(/ -1 (- (- -1 z0) (/ (sqrt (- (- 1 z1) z1)) (* (* 3544907808303833/2000000000000000 z1) (exp (* z1 z1))))))

Percentage Accurate: 99.8% → 99.8%

Time: 2.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 -1.0
 (-
  (- -1.0 z0)
  (/
   (sqrt (- (- 1.0 z1) z1))
   (* (* 1.7724539041519165 z1) (exp (* z1 z1)))))))

C

double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((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 = (-1.0d0) / (((-1.0d0) - z0) - (sqrt(((1.0d0 - z1) - z1)) / ((1.7724539041519165d0 * z1) * exp((z1 * z1)))))
end function

Java

public static double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (Math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * Math.exp((z1 * z1)))));
}

Python

def code(z0, z1):
	return -1.0 / ((-1.0 - z0) - (math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * math.exp((z1 * z1)))))

Julia

function code(z0, z1)
	return Float64(-1.0 / Float64(Float64(-1.0 - z0) - Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) / Float64(Float64(1.7724539041519165 * z1) * exp(Float64(z1 * z1))))))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -1.0 / ((-1.0 - z0) - (sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((z1 * z1)))));
end

Wolfram

code[z0_, z1_] := N[(-1.0 / N[(N[(-1.0 - z0), $MachinePrecision] - N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] / N[(N[(1.7724539041519165 * z1), $MachinePrecision] * N[Exp[N[(z1 * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 -1.0
 (-
  (- -1.0 z0)
  (/
   (sqrt (- (- 1.0 z1) z1))
   (* (* 1.7724539041519165 z1) (exp (* z1 z1)))))))

C

double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((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 = (-1.0d0) / (((-1.0d0) - z0) - (sqrt(((1.0d0 - z1) - z1)) / ((1.7724539041519165d0 * z1) * exp((z1 * z1)))))
end function

Java

public static double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (Math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * Math.exp((z1 * z1)))));
}

Python

def code(z0, z1):
	return -1.0 / ((-1.0 - z0) - (math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * math.exp((z1 * z1)))))

Julia

function code(z0, z1)
	return Float64(-1.0 / Float64(Float64(-1.0 - z0) - Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) / Float64(Float64(1.7724539041519165 * z1) * exp(Float64(z1 * z1))))))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -1.0 / ((-1.0 - z0) - (sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((z1 * z1)))));
end

Wolfram

code[z0_, z1_] := N[(-1.0 / N[(N[(-1.0 - z0), $MachinePrecision] - N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] / N[(N[(1.7724539041519165 * z1), $MachinePrecision] * N[Exp[N[(z1 * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 1.0× speedup

Math

\[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 -1.0
 (-
  (- -1.0 z0)
  (/
   (sqrt (- 1.0 z1))
   (* (* 1.7724539041519165 z1) (exp (* z1 z1)))))))

C

double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (sqrt((1.0 - z1)) / ((1.7724539041519165 * z1) * exp((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 = (-1.0d0) / (((-1.0d0) - z0) - (sqrt((1.0d0 - z1)) / ((1.7724539041519165d0 * z1) * exp((z1 * z1)))))
end function

Java

public static double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (Math.sqrt((1.0 - z1)) / ((1.7724539041519165 * z1) * Math.exp((z1 * z1)))));
}

Python

def code(z0, z1):
	return -1.0 / ((-1.0 - z0) - (math.sqrt((1.0 - z1)) / ((1.7724539041519165 * z1) * math.exp((z1 * z1)))))

Julia

function code(z0, z1)
	return Float64(-1.0 / Float64(Float64(-1.0 - z0) - Float64(sqrt(Float64(1.0 - z1)) / Float64(Float64(1.7724539041519165 * z1) * exp(Float64(z1 * z1))))))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -1.0 / ((-1.0 - z0) - (sqrt((1.0 - z1)) / ((1.7724539041519165 * z1) * exp((z1 * z1)))));
end

Wolfram

code[z0_, z1_] := N[(-1.0 / N[(N[(-1.0 - z0), $MachinePrecision] - N[(N[Sqrt[N[(1.0 - z1), $MachinePrecision]], $MachinePrecision] / N[(N[(1.7724539041519165 * z1), $MachinePrecision] * N[Exp[N[(z1 * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

2. Taylor expanded in z1 around 0

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\color{blue}{1} - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]
3. Step-by-step derivation

4. Applied rewrites 99.1%

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\color{blue}{1} - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 2.7× speedup

Math

\[\frac{1}{\frac{\sqrt{1 - z1}}{\left(z1 \cdot z1 - -1\right) \cdot \left(1.7724539041519165 \cdot z1\right)} - \left(-1 - z0\right)} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/
 1.0
 (-
  (/
   (sqrt (- 1.0 z1))
   (* (- (* z1 z1) -1.0) (* 1.7724539041519165 z1)))
  (- -1.0 z0))))

C

double code(double z0, double z1) {
	return 1.0 / ((sqrt((1.0 - z1)) / (((z1 * z1) - -1.0) * (1.7724539041519165 * z1))) - (-1.0 - z0));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = 1.0d0 / ((sqrt((1.0d0 - z1)) / (((z1 * z1) - (-1.0d0)) * (1.7724539041519165d0 * z1))) - ((-1.0d0) - z0))
end function

Java

public static double code(double z0, double z1) {
	return 1.0 / ((Math.sqrt((1.0 - z1)) / (((z1 * z1) - -1.0) * (1.7724539041519165 * z1))) - (-1.0 - z0));
}

Python

def code(z0, z1):
	return 1.0 / ((math.sqrt((1.0 - z1)) / (((z1 * z1) - -1.0) * (1.7724539041519165 * z1))) - (-1.0 - z0))

Julia

function code(z0, z1)
	return Float64(1.0 / Float64(Float64(sqrt(Float64(1.0 - z1)) / Float64(Float64(Float64(z1 * z1) - -1.0) * Float64(1.7724539041519165 * z1))) - Float64(-1.0 - z0)))
end

MATLAB

function tmp = code(z0, z1)
	tmp = 1.0 / ((sqrt((1.0 - z1)) / (((z1 * z1) - -1.0) * (1.7724539041519165 * z1))) - (-1.0 - z0));
end

Wolfram

code[z0_, z1_] := N[(1.0 / N[(N[(N[Sqrt[N[(1.0 - z1), $MachinePrecision]], $MachinePrecision] / N[(N[(N[(z1 * z1), $MachinePrecision] - -1.0), $MachinePrecision] * N[(1.7724539041519165 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 - z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

2. Taylor expanded in z1 around 0

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\color{blue}{1} - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]
3. Step-by-step derivation

4. Applied rewrites 99.1%

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\color{blue}{1} - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

5. Taylor expanded in z1 around 0

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot \color{blue}{\left(1 + {z1}^{2}\right)}}} \]
6. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + \color{blue}{{z1}^{2}}\right)}} \]

   2. lower-pow.f64 98.9%

      \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot \left(1 + {z1}^{\color{blue}{2}}\right)}} \]

7. Applied rewrites 98.9%

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot \color{blue}{\left(1 + {z1}^{2}\right)}}} \]
8. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)}}} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(\left(\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)}\right)\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{1}}{\mathsf{neg}\left(\left(\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)}\right)\right)} \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{\mathsf{neg}\left(\left(\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)}\right)\right)}} \]

   5. lift--.f64 N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\color{blue}{\left(\left(-1 - z0\right) - \frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)}\right)}\right)} \]

   6. sub-negate-rev N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{1 - z1}}{\left(\frac{3544907808303833}{2000000000000000} \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)} - \left(-1 - z0\right)}} \]

   7. lower--.f64 98.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{1 - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot \left(1 + {z1}^{2}\right)} - \left(-1 - z0\right)}} \]

9. Applied rewrites 98.9%

   \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{1 - z1}}{\left(z1 \cdot z1 - -1\right) \cdot \left(1.7724539041519165 \cdot z1\right)} - \left(-1 - z0\right)}} \]
10. Add Preprocessing

Alternative 3: 98.4% accurate, 5.5× speedup

Math

\[\frac{-1}{\left(-1 - z0\right) - \frac{0.5641895665989011}{z1}} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (/ -1.0 (- (- -1.0 z0) (/ 0.5641895665989011 z1))))

C

double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (0.5641895665989011 / 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 = (-1.0d0) / (((-1.0d0) - z0) - (0.5641895665989011d0 / z1))
end function

Java

public static double code(double z0, double z1) {
	return -1.0 / ((-1.0 - z0) - (0.5641895665989011 / z1));
}

Python

def code(z0, z1):
	return -1.0 / ((-1.0 - z0) - (0.5641895665989011 / z1))

Julia

function code(z0, z1)
	return Float64(-1.0 / Float64(Float64(-1.0 - z0) - Float64(0.5641895665989011 / z1)))
end

MATLAB

function tmp = code(z0, z1)
	tmp = -1.0 / ((-1.0 - z0) - (0.5641895665989011 / z1));
end

Wolfram

code[z0_, z1_] := N[(-1.0 / N[(N[(-1.0 - z0), $MachinePrecision] - N[(0.5641895665989011 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

2. Taylor expanded in z1 around 0

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \color{blue}{\frac{\frac{2000000000000000}{3544907808303833}}{z1}}} \]
3. Step-by-step derivation

   1. lower-/.f64 98.4%

      \[\leadsto \frac{-1}{\left(-1 - z0\right) - \frac{0.5641895665989011}{\color{blue}{z1}}} \]

4. Applied rewrites 98.4%

   \[\leadsto \frac{-1}{\left(-1 - z0\right) - \color{blue}{\frac{0.5641895665989011}{z1}}} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z0 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z0 \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;\frac{-1}{-1 - \frac{0.5641895665989011}{z1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= z0 -1e+31)
  (/ 1.0 z0)
  (if (<= z0 2.65e+73)
    (/ -1.0 (- -1.0 (/ 0.5641895665989011 z1)))
    (/ 1.0 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (z0 <= -1e+31) {
		tmp = 1.0 / z0;
	} else if (z0 <= 2.65e+73) {
		tmp = -1.0 / (-1.0 - (0.5641895665989011 / z1));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z0 <= (-1d+31)) then
        tmp = 1.0d0 / z0
    else if (z0 <= 2.65d+73) then
        tmp = (-1.0d0) / ((-1.0d0) - (0.5641895665989011d0 / z1))
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (z0 <= -1e+31) {
		tmp = 1.0 / z0;
	} else if (z0 <= 2.65e+73) {
		tmp = -1.0 / (-1.0 - (0.5641895665989011 / z1));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if z0 <= -1e+31:
		tmp = 1.0 / z0
	elif z0 <= 2.65e+73:
		tmp = -1.0 / (-1.0 - (0.5641895665989011 / z1))
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (z0 <= -1e+31)
		tmp = Float64(1.0 / z0);
	elseif (z0 <= 2.65e+73)
		tmp = Float64(-1.0 / Float64(-1.0 - Float64(0.5641895665989011 / z1)));
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (z0 <= -1e+31)
		tmp = 1.0 / z0;
	elseif (z0 <= 2.65e+73)
		tmp = -1.0 / (-1.0 - (0.5641895665989011 / z1));
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[z0, -1e+31], N[(1.0 / z0), $MachinePrecision], If[LessEqual[z0, 2.65e+73], N[(-1.0 / N[(-1.0 - N[(0.5641895665989011 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -9.9999999999999996e30 or 2.65e73 < z0

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -9.9999999999999996e30 < z0 < 2.65e73

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \frac{-1}{\color{blue}{-1} - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]
   3. Step-by-step derivation

   4. Applied rewrites 66.6%

      \[\leadsto \frac{-1}{\color{blue}{-1} - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \frac{-1}{-1 - \color{blue}{\frac{\frac{2000000000000000}{3544907808303833} + \frac{-2000000000000000}{3544907808303833} \cdot z1}{z1}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{-1}{-1 - \frac{\frac{2000000000000000}{3544907808303833} + \frac{-2000000000000000}{3544907808303833} \cdot z1}{\color{blue}{z1}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{-1}{-1 - \frac{\frac{2000000000000000}{3544907808303833} + \frac{-2000000000000000}{3544907808303833} \cdot z1}{z1}} \]

      3. lower-*.f64 53.2%

         \[\leadsto \frac{-1}{-1 - \frac{0.5641895665989011 + -0.5641895665989011 \cdot z1}{z1}} \]

   7. Applied rewrites 53.2%

      \[\leadsto \frac{-1}{-1 - \color{blue}{\frac{0.5641895665989011 + -0.5641895665989011 \cdot z1}{z1}}} \]

   8. Taylor expanded in z1 around 0

      \[\leadsto \frac{-1}{-1 - \frac{\frac{2000000000000000}{3544907808303833}}{z1}} \]
   9. Step-by-step derivation

   10. Applied rewrites 65.2%

       \[\leadsto \frac{-1}{-1 - \frac{0.5641895665989011}{z1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z0 \cdot z1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;z1 \cdot 1.7724539041519165\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0
        (/
         (sqrt (- (- 1.0 z1) z1))
         (* (* 1.7724539041519165 z1) (exp (* z1 z1))))))
  (if (<= t_0 -5e+43)
    (* z1 (+ 1.7724539041519165 (* -3.141592842343371 (* z0 z1))))
    (if (<= t_0 2e+153) (/ 1.0 z0) (* z1 1.7724539041519165)))))

C

double code(double z0, double z1) {
	double t_0 = sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((z1 * z1)));
	double tmp;
	if (t_0 <= -5e+43) {
		tmp = z1 * (1.7724539041519165 + (-3.141592842343371 * (z0 * z1)));
	} else if (t_0 <= 2e+153) {
		tmp = 1.0 / z0;
	} else {
		tmp = z1 * 1.7724539041519165;
	}
	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 = sqrt(((1.0d0 - z1) - z1)) / ((1.7724539041519165d0 * z1) * exp((z1 * z1)))
    if (t_0 <= (-5d+43)) then
        tmp = z1 * (1.7724539041519165d0 + ((-3.141592842343371d0) * (z0 * z1)))
    else if (t_0 <= 2d+153) then
        tmp = 1.0d0 / z0
    else
        tmp = z1 * 1.7724539041519165d0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = Math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * Math.exp((z1 * z1)));
	double tmp;
	if (t_0 <= -5e+43) {
		tmp = z1 * (1.7724539041519165 + (-3.141592842343371 * (z0 * z1)));
	} else if (t_0 <= 2e+153) {
		tmp = 1.0 / z0;
	} else {
		tmp = z1 * 1.7724539041519165;
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = math.sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * math.exp((z1 * z1)))
	tmp = 0
	if t_0 <= -5e+43:
		tmp = z1 * (1.7724539041519165 + (-3.141592842343371 * (z0 * z1)))
	elif t_0 <= 2e+153:
		tmp = 1.0 / z0
	else:
		tmp = z1 * 1.7724539041519165
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) / Float64(Float64(1.7724539041519165 * z1) * exp(Float64(z1 * z1))))
	tmp = 0.0
	if (t_0 <= -5e+43)
		tmp = Float64(z1 * Float64(1.7724539041519165 + Float64(-3.141592842343371 * Float64(z0 * z1))));
	elseif (t_0 <= 2e+153)
		tmp = Float64(1.0 / z0);
	else
		tmp = Float64(z1 * 1.7724539041519165);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = sqrt(((1.0 - z1) - z1)) / ((1.7724539041519165 * z1) * exp((z1 * z1)));
	tmp = 0.0;
	if (t_0 <= -5e+43)
		tmp = z1 * (1.7724539041519165 + (-3.141592842343371 * (z0 * z1)));
	elseif (t_0 <= 2e+153)
		tmp = 1.0 / z0;
	else
		tmp = z1 * 1.7724539041519165;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] / N[(N[(1.7724539041519165 * z1), $MachinePrecision] * N[Exp[N[(z1 * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+43], N[(z1 * N[(1.7724539041519165 + N[(-3.141592842343371 * N[(z0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+153], N[(1.0 / z0), $MachinePrecision], N[(z1 * 1.7724539041519165), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) (*.f64 (*.f64 #s(literal 3544907808303833/2000000000000000 binary64) z1) (exp.f64 (*.f64 z1 z1)))) < -5.0000000000000004e43

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \color{blue}{\frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{\left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \color{blue}{\left(\frac{1544907808303833}{3544907808303833} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.4%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   7. Applied rewrites 50.4%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   8. Taylor expanded in z0 around inf

      \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z0 \cdot \color{blue}{z1}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 50.1%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z0 \cdot z1\right)\right) \]

   10. Applied rewrites 50.1%

       \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z0 \cdot \color{blue}{z1}\right)\right) \]

   if -5.0000000000000004e43 < (/.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) (*.f64 (*.f64 #s(literal 3544907808303833/2000000000000000 binary64) z1) (exp.f64 (*.f64 z1 z1)))) < 2e153

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if 2e153 < (/.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) (*.f64 (*.f64 #s(literal 3544907808303833/2000000000000000 binary64) z1) (exp.f64 (*.f64 z1 z1))))

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \color{blue}{\frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{\left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \color{blue}{\left(\frac{1544907808303833}{3544907808303833} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.4%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   7. Applied rewrites 50.4%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   8. Taylor expanded in z1 around 0

      \[\leadsto z1 \cdot \frac{3544907808303833}{2000000000000000} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.2%

       \[\leadsto z1 \cdot 1.7724539041519165 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z1 \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z1 \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;z1 \cdot 1.7724539041519165\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= z1 -1.4e-35)
  (/ 1.0 z0)
  (if (<= z1 2.8e-155) (* z1 1.7724539041519165) (/ 1.0 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.4e-35) {
		tmp = 1.0 / z0;
	} else if (z1 <= 2.8e-155) {
		tmp = z1 * 1.7724539041519165;
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z1 <= (-1.4d-35)) then
        tmp = 1.0d0 / z0
    else if (z1 <= 2.8d-155) then
        tmp = z1 * 1.7724539041519165d0
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.4e-35) {
		tmp = 1.0 / z0;
	} else if (z1 <= 2.8e-155) {
		tmp = z1 * 1.7724539041519165;
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if z1 <= -1.4e-35:
		tmp = 1.0 / z0
	elif z1 <= 2.8e-155:
		tmp = z1 * 1.7724539041519165
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (z1 <= -1.4e-35)
		tmp = Float64(1.0 / z0);
	elseif (z1 <= 2.8e-155)
		tmp = Float64(z1 * 1.7724539041519165);
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (z1 <= -1.4e-35)
		tmp = 1.0 / z0;
	elseif (z1 <= 2.8e-155)
		tmp = z1 * 1.7724539041519165;
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[z1, -1.4e-35], N[(1.0 / z0), $MachinePrecision], If[LessEqual[z1, 2.8e-155], N[(z1 * 1.7724539041519165), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z1 < -1.4e-35 or 2.8e-155 < z1

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -1.4e-35 < z1 < 2.8e-155

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \color{blue}{\frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{\left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \color{blue}{\left(\frac{1544907808303833}{3544907808303833} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.4%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   7. Applied rewrites 50.4%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   8. Taylor expanded in z1 around 0

      \[\leadsto z1 \cdot \frac{3544907808303833}{2000000000000000} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.2%

       \[\leadsto z1 \cdot 1.7724539041519165 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.6% accurate, 6.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z1 \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z1 \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;z1 \cdot \left(1.7724539041519165 + -1.3691389381914547 \cdot z1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= z1 -1.4e-35)
  (/ 1.0 z0)
  (if (<= z1 2.8e-155)
    (* z1 (+ 1.7724539041519165 (* -1.3691389381914547 z1)))
    (/ 1.0 z0))))

C

double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.4e-35) {
		tmp = 1.0 / z0;
	} else if (z1 <= 2.8e-155) {
		tmp = z1 * (1.7724539041519165 + (-1.3691389381914547 * z1));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z1 <= (-1.4d-35)) then
        tmp = 1.0d0 / z0
    else if (z1 <= 2.8d-155) then
        tmp = z1 * (1.7724539041519165d0 + ((-1.3691389381914547d0) * z1))
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if (z1 <= -1.4e-35) {
		tmp = 1.0 / z0;
	} else if (z1 <= 2.8e-155) {
		tmp = z1 * (1.7724539041519165 + (-1.3691389381914547 * z1));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if z1 <= -1.4e-35:
		tmp = 1.0 / z0
	elif z1 <= 2.8e-155:
		tmp = z1 * (1.7724539041519165 + (-1.3691389381914547 * z1))
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (z1 <= -1.4e-35)
		tmp = Float64(1.0 / z0);
	elseif (z1 <= 2.8e-155)
		tmp = Float64(z1 * Float64(1.7724539041519165 + Float64(-1.3691389381914547 * z1)));
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if (z1 <= -1.4e-35)
		tmp = 1.0 / z0;
	elseif (z1 <= 2.8e-155)
		tmp = z1 * (1.7724539041519165 + (-1.3691389381914547 * z1));
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[z1, -1.4e-35], N[(1.0 / z0), $MachinePrecision], If[LessEqual[z1, 2.8e-155], N[(z1 * N[(1.7724539041519165 + N[(-1.3691389381914547 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z1 < -1.4e-35 or 2.8e-155 < z1

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -1.4e-35 < z1 < 2.8e-155

   1. Initial program 99.8%

      \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

   2. Taylor expanded in z0 around inf

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

      1. lower-/.f64 34.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \color{blue}{\frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{\left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \color{blue}{\left(\frac{1544907808303833}{3544907808303833} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.4%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   7. Applied rewrites 50.4%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto z1 \cdot \left(1.7724539041519165 + \frac{-5476555752765818812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{z1}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 50.5%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.3691389381914547 \cdot z1\right) \]

   10. Applied rewrites 50.5%

       \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.3691389381914547 \cdot \color{blue}{z1}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 50.2% accurate, 26.7× speedup

Math

\[z1 \cdot 1.7724539041519165 \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (* z1 1.7724539041519165))

C

double code(double z0, double z1) {
	return z1 * 1.7724539041519165;
}

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 = z1 * 1.7724539041519165d0
end function

Java

public static double code(double z0, double z1) {
	return z1 * 1.7724539041519165;
}

Python

def code(z0, z1):
	return z1 * 1.7724539041519165

Julia

function code(z0, z1)
	return Float64(z1 * 1.7724539041519165)
end

MATLAB

function tmp = code(z0, z1)
	tmp = z1 * 1.7724539041519165;
end

Wolfram

code[z0_, z1_] := N[(z1 * 1.7724539041519165), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{-1}{\left(-1 - z0\right) - \frac{\sqrt{\left(1 - z1\right) - z1}}{\left(1.7724539041519165 \cdot z1\right) \cdot e^{z1 \cdot z1}}} \]

2. Taylor expanded in z0 around inf

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

   1. lower-/.f64 34.9%

      \[\leadsto \frac{1}{\color{blue}{z0}} \]

4. Applied rewrites 34.9%

   \[\leadsto \color{blue}{\frac{1}{z0}} \]

5. Taylor expanded in z1 around 0

   \[\leadsto \color{blue}{z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \color{blue}{\left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \color{blue}{\frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \color{blue}{\left(z1 \cdot \left(\frac{1544907808303833}{3544907808303833} + z0\right)\right)}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{3544907808303833}{2000000000000000} + \frac{-12566371369373484812148442491889}{4000000000000000000000000000000} \cdot \left(z1 \cdot \color{blue}{\left(\frac{1544907808303833}{3544907808303833} + z0\right)}\right)\right) \]

   5. lower-+.f64 50.4%

      \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

7. Applied rewrites 50.4%

   \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.141592842343371 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

8. Taylor expanded in z1 around 0

   \[\leadsto z1 \cdot \frac{3544907808303833}{2000000000000000} \]
9. Step-by-step derivation

10. Applied rewrites 50.2%

    \[\leadsto z1 \cdot 1.7724539041519165 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z1)
  :name "(/ -1 (- (- -1 z0) (/ (sqrt (- (- 1 z1) z1)) (* (* 3544907808303833/2000000000000000 z1) (exp (* z1 z1))))))"
  :precision binary64
  (/ -1.0 (- (- -1.0 z0) (/ (sqrt (- (- 1.0 z1) z1)) (* (* 1.7724539041519165 z1) (exp (* z1 z1)))))))