Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A

Percentage Accurate: 95.4% → 99.6%

Time: 6.3s

Alternatives: 9

Speedup: 3.7×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.0085:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right), z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -195.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.0085)
     (+
      x
      (/
       y
       (-
        (fma
         (fma 0.5641895835477563 z 1.1283791670955126)
         z
         1.1283791670955126)
        (* x y))))
     (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -195.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.0085)
		tmp = Float64(x + Float64(y / Float64(fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - Float64(x * y))));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -195.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0085], N[(x + N[(y / N[(N[(N[(0.5641895835477563 * z + 1.1283791670955126), $MachinePrecision] * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -195

   1. Initial program 92.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 100.0%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   if -195 < z < 0.0085000000000000006

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{10000000000000000} \cdot z\right)\right)} - x \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y}{\color{blue}{\left(z \cdot \left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{10000000000000000} \cdot z\right) + \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{10000000000000000} \cdot z\right) \cdot z} + \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{10000000000000000} \cdot z, z, \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\color{blue}{\frac{5641895835477563}{10000000000000000} \cdot z + \frac{5641895835477563}{5000000000000000}}, z, \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      5. lower-fma.f64 99.9

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right)}, z, 1.1283791670955126\right) - x \cdot y} \]

   5. Applied rewrites 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right), z, 1.1283791670955126\right)} - x \cdot y} \]

   if 0.0085000000000000006 < z

   1. Initial program 94.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 63.0

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ t_1 := x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \mathbf{if}\;t\_1 \leq -50000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-37}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{-33}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x)))
        (t_1 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))))
   (if (<= t_1 -50000000.0)
     t_0
     (if (<= t_1 -1e-37)
       (+ x (* 0.8862269254527579 y))
       (if (<= t_1 1e-33) (* 1.0 x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double t_1 = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	double tmp;
	if (t_1 <= -50000000.0) {
		tmp = t_0;
	} else if (t_1 <= -1e-37) {
		tmp = x + (0.8862269254527579 * y);
	} else if (t_1 <= 1e-33) {
		tmp = 1.0 * x;
	} 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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + ((-1.0d0) / x)
    t_1 = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
    if (t_1 <= (-50000000.0d0)) then
        tmp = t_0
    else if (t_1 <= (-1d-37)) then
        tmp = x + (0.8862269254527579d0 * y)
    else if (t_1 <= 1d-33) then
        tmp = 1.0d0 * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double t_1 = x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
	double tmp;
	if (t_1 <= -50000000.0) {
		tmp = t_0;
	} else if (t_1 <= -1e-37) {
		tmp = x + (0.8862269254527579 * y);
	} else if (t_1 <= 1e-33) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	t_1 = x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))
	tmp = 0
	if t_1 <= -50000000.0:
		tmp = t_0
	elif t_1 <= -1e-37:
		tmp = x + (0.8862269254527579 * y)
	elif t_1 <= 1e-33:
		tmp = 1.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(-1.0 / x))
	t_1 = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
	tmp = 0.0
	if (t_1 <= -50000000.0)
		tmp = t_0;
	elseif (t_1 <= -1e-37)
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	elseif (t_1 <= 1e-33)
		tmp = Float64(1.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (-1.0 / x);
	t_1 = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	tmp = 0.0;
	if (t_1 <= -50000000.0)
		tmp = t_0;
	elseif (t_1 <= -1e-37)
		tmp = x + (0.8862269254527579 * y);
	elseif (t_1 <= 1e-33)
		tmp = 1.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000.0], t$95$0, If[LessEqual[t$95$1, -1e-37], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-33], N[(1.0 * x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < -5e7 or 1.0000000000000001e-33 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y))))

   1. Initial program 95.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 91.9

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 91.9%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   if -5e7 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < -1.00000000000000007e-37

   1. Initial program 99.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{y \cdot z}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      2. unpow2 N/A

         \[\leadsto x + \left(\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right) \cdot \left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      3. associate-/r* N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      4. div-add-rev N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      6. lower-+.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      7. lower-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      8. *-commutative N/A

         \[\leadsto x + \frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \color{blue}{\left(z \cdot y\right)}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      9. associate-*r* N/A

         \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right)} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right) \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      12. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\frac{-5641895835477563}{5000000000000000}} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      13. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right)} \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      14. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      15. *-commutative N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      17. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - y \cdot x} + y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

   5. Applied rewrites 90.3%

      \[\leadsto x + \color{blue}{\frac{\frac{\left(-1.1283791670955126 \cdot z\right) \cdot y}{1.1283791670955126 - y \cdot x} + y}{1.1283791670955126 - y \cdot x}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot \color{blue}{\left(y + -1 \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 84.9%

      \[\leadsto x + \mathsf{fma}\left(-0.8862269254527579, z, 0.8862269254527579\right) \cdot \color{blue}{y} \]

   9. Taylor expanded in z around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto x + 0.8862269254527579 \cdot y \]

   if -1.00000000000000007e-37 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < 1.0000000000000001e-33

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 1.4

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 1.4%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 86.2%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+259}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))))
   (if (<= t_0 2e+259) t_0 (+ x (/ -1.0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	double tmp;
	if (t_0 <= 2e+259) {
		tmp = t_0;
	} else {
		tmp = x + (-1.0 / x);
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
    if (t_0 <= 2d+259) then
        tmp = t_0
    else
        tmp = x + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
	double tmp;
	if (t_0 <= 2e+259) {
		tmp = t_0;
	} else {
		tmp = x + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))
	tmp = 0
	if t_0 <= 2e+259:
		tmp = t_0
	else:
		tmp = x + (-1.0 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
	tmp = 0.0
	if (t_0 <= 2e+259)
		tmp = t_0;
	else
		tmp = Float64(x + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	tmp = 0.0;
	if (t_0 <= 2e+259)
		tmp = t_0;
	else
		tmp = x + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+259], t$95$0, N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < 2e259

   1. Initial program 98.6%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   if 2e259 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y))))

   1. Initial program 69.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 100.0%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -190:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.0085:\\ \;\;\;\;x + \frac{y}{\left(z - -1\right) \cdot 1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -190.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.0085)
     (+ x (/ y (- (* (- z -1.0) 1.1283791670955126) (* x y))))
     (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -190.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (((z - -1.0) * 1.1283791670955126) - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-190.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 0.0085d0) then
        tmp = x + (y / (((z - (-1.0d0)) * 1.1283791670955126d0) - (x * y)))
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -190.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (((z - -1.0) * 1.1283791670955126) - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -190.0:
		tmp = x + (-1.0 / x)
	elif z <= 0.0085:
		tmp = x + (y / (((z - -1.0) * 1.1283791670955126) - (x * y)))
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -190.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.0085)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(z - -1.0) * 1.1283791670955126) - Float64(x * y))));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -190.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 0.0085)
		tmp = x + (y / (((z - -1.0) * 1.1283791670955126) - (x * y)));
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -190.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0085], N[(x + N[(y / N[(N[(N[(z - -1.0), $MachinePrecision] * 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -190

   1. Initial program 92.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 100.0%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   if -190 < z < 0.0085000000000000006

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\frac{5641895835477563}{5000000000000000}} - x \cdot y} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.0%

      \[\leadsto x + \frac{y}{\color{blue}{1.1283791670955126} - x \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{5000000000000000} \cdot z\right)} - x \cdot y} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot z + \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{z \cdot \frac{5641895835477563}{5000000000000000}} + \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      3. lower-fma.f64 99.8

         \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(z, 1.1283791670955126, 1.1283791670955126\right)} - x \cdot y} \]

   8. Applied rewrites 99.8%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(z, 1.1283791670955126, 1.1283791670955126\right)} - x \cdot y} \]
   9. Step-by-step derivation

   10. Applied rewrites 99.8%

       \[\leadsto x + \frac{y}{\left(z - -1\right) \cdot \color{blue}{1.1283791670955126} - x \cdot y} \]

   if 0.0085000000000000006 < z

   1. Initial program 94.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 63.0

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -190:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.0085:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -190.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.0085)
     (+ x (/ y (- (fma 1.1283791670955126 z 1.1283791670955126) (* x y))))
     (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -190.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (fma(1.1283791670955126, z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -190.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.0085)
		tmp = Float64(x + Float64(y / Float64(fma(1.1283791670955126, z, 1.1283791670955126) - Float64(x * y))));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -190.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0085], N[(x + N[(y / N[(N[(1.1283791670955126 * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -190

   1. Initial program 92.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 100.0%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   if -190 < z < 0.0085000000000000006

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + \frac{5641895835477563}{5000000000000000} \cdot z\right)} - x \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot z + \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      2. lower-fma.f64 99.8

         \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right)} - x \cdot y} \]

   5. Applied rewrites 99.8%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right)} - x \cdot y} \]

   if 0.0085000000000000006 < z

   1. Initial program 94.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 63.0

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.0085:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -195.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.0085) (+ x (/ y (- 1.1283791670955126 (* x y)))) (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-195.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 0.0085d0) then
        tmp = x + (y / (1.1283791670955126d0 - (x * y)))
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.0085) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -195.0:
		tmp = x + (-1.0 / x)
	elif z <= 0.0085:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -195.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.0085)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(x * y))));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -195.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 0.0085)
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -195.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0085], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -195

   1. Initial program 92.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   5. Applied rewrites 100.0%

      \[\leadsto x + \color{blue}{\frac{-1}{x}} \]

   if -195 < z < 0.0085000000000000006

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\frac{5641895835477563}{5000000000000000}} - x \cdot y} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.0%

      \[\leadsto x + \frac{y}{\color{blue}{1.1283791670955126} - x \cdot y} \]

   if 0.0085000000000000006 < z

   1. Initial program 94.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 63.0

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-10}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-96}:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-68}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.06e-10)
   (* 1.0 x)
   (if (<= x -6e-96)
     (/ -1.0 x)
     (if (<= x 1.6e-68) (+ x (* 0.8862269254527579 y)) (* 1.0 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-10) {
		tmp = 1.0 * x;
	} else if (x <= -6e-96) {
		tmp = -1.0 / x;
	} else if (x <= 1.6e-68) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.06d-10)) then
        tmp = 1.0d0 * x
    else if (x <= (-6d-96)) then
        tmp = (-1.0d0) / x
    else if (x <= 1.6d-68) then
        tmp = x + (0.8862269254527579d0 * y)
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-10) {
		tmp = 1.0 * x;
	} else if (x <= -6e-96) {
		tmp = -1.0 / x;
	} else if (x <= 1.6e-68) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.06e-10:
		tmp = 1.0 * x
	elif x <= -6e-96:
		tmp = -1.0 / x
	elif x <= 1.6e-68:
		tmp = x + (0.8862269254527579 * y)
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.06e-10)
		tmp = Float64(1.0 * x);
	elseif (x <= -6e-96)
		tmp = Float64(-1.0 / x);
	elseif (x <= 1.6e-68)
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.06e-10)
		tmp = 1.0 * x;
	elseif (x <= -6e-96)
		tmp = -1.0 / x;
	elseif (x <= 1.6e-68)
		tmp = x + (0.8862269254527579 * y);
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.06e-10], N[(1.0 * x), $MachinePrecision], If[LessEqual[x, -6e-96], N[(-1.0 / x), $MachinePrecision], If[LessEqual[x, 1.6e-68], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.06e-10 or 1.5999999999999999e-68 < x

   1. Initial program 97.5%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 92.8

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 93.4%

      \[\leadsto 1 \cdot x \]

   if -1.06e-10 < x < -6e-96

   1. Initial program 94.3%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 67.1

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 67.1%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 29.2%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 67.2%

       \[\leadsto \frac{-1}{\color{blue}{x}} \]

   if -6e-96 < x < 1.5999999999999999e-68

   1. Initial program 94.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{y \cdot z}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      2. unpow2 N/A

         \[\leadsto x + \left(\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right) \cdot \left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      3. associate-/r* N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      4. div-add-rev N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      6. lower-+.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      7. lower-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      8. *-commutative N/A

         \[\leadsto x + \frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \color{blue}{\left(z \cdot y\right)}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      9. associate-*r* N/A

         \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right)} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right) \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      12. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\frac{-5641895835477563}{5000000000000000}} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      13. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right)} \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      14. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      15. *-commutative N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      17. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - y \cdot x} + y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

   5. Applied rewrites 59.0%

      \[\leadsto x + \color{blue}{\frac{\frac{\left(-1.1283791670955126 \cdot z\right) \cdot y}{1.1283791670955126 - y \cdot x} + y}{1.1283791670955126 - y \cdot x}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot \color{blue}{\left(y + -1 \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.4%

      \[\leadsto x + \mathsf{fma}\left(-0.8862269254527579, z, 0.8862269254527579\right) \cdot \color{blue}{y} \]

   9. Taylor expanded in z around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 51.6%

       \[\leadsto x + 0.8862269254527579 \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 72.8% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-110} \lor \neg \left(x \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-110) (not (<= x 1.6e-68)))
   (* 1.0 x)
   (+ x (* 0.8862269254527579 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-110) || !(x <= 1.6e-68)) {
		tmp = 1.0 * x;
	} else {
		tmp = x + (0.8862269254527579 * y);
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7d-110)) .or. (.not. (x <= 1.6d-68))) then
        tmp = 1.0d0 * x
    else
        tmp = x + (0.8862269254527579d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-110) || !(x <= 1.6e-68)) {
		tmp = 1.0 * x;
	} else {
		tmp = x + (0.8862269254527579 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-110) or not (x <= 1.6e-68):
		tmp = 1.0 * x
	else:
		tmp = x + (0.8862269254527579 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-110) || !(x <= 1.6e-68))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e-110) || ~((x <= 1.6e-68)))
		tmp = 1.0 * x;
	else
		tmp = x + (0.8862269254527579 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-110], N[Not[LessEqual[x, 1.6e-68]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999947e-110 or 1.5999999999999999e-68 < x

   1. Initial program 97.2%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

      5. unpow2 N/A

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

      6. lower-*.f64 89.7

         \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   5. Applied rewrites 89.7%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 87.0%

      \[\leadsto 1 \cdot x \]

   if -6.99999999999999947e-110 < x < 1.5999999999999999e-68

   1. Initial program 94.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{y \cdot z}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}^{2}}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      2. unpow2 N/A

         \[\leadsto x + \left(\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right) \cdot \left(\frac{5641895835477563}{5000000000000000} - x \cdot y\right)}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      3. associate-/r* N/A

         \[\leadsto x + \left(\color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + \frac{y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}\right) \]

      4. div-add-rev N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

      6. lower-+.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      7. lower-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \left(y \cdot z\right)}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      8. *-commutative N/A

         \[\leadsto x + \frac{\frac{\frac{-5641895835477563}{5000000000000000} \cdot \color{blue}{\left(z \cdot y\right)}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      9. associate-*r* N/A

         \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right)} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\left(\mathsf{neg}\left(\frac{5641895835477563}{5000000000000000}\right)\right) \cdot z\right) \cdot y}}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      12. metadata-eval N/A

          \[\leadsto x + \frac{\frac{\left(\color{blue}{\frac{-5641895835477563}{5000000000000000}} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      13. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right)} \cdot y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      14. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      15. *-commutative N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - \color{blue}{y \cdot x}} + y}{\frac{5641895835477563}{5000000000000000} - x \cdot y} \]

      17. lower--.f64 N/A

          \[\leadsto x + \frac{\frac{\left(\frac{-5641895835477563}{5000000000000000} \cdot z\right) \cdot y}{\frac{5641895835477563}{5000000000000000} - y \cdot x} + y}{\color{blue}{\frac{5641895835477563}{5000000000000000} - x \cdot y}} \]

   5. Applied rewrites 59.7%

      \[\leadsto x + \color{blue}{\frac{\frac{\left(-1.1283791670955126 \cdot z\right) \cdot y}{1.1283791670955126 - y \cdot x} + y}{1.1283791670955126 - y \cdot x}} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot \color{blue}{\left(y + -1 \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.9%

      \[\leadsto x + \mathsf{fma}\left(-0.8862269254527579, z, 0.8862269254527579\right) \cdot \color{blue}{y} \]

   9. Taylor expanded in z around 0

      \[\leadsto x + \frac{5000000000000000}{5641895835477563} \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 52.2%

       \[\leadsto x + 0.8862269254527579 \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-110} \lor \neg \left(x \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.2% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z) {
	return 1.0 * x;
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 * x;
}

Python

def code(x, y, z):
	return 1.0 * x

Julia

function code(x, y, z)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{{x}^{2}}\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right) \cdot x} \]

   3. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(1 - \frac{1}{{x}^{2}}\right)} \cdot x \]

   4. lower-/.f64 N/A

      \[\leadsto \left(1 - \color{blue}{\frac{1}{{x}^{2}}}\right) \cdot x \]

   5. unpow2 N/A

      \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

   6. lower-*.f64 65.9

      \[\leadsto \left(1 - \frac{1}{\color{blue}{x \cdot x}}\right) \cdot x \]

5. Applied rewrites 65.9%

   \[\leadsto \color{blue}{\left(1 - \frac{1}{x \cdot x}\right) \cdot x} \]

6. Taylor expanded in x around inf

   \[\leadsto 1 \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 70.9%

   \[\leadsto 1 \cdot x \]
9. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - x));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / (((1.1283791670955126d0 / y) * exp(z)) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * Math.exp(z)) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / (((1.1283791670955126 / y) * math.exp(z)) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(Float64(1.1283791670955126 / y) * exp(z)) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(N[(1.1283791670955126 / y), $MachinePrecision] * N[Exp[z], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ 1 (- (* (/ 5641895835477563/5000000000000000 y) (exp z)) x))))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))