z0) / z1) - -0.053051646556513725) * z0) - (0.07957747033803834 * z1)) / ((z1 * z0) * z1)) <= -5e+31)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = ((0.053051646556513725 * (z0 / z1)) - 0.07957747033803834) / (z1 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[(N[(N[(N[(N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] - -0.053051646556513725), $MachinePrecision] * z0), $MachinePrecision] - N[(0.07957747033803834 * z1), $MachinePrecision]), $MachinePrecision] / N[(N[(z1 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], -5e+31], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.053051646556513725 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision] - 0.07957747033803834), $MachinePrecision] / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1)) < -5.0000000000000003e31

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if -5.0000000000000003e31 < (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1) #s(literal -2122065862260549/40000000000000000 binary64)) z0) (*.f64 #s(literal 3978873516901917/50000000000000000 binary64) z1)) (*.f64 (*.f64 z1 z0) z1))

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1}} \]

      2. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      3. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      6. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      8. lower-/.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{\frac{2122065862260549}{40000000000000000} + \frac{-552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}{z1} + \frac{3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. lower-/.f64 99.6%

          \[\leadsto -1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{0.053051646556513725 + -0.02210485264800276 \cdot \frac{z0}{z1}}{z1} + 0.07957747033803834 \cdot \frac{1}{z0}}{z1}} \]

   6. Applied rewrites 77.1%

      \[\leadsto \frac{\frac{\left(0.053051646556513725 \cdot z1 + z0 \cdot -0.02210485264800276\right) \cdot z0}{z1 \cdot z1} - 0.07957747033803834}{\color{blue}{z1 \cdot z0}} \]

   7. Taylor expanded in z0 around 0

      \[\leadsto \frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - 0.07957747033803834}{z1 \cdot z0} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{2122065862260549}{40000000000000000} \cdot \frac{z0}{z1} - \frac{3978873516901917}{50000000000000000}}{z1 \cdot z0} \]

      2. lower-/.f64 64.5%

         \[\leadsto \frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z1 \cdot z0} \]

   9. Applied rewrites 64.5%

      \[\leadsto \frac{0.053051646556513725 \cdot \frac{z0}{z1} - 0.07957747033803834}{z1 \cdot z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z1 \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{-0.07957747033803834}{z1}}{z0}\\ \mathbf{elif}\;z1 \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\frac{-0.07957747033803834 \cdot z1}{\left(z1 \cdot z1\right) \cdot z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-0.07957747033803834}{z0}}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= z1 -1.5e-156)
  (/ (/ -0.07957747033803834 z1) z0)
  (if (<= z1 2e-69)
    (/ (* -0.07957747033803834 z1) (* (* z1 z1) z0))
    (/ (/ -0.07957747033803834 z0) z1))))

C

double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.5e-156) {
		tmp = (-0.07957747033803834 / z1) / z0;
	} else if (z1 <= 2e-69) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (-0.07957747033803834 / z0) / z1;
	}
	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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z1 <= (-1.5d-156)) then
        tmp = ((-0.07957747033803834d0) / z1) / z0
    else if (z1 <= 2d-69) then
        tmp = ((-0.07957747033803834d0) * z1) / ((z1 * z1) * z0)
    else
        tmp = ((-0.07957747033803834d0) / z0) / z1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.5e-156) {
		tmp = (-0.07957747033803834 / z1) / z0;
	} else if (z1 <= 2e-69) {
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	} else {
		tmp = (-0.07957747033803834 / z0) / z1;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if z1 <= -1.5e-156:
		tmp = (-0.07957747033803834 / z1) / z0
	elif z1 <= 2e-69:
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0)
	else:
		tmp = (-0.07957747033803834 / z0) / z1
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (z1 <= -1.5e-156)
		tmp = Float64(Float64(-0.07957747033803834 / z1) / z0);
	elseif (z1 <= 2e-69)
		tmp = Float64(Float64(-0.07957747033803834 * z1) / Float64(Float64(z1 * z1) * z0));
	else
		tmp = Float64(Float64(-0.07957747033803834 / z0) / z1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (z1 <= -1.5e-156)
		tmp = (-0.07957747033803834 / z1) / z0;
	elseif (z1 <= 2e-69)
		tmp = (-0.07957747033803834 * z1) / ((z1 * z1) * z0);
	else
		tmp = (-0.07957747033803834 / z0) / z1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[z1, -1.5e-156], N[(N[(-0.07957747033803834 / z1), $MachinePrecision] / z0), $MachinePrecision], If[LessEqual[z1, 2e-69], N[(N[(-0.07957747033803834 * z1), $MachinePrecision] / N[(N[(z1 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision], N[(N[(-0.07957747033803834 / z0), $MachinePrecision] / z1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z1 < -1.5000000000000001e-156

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

      2. lower-*.f64 59.1%

         \[\leadsto \frac{-0.07957747033803834}{z0 \cdot \color{blue}{z1}} \]

   4. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\frac{-0.07957747033803834}{z0 \cdot z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot \color{blue}{z1}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{z1 \cdot \color{blue}{z0}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z1}}{\color{blue}{z0}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z1}}{\color{blue}{z0}} \]

      6. lower-/.f64 59.3%

         \[\leadsto \frac{\frac{-0.07957747033803834}{z1}}{z0} \]

   6. Applied rewrites 59.3%

      \[\leadsto \frac{\frac{-0.07957747033803834}{z1}}{\color{blue}{z0}} \]

   if -1.5000000000000001e-156 < z1 < 1.9999999999999999e-69

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      2. mult-flip N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1}} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(z0 \cdot \frac{-552621316200069}{25000000000000000}\right)} \cdot \frac{1}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{z0 \cdot \left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right)} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\frac{-552621316200069}{25000000000000000} \cdot \frac{1}{z1}\right) \cdot z0} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      8. mult-flip-rev N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{\frac{-552621316200069}{25000000000000000}}{z1}} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

      9. lower-/.f64 77.7%

         \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1}} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   3. Applied rewrites 77.7%

      \[\leadsto \frac{\left(\color{blue}{\frac{-0.02210485264800276}{z1} \cdot z0} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right)} \cdot z1} \]

      3. associate-*l* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z0 \cdot z1\right)}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1 \cdot \color{blue}{\left(z1 \cdot z0\right)}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000}}{z1} \cdot z0 - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

      7. lower-*.f64 71.9%

         \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right)} \cdot z0} \]

   5. Applied rewrites 71.9%

      \[\leadsto \frac{\left(\frac{-0.02210485264800276}{z1} \cdot z0 - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\color{blue}{\left(z1 \cdot z1\right) \cdot z0}} \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-3978873516901917}{50000000000000000} \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]
   7. Step-by-step derivation

      1. lower-*.f64 55.8%

         \[\leadsto \frac{-0.07957747033803834 \cdot \color{blue}{z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   8. Applied rewrites 55.8%

      \[\leadsto \frac{\color{blue}{-0.07957747033803834 \cdot z1}}{\left(z1 \cdot z1\right) \cdot z0} \]

   if 1.9999999999999999e-69 < z1

   1. Initial program 77.7%

      \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

      2. lower-*.f64 59.1%

         \[\leadsto \frac{-0.07957747033803834}{z0 \cdot \color{blue}{z1}} \]

   4. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\frac{-0.07957747033803834}{z0 \cdot z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot \color{blue}{z1}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{\color{blue}{z1}} \]

      4. mult-flip-rev N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{z1} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{z1} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

      8. metadata-eval N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

      10. mult-flip-rev N/A

          \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1} \]

      11. lower-/.f64 59.3%

          \[\leadsto \frac{\frac{-0.07957747033803834}{z0}}{z1} \]

   6. Applied rewrites 59.3%

      \[\leadsto \frac{\frac{-0.07957747033803834}{z0}}{\color{blue}{z1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 59.3% accurate, 2.3× speedup

Math

\[\frac{\frac{-0.07957747033803834}{z0}}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/ (/ -0.07957747033803834 z0) z1))

C

double code(double z0, double z1) {
	return (-0.07957747033803834 / z0) / z1;
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = ((-0.07957747033803834d0) / z0) / z1
end function

Java

public static double code(double z0, double z1) {
	return (-0.07957747033803834 / z0) / z1;
}

Python

def code(z0, z1):
	return (-0.07957747033803834 / z0) / z1

Julia

function code(z0, z1)
	return Float64(Float64(-0.07957747033803834 / z0) / z1)
end

MATLAB

function tmp = code(z0, z1)
	tmp = (-0.07957747033803834 / z0) / z1;
end

Wolfram

code[z0_, z1_] := N[(N[(-0.07957747033803834 / z0), $MachinePrecision] / z1), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot z1}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

   2. lower-*.f64 59.1%

      \[\leadsto \frac{-0.07957747033803834}{z0 \cdot \color{blue}{z1}} \]

4. Applied rewrites 59.1%

   \[\leadsto \color{blue}{\frac{-0.07957747033803834}{z0 \cdot z1}} \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot \color{blue}{z1}} \]

   3. associate-/r* N/A

      \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{\color{blue}{z1}} \]

   4. mult-flip-rev N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{z1} \]

   6. lift-/.f64 N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{z1} \]

   7. lower-/.f64 N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{3978873516901917}{50000000000000000}\right)\right) \cdot \frac{1}{z0}}{\color{blue}{z1}} \]

   8. metadata-eval N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   9. lift-/.f64 N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000} \cdot \frac{1}{z0}}{z1} \]

   10. mult-flip-rev N/A

       \[\leadsto \frac{\frac{\frac{-3978873516901917}{50000000000000000}}{z0}}{z1} \]

   11. lower-/.f64 59.3%

       \[\leadsto \frac{\frac{-0.07957747033803834}{z0}}{z1} \]

6. Applied rewrites 59.3%

   \[\leadsto \frac{\frac{-0.07957747033803834}{z0}}{\color{blue}{z1}} \]
7. Add Preprocessing

Alternative 15: 59.1% accurate, 2.5× speedup

Math

\[-0.07957747033803834 \cdot \frac{1}{z1 \cdot z0} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (* -0.07957747033803834 (/ 1.0 (* z1 z0))))

C

double code(double z0, double z1) {
	return -0.07957747033803834 * (1.0 / (z1 * 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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = (-0.07957747033803834d0) * (1.0d0 / (z1 * z0))
end function

Java

public static double code(double z0, double z1) {
	return -0.07957747033803834 * (1.0 / (z1 * z0));
}

Python

def code(z0, z1):
	return -0.07957747033803834 * (1.0 / (z1 * z0))

Julia

function code(z0, z1)
	return Float64(-0.07957747033803834 * Float64(1.0 / Float64(z1 * z0)))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -0.07957747033803834 * (1.0 / (z1 * z0));
end

Wolfram

code[z0_, z1_] := N[(-0.07957747033803834 * N[(1.0 / N[(z1 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\left(z1 \cdot z0\right) \cdot z1}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{\left(z1 \cdot z0\right) \cdot z1}} \]

   3. *-commutative N/A

      \[\leadsto \frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{\color{blue}{z1 \cdot \left(z1 \cdot z0\right)}} \]

   4. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1}}{z1 \cdot z0}} \]

   5. mult-flip N/A

      \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

   6. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\frac{\frac{-552621316200069}{25000000000000000} \cdot z0}{z1} - \frac{-2122065862260549}{40000000000000000}\right) \cdot z0 - \frac{3978873516901917}{50000000000000000} \cdot z1}{z1} \cdot \frac{1}{z1 \cdot z0}} \]

3. Applied rewrites 92.1%

   \[\leadsto \color{blue}{\left(z0 \cdot \frac{\frac{z0 \cdot -0.02210485264800276}{z1} - -0.053051646556513725}{z1} - 0.07957747033803834\right) \cdot \frac{1}{z1 \cdot z0}} \]

4. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\frac{-3978873516901917}{50000000000000000}} \cdot \frac{1}{z1 \cdot z0} \]
5. Step-by-step derivation

6. Applied rewrites 59.1%

   \[\leadsto \color{blue}{-0.07957747033803834} \cdot \frac{1}{z1 \cdot z0} \]
7. Add Preprocessing

Alternative 16: 59.1% accurate, 3.2× speedup

Math

\[\frac{-0.07957747033803834}{z0 \cdot z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/ -0.07957747033803834 (* z0 z1)))

C

double code(double z0, double z1) {
	return -0.07957747033803834 / (z0 * z1);
}

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, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = (-0.07957747033803834d0) / (z0 * z1)
end function

Java

public static double code(double z0, double z1) {
	return -0.07957747033803834 / (z0 * z1);
}

Python

def code(z0, z1):
	return -0.07957747033803834 / (z0 * z1)

Julia

function code(z0, z1)
	return Float64(-0.07957747033803834 / Float64(z0 * z1))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -0.07957747033803834 / (z0 * z1);
end

Wolfram

code[z0_, z1_] := N[(-0.07957747033803834 / N[(z0 * z1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[\frac{\left(\frac{-0.02210485264800276 \cdot z0}{z1} - -0.053051646556513725\right) \cdot z0 - 0.07957747033803834 \cdot z1}{\left(z1 \cdot z0\right) \cdot z1} \]

2. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\frac{\frac{-3978873516901917}{50000000000000000}}{z0 \cdot z1}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{\frac{-3978873516901917}{50000000000000000}}{\color{blue}{z0 \cdot z1}} \]

   2. lower-*.f64 59.1%

      \[\leadsto \frac{-0.07957747033803834}{z0 \cdot \color{blue}{z1}} \]

4. Applied rewrites 59.1%

   \[\leadsto \color{blue}{\frac{-0.07957747033803834}{z0 \cdot z1}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z1)
  :name "(/ (- (* (- (/ (* -552621316200069/25000000000000000 z0) z1) -2122065862260549/40000000000000000) z0) (* 3978873516901917/50000000000000000 z1)) (* (* z1 z0) z1))"
  :precision binary64
  (/ (- (* (- (/ (* -0.02210485264800276 z0) z1) -0.053051646556513725) z0) (* 0.07957747033803834 z1)) (* (* z1 z0) z1)))