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

Percentage Accurate: 99.8% → 99.8%

Time: 1.5s

Alternatives: 8

Speedup: N/A×

• 76.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double z0, double z1) {
	return (-0.053051646556513725 - ((-0.02210485264800276 * z0) / 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 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double z0, double z1) {
	return (-0.053051646556513725 - ((-0.02210485264800276 * z0) / 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 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double z0, double z1) {
	return (-0.053051646556513725 / z1) + ((z0 / z1) * (0.02210485264800276 / 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 = ((-0.053051646556513725d0) / z1) + ((z0 / z1) * (0.02210485264800276d0 / z1))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lift-/.f64 N/A

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

   5. associate-/l/ N/A

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

   6. sqr-neg-rev N/A

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

   7. lift-*.f64 N/A

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

   8. frac-times N/A

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

   9. distribute-neg-frac2 N/A

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

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

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

   11. lower-+.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lower-neg.f64 N/A

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

   15. frac-2neg-rev N/A

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

   16. remove-double-neg N/A

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

   17. lower-/.f64 N/A

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

   18. metadata-eval N/A

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

   19. distribute-neg-frac N/A

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

   20. lower-/.f64 N/A

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

   21. lower-neg.f64 99.8%

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

3. Applied rewrites 99.8%

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

   1. lift-*.f64 N/A

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

   2. lift-neg.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. distribute-neg-frac N/A

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

   5. metadata-eval N/A

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

   6. lift-/.f64 N/A

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

   7. frac-2neg N/A

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

   8. frac-times N/A

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

   9. lift-neg.f64 N/A

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

   10. remove-double-neg N/A

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

   11. *-commutative N/A

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

   12. times-frac N/A

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

   13. metadata-eval N/A

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

   14. frac-2neg N/A

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

   15. lift-/.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. lower-/.f64 99.8%

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

5. Applied rewrites 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double z0, double z1) {
	return (-0.053051646556513725 - ((-0.02210485264800276 / 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 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) / z1) * z0)) / z1
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-/.f64 99.8%

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

3. Applied rewrites 99.8%

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

Alternative 3: 90.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z1 \leq -2.05 \cdot 10^{+157}:\\ \;\;\;\;\frac{1}{-18.84955632686615 \cdot z1 + -7.853981773058572 \cdot z0}\\ \mathbf{elif}\;z1 \leq 3.1 \cdot 10^{+164}:\\ \;\;\;\;\frac{z1 \cdot -0.053051646556513725 - z0 \cdot -0.02210485264800276}{z1 \cdot z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.053051646556513725}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= z1 -2.05e+157)
  (/ 1.0 (+ (* -18.84955632686615 z1) (* -7.853981773058572 z0)))
  (if (<= z1 3.1e+164)
    (/
     (- (* z1 -0.053051646556513725) (* z0 -0.02210485264800276))
     (* z1 z1))
    (/ -0.053051646556513725 z1))))

C

double code(double z0, double z1) {
	double tmp;
	if (z1 <= -2.05e+157) {
		tmp = 1.0 / ((-18.84955632686615 * z1) + (-7.853981773058572 * z0));
	} else if (z1 <= 3.1e+164) {
		tmp = ((z1 * -0.053051646556513725) - (z0 * -0.02210485264800276)) / (z1 * z1);
	} else {
		tmp = -0.053051646556513725 / 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 <= (-2.05d+157)) then
        tmp = 1.0d0 / (((-18.84955632686615d0) * z1) + ((-7.853981773058572d0) * z0))
    else if (z1 <= 3.1d+164) then
        tmp = ((z1 * (-0.053051646556513725d0)) - (z0 * (-0.02210485264800276d0))) / (z1 * z1)
    else
        tmp = (-0.053051646556513725d0) / z1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (z1 <= -2.05e+157) {
		tmp = 1.0 / ((-18.84955632686615 * z1) + (-7.853981773058572 * z0));
	} else if (z1 <= 3.1e+164) {
		tmp = ((z1 * -0.053051646556513725) - (z0 * -0.02210485264800276)) / (z1 * z1);
	} else {
		tmp = -0.053051646556513725 / z1;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if z1 <= -2.05e+157:
		tmp = 1.0 / ((-18.84955632686615 * z1) + (-7.853981773058572 * z0))
	elif z1 <= 3.1e+164:
		tmp = ((z1 * -0.053051646556513725) - (z0 * -0.02210485264800276)) / (z1 * z1)
	else:
		tmp = -0.053051646556513725 / z1
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (z1 <= -2.05e+157)
		tmp = Float64(1.0 / Float64(Float64(-18.84955632686615 * z1) + Float64(-7.853981773058572 * z0)));
	elseif (z1 <= 3.1e+164)
		tmp = Float64(Float64(Float64(z1 * -0.053051646556513725) - Float64(z0 * -0.02210485264800276)) / Float64(z1 * z1));
	else
		tmp = Float64(-0.053051646556513725 / z1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (z1 <= -2.05e+157)
		tmp = 1.0 / ((-18.84955632686615 * z1) + (-7.853981773058572 * z0));
	elseif (z1 <= 3.1e+164)
		tmp = ((z1 * -0.053051646556513725) - (z0 * -0.02210485264800276)) / (z1 * z1);
	else
		tmp = -0.053051646556513725 / z1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[z1, -2.05e+157], N[(1.0 / N[(N[(-18.84955632686615 * z1), $MachinePrecision] + N[(-7.853981773058572 * z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z1, 3.1e+164], N[(N[(N[(z1 * -0.053051646556513725), $MachinePrecision] - N[(z0 * -0.02210485264800276), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision], N[(-0.053051646556513725 / z1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z1 < -2.0500000000000001e157

   1. Initial program 99.8%

      \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-to-fraction N/A

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

      5. mult-flip N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 69.9%

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

   3. Applied rewrites 69.9%

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

   4. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   5. Step-by-step derivation

      1. lower-*.f64 45.4%

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

   6. Applied rewrites 45.4%

      \[\leadsto \color{blue}{\left(0.02210485264800276 \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1 \cdot z1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \color{blue}{\frac{1}{z1 \cdot z1}} \]

      3. mult-flip-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{552621316200069}{25000000000000000} \cdot z0}{z1 \cdot z1}} \]

      4. div-flip N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot z1}{\frac{552621316200069}{25000000000000000} \cdot z0}}} \]

      5. lower-unsound-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot z1}{\frac{552621316200069}{25000000000000000} \cdot z0}}} \]

      6. lower-unsound-/.f64 45.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{z1 \cdot z1}{0.02210485264800276 \cdot z0}}} \]

   8. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot z1}{0.02210485264800276 \cdot z0}}} \]

   9. Taylor expanded in z0 around 0

      \[\leadsto \frac{1}{\color{blue}{\frac{-40000000000000000}{2122065862260549} \cdot z1 + \frac{-11789254745601472000000000000000}{1501054507923869106874787260467} \cdot z0}} \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \frac{1}{\frac{-40000000000000000}{2122065862260549} \cdot z1 + \color{blue}{\frac{-11789254745601472000000000000000}{1501054507923869106874787260467} \cdot z0}} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{-40000000000000000}{2122065862260549} \cdot z1 + \color{blue}{\frac{-11789254745601472000000000000000}{1501054507923869106874787260467}} \cdot z0} \]

       3. lower-*.f64 50.2%

          \[\leadsto \frac{1}{-18.84955632686615 \cdot z1 + -7.853981773058572 \cdot \color{blue}{z0}} \]

   11. Applied rewrites 50.2%

       \[\leadsto \frac{1}{\color{blue}{-18.84955632686615 \cdot z1 + -7.853981773058572 \cdot z0}} \]

   if -2.0500000000000001e157 < z1 < 3.1000000000000002e164

   1. Initial program 99.8%

      \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-to-fraction N/A

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

      5. associate-/l/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 70.3%

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

   3. Applied rewrites 70.3%

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

   if 3.1000000000000002e164 < z1

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

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

Alternative 4: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{0.02210485264800276}{z1} \cdot z0}{z1}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{-0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.02210485264800276 \cdot z0}{z1}}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         (- -0.053051646556513725 (/ (* -0.02210485264800276 z0) z1))
         z1)))
  (if (<= t_0 -2e+86)
    (/ (* (/ 0.02210485264800276 z1) z0) z1)
    (if (<= t_0 2e+148)
      (/ -0.053051646556513725 z1)
      (/ (/ (* 0.02210485264800276 z0) z1) z1)))))

C

double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = ((0.02210485264800276 / z1) * z0) / z1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = ((0.02210485264800276 * z0) / z1) / 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) :: t_0
    real(8) :: tmp
    t_0 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
    if (t_0 <= (-2d+86)) then
        tmp = ((0.02210485264800276d0 / z1) * z0) / z1
    else if (t_0 <= 2d+148) then
        tmp = (-0.053051646556513725d0) / z1
    else
        tmp = ((0.02210485264800276d0 * z0) / z1) / z1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = ((0.02210485264800276 / z1) * z0) / z1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = ((0.02210485264800276 * z0) / z1) / z1;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1
	tmp = 0
	if t_0 <= -2e+86:
		tmp = ((0.02210485264800276 / z1) * z0) / z1
	elif t_0 <= 2e+148:
		tmp = -0.053051646556513725 / z1
	else:
		tmp = ((0.02210485264800276 * z0) / z1) / z1
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-0.053051646556513725 - Float64(Float64(-0.02210485264800276 * z0) / z1)) / z1)
	tmp = 0.0
	if (t_0 <= -2e+86)
		tmp = Float64(Float64(Float64(0.02210485264800276 / z1) * z0) / z1);
	elseif (t_0 <= 2e+148)
		tmp = Float64(-0.053051646556513725 / z1);
	else
		tmp = Float64(Float64(Float64(0.02210485264800276 * z0) / z1) / z1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	tmp = 0.0;
	if (t_0 <= -2e+86)
		tmp = ((0.02210485264800276 / z1) * z0) / z1;
	elseif (t_0 <= 2e+148)
		tmp = -0.053051646556513725 / z1;
	else
		tmp = ((0.02210485264800276 * z0) / z1) / z1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-0.053051646556513725 - N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+86], N[(N[(N[(0.02210485264800276 / z1), $MachinePrecision] * z0), $MachinePrecision] / z1), $MachinePrecision], If[LessEqual[t$95$0, 2e+148], N[(-0.053051646556513725 / z1), $MachinePrecision], N[(N[(N[(0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision] / z1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < -2e86

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{\frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}}{z1} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot \color{blue}{\frac{z0}{z1}}}{z1} \]

      2. lower-/.f64 51.1%

         \[\leadsto \frac{0.02210485264800276 \cdot \frac{z0}{\color{blue}{z1}}}{z1} \]

   4. Applied rewrites 51.1%

      \[\leadsto \frac{\color{blue}{0.02210485264800276 \cdot \frac{z0}{z1}}}{z1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot \color{blue}{\frac{z0}{z1}}}{z1} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{z0}{z1} \cdot \color{blue}{\frac{552621316200069}{25000000000000000}}}{z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\frac{z0}{z1} \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      4. mult-flip N/A

         \[\leadsto \frac{\left(z0 \cdot \frac{1}{z1}\right) \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot \frac{1}{z1}\right) \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      6. associate-*l* N/A

         \[\leadsto \frac{z0 \cdot \color{blue}{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right)}}{z1} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot \color{blue}{z0}}{z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot \color{blue}{z0}}{z1} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot z0}{z1} \]

      10. associate-*l/ N/A

          \[\leadsto \frac{\frac{1 \cdot \frac{552621316200069}{25000000000000000}}{z1} \cdot z0}{z1} \]

      11. metadata-eval N/A

          \[\leadsto \frac{\frac{\frac{552621316200069}{25000000000000000}}{z1} \cdot z0}{z1} \]

      12. lower-/.f64 51.1%

          \[\leadsto \frac{\frac{0.02210485264800276}{z1} \cdot z0}{z1} \]

   6. Applied rewrites 51.1%

      \[\leadsto \frac{\frac{0.02210485264800276}{z1} \cdot \color{blue}{z0}}{z1} \]

   if -2e86 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < 2.0000000000000001e148

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

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

   if 2.0000000000000001e148 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1)

   1. Initial program 99.8%

      \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-to-fraction N/A

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

      5. mult-flip N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 69.9%

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

   3. Applied rewrites 69.9%

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

   4. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   5. Step-by-step derivation

      1. lower-*.f64 45.4%

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

   6. Applied rewrites 45.4%

      \[\leadsto \color{blue}{\left(0.02210485264800276 \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1 \cdot z1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \color{blue}{\frac{1}{z1 \cdot z1}} \]

      3. mult-flip-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{552621316200069}{25000000000000000} \cdot z0}{z1 \cdot z1}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot z0}{\color{blue}{z1 \cdot z1}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\frac{552621316200069}{25000000000000000} \cdot z0}{z1}}{z1}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\frac{552621316200069}{25000000000000000} \cdot z0}{z1}}{z1}} \]

      7. lower-/.f64 51.1%

         \[\leadsto \frac{\color{blue}{\frac{0.02210485264800276 \cdot z0}{z1}}}{z1} \]

   8. Applied rewrites 51.1%

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

Alternative 5: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1}\\ t_1 := \frac{\frac{0.02210485264800276}{z1} \cdot z0}{z1}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{-0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         (- -0.053051646556513725 (/ (* -0.02210485264800276 z0) z1))
         z1))
       (t_1 (/ (* (/ 0.02210485264800276 z1) z0) z1)))
  (if (<= t_0 -2e+86)
    t_1
    (if (<= t_0 2e+148) (/ -0.053051646556513725 z1) t_1))))

C

double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = ((0.02210485264800276 / z1) * z0) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
    t_1 = ((0.02210485264800276d0 / z1) * z0) / z1
    if (t_0 <= (-2d+86)) then
        tmp = t_1
    else if (t_0 <= 2d+148) then
        tmp = (-0.053051646556513725d0) / z1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = ((0.02210485264800276 / z1) * z0) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1
	t_1 = ((0.02210485264800276 / z1) * z0) / z1
	tmp = 0
	if t_0 <= -2e+86:
		tmp = t_1
	elif t_0 <= 2e+148:
		tmp = -0.053051646556513725 / z1
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-0.053051646556513725 - Float64(Float64(-0.02210485264800276 * z0) / z1)) / z1)
	t_1 = Float64(Float64(Float64(0.02210485264800276 / z1) * z0) / z1)
	tmp = 0.0
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = Float64(-0.053051646556513725 / z1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	t_1 = ((0.02210485264800276 / z1) * z0) / z1;
	tmp = 0.0;
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = -0.053051646556513725 / z1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-0.053051646556513725 - N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(0.02210485264800276 / z1), $MachinePrecision] * z0), $MachinePrecision] / z1), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+86], t$95$1, If[LessEqual[t$95$0, 2e+148], N[(-0.053051646556513725 / z1), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < -2e86 or 2.0000000000000001e148 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1)

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{\frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}}{z1} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot \color{blue}{\frac{z0}{z1}}}{z1} \]

      2. lower-/.f64 51.1%

         \[\leadsto \frac{0.02210485264800276 \cdot \frac{z0}{\color{blue}{z1}}}{z1} \]

   4. Applied rewrites 51.1%

      \[\leadsto \frac{\color{blue}{0.02210485264800276 \cdot \frac{z0}{z1}}}{z1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot \color{blue}{\frac{z0}{z1}}}{z1} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{z0}{z1} \cdot \color{blue}{\frac{552621316200069}{25000000000000000}}}{z1} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{\frac{z0}{z1} \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      4. mult-flip N/A

         \[\leadsto \frac{\left(z0 \cdot \frac{1}{z1}\right) \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 \cdot \frac{1}{z1}\right) \cdot \frac{552621316200069}{25000000000000000}}{z1} \]

      6. associate-*l* N/A

         \[\leadsto \frac{z0 \cdot \color{blue}{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right)}}{z1} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot \color{blue}{z0}}{z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot \color{blue}{z0}}{z1} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{1}{z1} \cdot \frac{552621316200069}{25000000000000000}\right) \cdot z0}{z1} \]

      10. associate-*l/ N/A

          \[\leadsto \frac{\frac{1 \cdot \frac{552621316200069}{25000000000000000}}{z1} \cdot z0}{z1} \]

      11. metadata-eval N/A

          \[\leadsto \frac{\frac{\frac{552621316200069}{25000000000000000}}{z1} \cdot z0}{z1} \]

      12. lower-/.f64 51.1%

          \[\leadsto \frac{\frac{0.02210485264800276}{z1} \cdot z0}{z1} \]

   6. Applied rewrites 51.1%

      \[\leadsto \frac{\frac{0.02210485264800276}{z1} \cdot \color{blue}{z0}}{z1} \]

   if -2e86 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < 2.0000000000000001e148

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

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

Alternative 6: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1}\\ t_1 := \frac{0.02210485264800276 \cdot \frac{z0}{z1}}{z1}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{-0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         (- -0.053051646556513725 (/ (* -0.02210485264800276 z0) z1))
         z1))
       (t_1 (/ (* 0.02210485264800276 (/ z0 z1)) z1)))
  (if (<= t_0 -2e+86)
    t_1
    (if (<= t_0 2e+148) (/ -0.053051646556513725 z1) t_1))))

C

double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = (0.02210485264800276 * (z0 / z1)) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
    t_1 = (0.02210485264800276d0 * (z0 / z1)) / z1
    if (t_0 <= (-2d+86)) then
        tmp = t_1
    else if (t_0 <= 2d+148) then
        tmp = (-0.053051646556513725d0) / z1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = (0.02210485264800276 * (z0 / z1)) / z1;
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1
	t_1 = (0.02210485264800276 * (z0 / z1)) / z1
	tmp = 0
	if t_0 <= -2e+86:
		tmp = t_1
	elif t_0 <= 2e+148:
		tmp = -0.053051646556513725 / z1
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-0.053051646556513725 - Float64(Float64(-0.02210485264800276 * z0) / z1)) / z1)
	t_1 = Float64(Float64(0.02210485264800276 * Float64(z0 / z1)) / z1)
	tmp = 0.0
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = Float64(-0.053051646556513725 / z1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	t_1 = (0.02210485264800276 * (z0 / z1)) / z1;
	tmp = 0.0;
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = -0.053051646556513725 / z1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-0.053051646556513725 - N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.02210485264800276 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+86], t$95$1, If[LessEqual[t$95$0, 2e+148], N[(-0.053051646556513725 / z1), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < -2e86 or 2.0000000000000001e148 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1)

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around inf

      \[\leadsto \frac{\color{blue}{\frac{552621316200069}{25000000000000000} \cdot \frac{z0}{z1}}}{z1} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{552621316200069}{25000000000000000} \cdot \color{blue}{\frac{z0}{z1}}}{z1} \]

      2. lower-/.f64 51.1%

         \[\leadsto \frac{0.02210485264800276 \cdot \frac{z0}{\color{blue}{z1}}}{z1} \]

   4. Applied rewrites 51.1%

      \[\leadsto \frac{\color{blue}{0.02210485264800276 \cdot \frac{z0}{z1}}}{z1} \]

   if -2e86 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < 2.0000000000000001e148

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

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

Alternative 7: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1}\\ t_1 := \frac{0.02210485264800276 \cdot z0}{z1 \cdot z1}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{-0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         (- -0.053051646556513725 (/ (* -0.02210485264800276 z0) z1))
         z1))
       (t_1 (/ (* 0.02210485264800276 z0) (* z1 z1))))
  (if (<= t_0 -2e+86)
    t_1
    (if (<= t_0 2e+148) (/ -0.053051646556513725 z1) t_1))))

C

double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = (0.02210485264800276 * z0) / (z1 * z1);
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((-0.053051646556513725d0) - (((-0.02210485264800276d0) * z0) / z1)) / z1
    t_1 = (0.02210485264800276d0 * z0) / (z1 * z1)
    if (t_0 <= (-2d+86)) then
        tmp = t_1
    else if (t_0 <= 2d+148) then
        tmp = (-0.053051646556513725d0) / z1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	double t_1 = (0.02210485264800276 * z0) / (z1 * z1);
	double tmp;
	if (t_0 <= -2e+86) {
		tmp = t_1;
	} else if (t_0 <= 2e+148) {
		tmp = -0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1
	t_1 = (0.02210485264800276 * z0) / (z1 * z1)
	tmp = 0
	if t_0 <= -2e+86:
		tmp = t_1
	elif t_0 <= 2e+148:
		tmp = -0.053051646556513725 / z1
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-0.053051646556513725 - Float64(Float64(-0.02210485264800276 * z0) / z1)) / z1)
	t_1 = Float64(Float64(0.02210485264800276 * z0) / Float64(z1 * z1))
	tmp = 0.0
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = Float64(-0.053051646556513725 / z1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = (-0.053051646556513725 - ((-0.02210485264800276 * z0) / z1)) / z1;
	t_1 = (0.02210485264800276 * z0) / (z1 * z1);
	tmp = 0.0;
	if (t_0 <= -2e+86)
		tmp = t_1;
	elseif (t_0 <= 2e+148)
		tmp = -0.053051646556513725 / z1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[(-0.053051646556513725 - N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.02210485264800276 * z0), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+86], t$95$1, If[LessEqual[t$95$0, 2e+148], N[(-0.053051646556513725 / z1), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < -2e86 or 2.0000000000000001e148 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1)

   1. Initial program 99.8%

      \[\frac{-0.053051646556513725 - \frac{-0.02210485264800276 \cdot z0}{z1}}{z1} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-to-fraction N/A

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

      5. mult-flip N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 69.9%

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

   3. Applied rewrites 69.9%

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

   4. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   5. Step-by-step derivation

      1. lower-*.f64 45.4%

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

   6. Applied rewrites 45.4%

      \[\leadsto \color{blue}{\left(0.02210485264800276 \cdot z0\right)} \cdot \frac{1}{z1 \cdot z1} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \frac{1}{z1 \cdot z1}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{552621316200069}{25000000000000000} \cdot z0\right) \cdot \color{blue}{\frac{1}{z1 \cdot z1}} \]

      3. mult-flip-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{552621316200069}{25000000000000000} \cdot z0}{z1 \cdot z1}} \]

      4. lower-/.f64 45.7%

         \[\leadsto \color{blue}{\frac{0.02210485264800276 \cdot z0}{z1 \cdot z1}} \]

   8. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\frac{0.02210485264800276 \cdot z0}{z1 \cdot z1}} \]

   if -2e86 < (/.f64 (-.f64 #s(literal -2122065862260549/40000000000000000 binary64) (/.f64 (*.f64 #s(literal -552621316200069/25000000000000000 binary64) z0) z1)) z1) < 2.0000000000000001e148

   1. Initial program 99.8%

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

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

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

Alternative 8: 51.4% accurate, 2.6× speedup

Math

\[\frac{-0.053051646556513725}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/ -0.053051646556513725 z1))

C

double code(double z0, double z1) {
	return -0.053051646556513725 / 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 = (-0.053051646556513725d0) / z1
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z0 around 0

   \[\leadsto \frac{\color{blue}{\frac{-2122065862260549}{40000000000000000}}}{z1} \]
3. Step-by-step derivation

4. Applied rewrites 51.4%

   \[\leadsto \frac{\color{blue}{-0.053051646556513725}}{z1} \]
5. Add Preprocessing

Reproduce

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