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

Percentage Accurate: 71.8% → 99.8%

Time: 1.6s

Alternatives: 5

Speedup: 1.0×

• 75.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 71.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. mult-flip N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*l* N/A

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

   8. mult-flip N/A

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

   9. lift-*.f64 N/A

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

   10. associate-/r* N/A

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

   11. *-inverses N/A

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

   12. mult-flip N/A

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

   13. lower-/.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. associate-/l* N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 N/A

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

   19. lower-/.f64 91.5%

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

3. Applied rewrites 91.5%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*l/ N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. times-frac N/A

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

   7. lift-/.f64 N/A

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

   8. lift-/.f64 N/A

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

   9. 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

3. Applied rewrites 99.8%

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

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{0.053051646556513725 \cdot z1 - 0.02210485264800276 \cdot z0}{z1 \cdot z1}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-82}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-68}:\\ \;\;\;\;\frac{0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0
        (/
         (- (* 0.053051646556513725 z1) (* 0.02210485264800276 z0))
         (* z1 z1))))
  (if (<= t_0 -5e-82)
    t_0
    (if (<= t_0 2e-68) (/ 0.053051646556513725 z1) t_0))))

C

double code(double z1, double z0) {
	double t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	double tmp;
	if (t_0 <= -5e-82) {
		tmp = t_0;
	} else if (t_0 <= 2e-68) {
		tmp = 0.053051646556513725 / z1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((0.053051646556513725d0 * z1) - (0.02210485264800276d0 * z0)) / (z1 * z1)
    if (t_0 <= (-5d-82)) then
        tmp = t_0
    else if (t_0 <= 2d-68) then
        tmp = 0.053051646556513725d0 / z1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	double tmp;
	if (t_0 <= -5e-82) {
		tmp = t_0;
	} else if (t_0 <= 2e-68) {
		tmp = 0.053051646556513725 / z1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1)
	tmp = 0
	if t_0 <= -5e-82:
		tmp = t_0
	elif t_0 <= 2e-68:
		tmp = 0.053051646556513725 / z1
	else:
		tmp = t_0
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(Float64(Float64(0.053051646556513725 * z1) - Float64(0.02210485264800276 * z0)) / Float64(z1 * z1))
	tmp = 0.0
	if (t_0 <= -5e-82)
		tmp = t_0;
	elseif (t_0 <= 2e-68)
		tmp = Float64(0.053051646556513725 / z1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	tmp = 0.0;
	if (t_0 <= -5e-82)
		tmp = t_0;
	elseif (t_0 <= 2e-68)
		tmp = 0.053051646556513725 / z1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(N[(N[(0.053051646556513725 * z1), $MachinePrecision] - N[(0.02210485264800276 * z0), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-82], t$95$0, If[LessEqual[t$95$0, 2e-68], N[(0.053051646556513725 / z1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1)) < -4.9999999999999998e-82 or 2.0000000000000001e-68 < (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1))

   1. Initial program 71.8%

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

   if -4.9999999999999998e-82 < (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1)) < 2.0000000000000001e-68

   1. Initial program 71.8%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 51.3%

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

   4. Applied rewrites 51.3%

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

Alternative 4: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{0.053051646556513725 \cdot z1 - 0.02210485264800276 \cdot z0}{z1 \cdot z1}\\ t_1 := \frac{-0.02210485264800276 \cdot z0}{z1 \cdot z1}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+78}:\\ \;\;\;\;\frac{0.053051646556513725}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0
        (/
         (- (* 0.053051646556513725 z1) (* 0.02210485264800276 z0))
         (* z1 z1)))
       (t_1 (/ (* -0.02210485264800276 z0) (* z1 z1))))
  (if (<= t_0 -1e+186)
    t_1
    (if (<= t_0 2e+78) (/ 0.053051646556513725 z1) t_1))))

C

double code(double z1, double z0) {
	double t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	double t_1 = (-0.02210485264800276 * z0) / (z1 * z1);
	double tmp;
	if (t_0 <= -1e+186) {
		tmp = t_1;
	} else if (t_0 <= 2e+78) {
		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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((0.053051646556513725d0 * z1) - (0.02210485264800276d0 * z0)) / (z1 * z1)
    t_1 = ((-0.02210485264800276d0) * z0) / (z1 * z1)
    if (t_0 <= (-1d+186)) then
        tmp = t_1
    else if (t_0 <= 2d+78) then
        tmp = 0.053051646556513725d0 / z1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	double t_1 = (-0.02210485264800276 * z0) / (z1 * z1);
	double tmp;
	if (t_0 <= -1e+186) {
		tmp = t_1;
	} else if (t_0 <= 2e+78) {
		tmp = 0.053051646556513725 / z1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1)
	t_1 = (-0.02210485264800276 * z0) / (z1 * z1)
	tmp = 0
	if t_0 <= -1e+186:
		tmp = t_1
	elif t_0 <= 2e+78:
		tmp = 0.053051646556513725 / z1
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(Float64(Float64(0.053051646556513725 * z1) - Float64(0.02210485264800276 * z0)) / Float64(z1 * z1))
	t_1 = Float64(Float64(-0.02210485264800276 * z0) / Float64(z1 * z1))
	tmp = 0.0
	if (t_0 <= -1e+186)
		tmp = t_1;
	elseif (t_0 <= 2e+78)
		tmp = Float64(0.053051646556513725 / z1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = ((0.053051646556513725 * z1) - (0.02210485264800276 * z0)) / (z1 * z1);
	t_1 = (-0.02210485264800276 * z0) / (z1 * z1);
	tmp = 0.0;
	if (t_0 <= -1e+186)
		tmp = t_1;
	elseif (t_0 <= 2e+78)
		tmp = 0.053051646556513725 / z1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(N[(N[(0.053051646556513725 * z1), $MachinePrecision] - N[(0.02210485264800276 * z0), $MachinePrecision]), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-0.02210485264800276 * z0), $MachinePrecision] / N[(z1 * z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+186], t$95$1, If[LessEqual[t$95$0, 2e+78], N[(0.053051646556513725 / z1), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1)) < -9.9999999999999998e185 or 2e78 < (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1))

   1. Initial program 71.8%

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

   2. Taylor expanded in z1 around 0

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

      1. lower-*.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -9.9999999999999998e185 < (/.f64 (-.f64 (*.f64 #s(literal 2122065862260549/40000000000000000 binary64) z1) (*.f64 #s(literal 552621316200069/25000000000000000 binary64) z0)) (*.f64 z1 z1)) < 2e78

   1. Initial program 71.8%

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

   2. Taylor expanded in z1 around inf

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

      1. lower-/.f64 51.3%

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

   4. Applied rewrites 51.3%

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

Alternative 5: 51.3% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

2. Taylor expanded in z1 around inf

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

   1. lower-/.f64 51.3%

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

4. Applied rewrites 51.3%

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

Reproduce

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