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

Percentage Accurate: 95.4% → 99.8%

Time: 8.5s

Alternatives: 14

Speedup: 3.1×

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: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -750:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.8862269254527579}{e^{z}}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -750.0)
   (+ x (/ -1.0 x))
   (if (<= z 5.5e-6)
     (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))
     (fma (/ 0.8862269254527579 (exp z)) y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -750.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 5.5e-6) {
		tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	} else {
		tmp = fma((0.8862269254527579 / exp(z)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -750.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 5.5e-6)
		tmp = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))));
	else
		tmp = fma(Float64(0.8862269254527579 / exp(z)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -750.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-6], N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.8862269254527579 / N[Exp[z], $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -750

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -750 < z < 5.4999999999999999e-6

   1. Initial program 99.8%

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

   if 5.4999999999999999e-6 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{5000000000000000}{5641895835477563} \cdot y}{e^{z}}} + x \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{5000000000000000}{5641895835477563}}{e^{z}} \cdot y} + x \]

      4. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{5000000000000000}{5641895835477563} \cdot 1}}{e^{z}} \cdot y + x \]

      5. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(\frac{5000000000000000}{5641895835477563} \cdot \frac{1}{e^{z}}\right)} \cdot y + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{5000000000000000}{5641895835477563} \cdot \frac{1}{e^{z}}, y, x\right)} \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{5000000000000000}{5641895835477563} \cdot 1}{e^{z}}}, y, x\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{5000000000000000}{5641895835477563}}}{e^{z}}, y, x\right) \]

      9. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{5000000000000000}{5641895835477563}}{e^{z}}}, y, x\right) \]

      10. lower-exp.f64 100.0

          \[\leadsto \mathsf{fma}\left(\frac{0.8862269254527579}{\color{blue}{e^{z}}}, y, x\right) \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0.8862269254527579}{e^{z}}, y, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 86.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \mathbf{if}\;t\_0 \leq -10 \lor \neg \left(t\_0 \leq 100000000000\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{1 + z}, 0.8862269254527579, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))))
   (if (or (<= t_0 -10.0) (not (<= t_0 100000000000.0)))
     (+ x (/ -1.0 x))
     (fma (/ y (+ 1.0 z)) 0.8862269254527579 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 <= -10.0) || !(t_0 <= 100000000000.0)) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = fma((y / (1.0 + z)), 0.8862269254527579, 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 <= -10.0) || !(t_0 <= 100000000000.0))
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = fma(Float64(y / Float64(1.0 + z)), 0.8862269254527579, x);
	end
	return 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[Or[LessEqual[t$95$0, -10.0], N[Not[LessEqual[t$95$0, 100000000000.0]], $MachinePrecision]], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(1.0 + z), $MachinePrecision]), $MachinePrecision] * 0.8862269254527579 + x), $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)))) < -10 or 1e11 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y))))

   1. Initial program 92.6%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 92.0

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

   5. Applied rewrites 92.0%

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

   if -10 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < 1e11

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 98.3

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z}, \frac{5000000000000000}{5641895835477563}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 77.7%

       \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z}, 0.8862269254527579, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \leq -10 \lor \neg \left(x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \leq 100000000000\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{1 + z}, 0.8862269254527579, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \mathbf{if}\;t\_0 \leq -10 \lor \neg \left(t\_0 \leq 100000000000\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.8862269254527579, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))))
   (if (or (<= t_0 -10.0) (not (<= t_0 100000000000.0)))
     (+ x (/ -1.0 x))
     (fma 0.8862269254527579 y 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 <= -10.0) || !(t_0 <= 100000000000.0)) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = fma(0.8862269254527579, y, 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 <= -10.0) || !(t_0 <= 100000000000.0))
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = fma(0.8862269254527579, y, x);
	end
	return 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[Or[LessEqual[t$95$0, -10.0], N[Not[LessEqual[t$95$0, 100000000000.0]], $MachinePrecision]], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(0.8862269254527579 * y + x), $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)))) < -10 or 1e11 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y))))

   1. Initial program 92.6%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 92.0

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

   5. Applied rewrites 92.0%

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

   if -10 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < 1e11

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 98.3

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.6%

       \[\leadsto \mathsf{fma}\left(0.8862269254527579, \color{blue}{y}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \leq -10 \lor \neg \left(x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \leq 100000000000\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.8862269254527579, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -750:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\frac{e^{z}}{x}, 1.1283791670955126, -y\right) \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -750.0)
   (+ x (/ -1.0 x))
   (+ x (/ y (* (fma (/ (exp z) x) 1.1283791670955126 (- y)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -750.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (fma((exp(z) / x), 1.1283791670955126, -y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -750.0)
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = Float64(x + Float64(y / Float64(fma(Float64(exp(z) / x), 1.1283791670955126, Float64(-y)) * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -750.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(N[(N[Exp[z], $MachinePrecision] / x), $MachinePrecision] * 1.1283791670955126 + (-y)), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -750

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -750 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 99.8%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\frac{e^{z}}{x}, 1.1283791670955126, -y\right) \cdot x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, 1\right)}{x}, 1.1283791670955126, -y\right) \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -290.0)
   (+ x (/ -1.0 x))
   (+
    x
    (/
     y
     (* (fma (/ (fma (fma 0.5 z 1.0) z 1.0) x) 1.1283791670955126 (- y)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (fma((fma(fma(0.5, z, 1.0), z, 1.0) / x), 1.1283791670955126, -y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = Float64(x + Float64(y / Float64(fma(Float64(fma(fma(0.5, z, 1.0), z, 1.0) / x), 1.1283791670955126, Float64(-y)) * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -290.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(N[(N[(N[(0.5 * z + 1.0), $MachinePrecision] * z + 1.0), $MachinePrecision] / x), $MachinePrecision] * 1.1283791670955126 + (-y)), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -290

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -290 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\mathsf{fma}\left(\frac{1 + z \cdot \left(1 + \frac{1}{2} \cdot z\right)}{x}, \frac{5641895835477563}{5000000000000000}, -y\right) \cdot x} \]
   7. Step-by-step derivation

   8. Applied rewrites 96.8%

      \[\leadsto x + \frac{y}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, 1\right)}{x}, 1.1283791670955126, -y\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 10^{+43}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.18806319451591877, z, 0.5641895835477563\right), z, 1.1283791670955126\right), z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z, 0.5\right), z, 1\right), z, 1\right)}, 0.8862269254527579, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -15.0)
   (+ x (/ -1.0 x))
   (if (<= z 1e+43)
     (+
      x
      (/
       y
       (-
        (fma
         (fma
          (fma 0.18806319451591877 z 0.5641895835477563)
          z
          1.1283791670955126)
         z
         1.1283791670955126)
        (* x y))))
     (fma
      (/ y (fma (fma (fma 0.16666666666666666 z 0.5) z 1.0) z 1.0))
      0.8862269254527579
      x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -15.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1e+43) {
		tmp = x + (y / (fma(fma(fma(0.18806319451591877, z, 0.5641895835477563), z, 1.1283791670955126), z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = fma((y / fma(fma(fma(0.16666666666666666, z, 0.5), z, 1.0), z, 1.0)), 0.8862269254527579, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -15.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1e+43)
		tmp = Float64(x + Float64(y / Float64(fma(fma(fma(0.18806319451591877, z, 0.5641895835477563), z, 1.1283791670955126), z, 1.1283791670955126) - Float64(x * y))));
	else
		tmp = fma(Float64(y / fma(fma(fma(0.16666666666666666, z, 0.5), z, 1.0), z, 1.0)), 0.8862269254527579, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -15.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+43], N[(x + N[(y / N[(N[(N[(N[(0.18806319451591877 * z + 0.5641895835477563), $MachinePrecision] * z + 1.1283791670955126), $MachinePrecision] * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(N[(N[(0.16666666666666666 * z + 0.5), $MachinePrecision] * z + 1.0), $MachinePrecision] * z + 1.0), $MachinePrecision]), $MachinePrecision] * 0.8862269254527579 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15

   1. Initial program 88.3%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 98.7

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

   5. Applied rewrites 98.7%

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

   if -15 < z < 1.00000000000000001e43

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right)\right)\right)} - x \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y}{\color{blue}{\left(z \cdot \left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right)\right) + \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right)\right) \cdot z} + \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\frac{5641895835477563}{5000000000000000} + z \cdot \left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right), z, \frac{5641895835477563}{5000000000000000}\right)} - x \cdot y} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right) + \frac{5641895835477563}{5000000000000000}}, z, \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      5. *-commutative N/A

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\color{blue}{\left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z\right) \cdot z} + \frac{5641895835477563}{5000000000000000}, z, \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{5641895835477563}{10000000000000000} + \frac{5641895835477563}{30000000000000000} \cdot z, z, \frac{5641895835477563}{5000000000000000}\right)}, z, \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      7. +-commutative N/A

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{5641895835477563}{30000000000000000} \cdot z + \frac{5641895835477563}{10000000000000000}}, z, \frac{5641895835477563}{5000000000000000}\right), z, \frac{5641895835477563}{5000000000000000}\right) - x \cdot y} \]

      8. lower-fma.f64 98.0

         \[\leadsto x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(0.18806319451591877, z, 0.5641895835477563\right)}, z, 1.1283791670955126\right), z, 1.1283791670955126\right) - x \cdot y} \]

   5. Applied rewrites 98.0%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.18806319451591877, z, 0.5641895835477563\right), z, 1.1283791670955126\right), z, 1.1283791670955126\right)} - x \cdot y} \]

   if 1.00000000000000001e43 < z

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 100.0

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z \cdot \left(1 + z \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot z\right)\right)}, \frac{5000000000000000}{5641895835477563}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 94.4%

       \[\leadsto \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z, 0.5\right), z, 1\right), z, 1\right)}, 0.8862269254527579, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right), z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z, 0.5\right), z, 1\right), z, 1\right)}, 0.8862269254527579, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -290.0)
   (+ x (/ -1.0 x))
   (if (<= z 7.2e+42)
     (+
      x
      (/
       y
       (-
        (fma
         (fma 0.5641895835477563 z 1.1283791670955126)
         z
         1.1283791670955126)
        (* x y))))
     (fma
      (/ y (fma (fma (fma 0.16666666666666666 z 0.5) z 1.0) z 1.0))
      0.8862269254527579
      x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e+42) {
		tmp = x + (y / (fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = fma((y / fma(fma(fma(0.16666666666666666, z, 0.5), z, 1.0), z, 1.0)), 0.8862269254527579, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 7.2e+42)
		tmp = Float64(x + Float64(y / Float64(fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - Float64(x * y))));
	else
		tmp = fma(Float64(y / fma(fma(fma(0.16666666666666666, z, 0.5), z, 1.0), z, 1.0)), 0.8862269254527579, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -290.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+42], 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[(N[(y / N[(N[(N[(0.16666666666666666 * z + 0.5), $MachinePrecision] * z + 1.0), $MachinePrecision] * z + 1.0), $MachinePrecision]), $MachinePrecision] * 0.8862269254527579 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -290

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -290 < z < 7.2000000000000002e42

   1. Initial program 99.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 97.1

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

   5. Applied rewrites 97.1%

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

   if 7.2000000000000002e42 < z

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 100.0

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z \cdot \left(1 + z \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot z\right)\right)}, \frac{5000000000000000}{5641895835477563}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 94.4%

       \[\leadsto \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z, 0.5\right), z, 1\right), z, 1\right)}, 0.8862269254527579, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 96.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, 1\right)}, 0.8862269254527579, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -15.0)
   (+ x (/ -1.0 x))
   (if (<= z 3.3e+43)
     (+ x (/ y (- (fma 1.1283791670955126 z 1.1283791670955126) (* x y))))
     (fma (/ y (fma (fma 0.5 z 1.0) z 1.0)) 0.8862269254527579 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -15.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 3.3e+43) {
		tmp = x + (y / (fma(1.1283791670955126, z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = fma((y / fma(fma(0.5, z, 1.0), z, 1.0)), 0.8862269254527579, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -15.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 3.3e+43)
		tmp = Float64(x + Float64(y / Float64(fma(1.1283791670955126, z, 1.1283791670955126) - Float64(x * y))));
	else
		tmp = fma(Float64(y / fma(fma(0.5, z, 1.0), z, 1.0)), 0.8862269254527579, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -15.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+43], N[(x + N[(y / N[(N[(1.1283791670955126 * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(N[(0.5 * z + 1.0), $MachinePrecision] * z + 1.0), $MachinePrecision]), $MachinePrecision] * 0.8862269254527579 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15

   1. Initial program 88.3%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 98.7

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

   5. Applied rewrites 98.7%

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

   if -15 < z < 3.3000000000000001e43

   1. Initial program 99.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 97.2

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

   5. Applied rewrites 97.2%

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

   if 3.3000000000000001e43 < z

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 100.0

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z \cdot \left(1 + \frac{1}{2} \cdot z\right)}, \frac{5000000000000000}{5641895835477563}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 90.6%

       \[\leadsto \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, 1\right)}, 0.8862269254527579, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 95.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right), z, 1.1283791670955126\right) - x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -290.0)
   (+ x (/ -1.0 x))
   (+
    x
    (/
     y
     (-
      (fma (fma 0.5641895835477563 z 1.1283791670955126) z 1.1283791670955126)
      (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - (x * y)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = Float64(x + Float64(y / Float64(fma(fma(0.5641895835477563, z, 1.1283791670955126), z, 1.1283791670955126) - Float64(x * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -290.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(N[(0.5641895835477563 * z + 1.1283791670955126), $MachinePrecision] * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -290

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -290 < z

   1. Initial program 97.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 93.6

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

   5. Applied rewrites 93.6%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.5641895835477563, z, 1.1283791670955126\right), z, 1.1283791670955126\right)} - x \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 93.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 1.1283791670955126 - x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -290.0)
   (+ x (/ -1.0 x))
   (if (<= z 1.0)
     (+ x (/ y (- 1.1283791670955126 (* x y))))
     (+ x (/ y (- (* z 1.1283791670955126) (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.0) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x + (y / ((z * 1.1283791670955126) - (x * 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 (z <= (-290.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 1.0d0) then
        tmp = x + (y / (1.1283791670955126d0 - (x * y)))
    else
        tmp = x + (y / ((z * 1.1283791670955126d0) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.0) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x + (y / ((z * 1.1283791670955126) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -290.0:
		tmp = x + (-1.0 / x)
	elif z <= 1.0:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = x + (y / ((z * 1.1283791670955126) - (x * y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(x * y))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z * 1.1283791670955126) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -290.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 1.0)
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	else
		tmp = x + (y / ((z * 1.1283791670955126) - (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -290.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z * 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -290

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -290 < z < 1

   1. Initial program 99.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 96.6%

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

   if 1 < z

   1. Initial program 90.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 79.1%

      \[\leadsto x + \frac{y}{z \cdot \color{blue}{1.1283791670955126} - x \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 92.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{1 + z}, 0.8862269254527579, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -290.0)
   (+ x (/ -1.0 x))
   (if (<= z 1.35e+73)
     (+ x (/ y (- 1.1283791670955126 (* x y))))
     (fma (/ y (+ 1.0 z)) 0.8862269254527579 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -290.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e+73) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = fma((y / (1.0 + z)), 0.8862269254527579, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1.35e+73)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(x * y))));
	else
		tmp = fma(Float64(y / Float64(1.0 + z)), 0.8862269254527579, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -290.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+73], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(1.0 + z), $MachinePrecision]), $MachinePrecision] * 0.8862269254527579 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -290

   1. Initial program 88.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 -290 < z < 1.35e73

   1. Initial program 99.8%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 94.0%

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

   if 1.35e73 < z

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

         \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

      6. metadata-eval N/A

         \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. *-lft-identity N/A

         \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

      10. metadata-eval N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

      5. lower-exp.f64 100.0

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z}, \frac{5000000000000000}{5641895835477563}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 83.3%

       \[\leadsto \mathsf{fma}\left(\frac{y}{1 + z}, 0.8862269254527579, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 93.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right) - x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -15.0)
   (+ x (/ -1.0 x))
   (+ x (/ y (- (fma 1.1283791670955126 z 1.1283791670955126) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -15.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (fma(1.1283791670955126, z, 1.1283791670955126) - (x * y)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -15.0)
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = Float64(x + Float64(y / Float64(fma(1.1283791670955126, z, 1.1283791670955126) - Float64(x * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -15.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(1.1283791670955126 * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -15

   1. Initial program 88.3%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 98.7

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

   5. Applied rewrites 98.7%

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

   if -15 < z

   1. Initial program 97.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 92.2

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

   5. Applied rewrites 92.2%

      \[\leadsto x + \frac{y}{\color{blue}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right)} - x \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 59.8% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.8862269254527579, y, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma 0.8862269254527579 y x))

C

double code(double x, double y, double z) {
	return fma(0.8862269254527579, y, x);
}

Julia

function code(x, y, z)
	return fma(0.8862269254527579, y, x)
end

Wolfram

code[x_, y_, z_] := N[(0.8862269254527579 * y + x), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. *-lft-identity N/A

      \[\leadsto x + \frac{y}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - \color{blue}{1 \cdot y}\right) \cdot x} \]

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

      \[\leadsto x + \frac{y}{\color{blue}{\left(\frac{5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right)} \cdot x} \]

   4. metadata-eval N/A

      \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000}\right)\right)} \cdot \frac{e^{z}}{x} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

   5. distribute-lft-neg-out N/A

      \[\leadsto x + \frac{y}{\left(\color{blue}{\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right)} + \left(\mathsf{neg}\left(1\right)\right) \cdot y\right) \cdot x} \]

   6. metadata-eval N/A

      \[\leadsto x + \frac{y}{\left(\left(\mathsf{neg}\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x}\right)\right) + \color{blue}{-1} \cdot y\right) \cdot x} \]

   7. mul-1-neg N/A

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

   8. distribute-neg-in N/A

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

   9. *-lft-identity N/A

      \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{1 \cdot y}\right)\right)\right) \cdot x} \]

   10. metadata-eval N/A

       \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot y\right)\right)\right) \cdot x} \]

   11. cancel-sign-sub-inv N/A

       \[\leadsto x + \frac{y}{\left(\mathsf{neg}\left(\color{blue}{\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)}\right)\right) \cdot x} \]

   12. lower-*.f64 N/A

       \[\leadsto x + \frac{y}{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{-5641895835477563}{5000000000000000} \cdot \frac{e^{z}}{x} - -1 \cdot y\right)\right)\right) \cdot x}} \]

5. Applied rewrites 96.7%

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

6. Taylor expanded in y around 0

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

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{5000000000000000}{5641895835477563} \cdot \frac{y}{e^{z}} + x} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} + x \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, \frac{5000000000000000}{5641895835477563}, x\right)} \]

   4. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{e^{z}}}, \frac{5000000000000000}{5641895835477563}, x\right) \]

   5. lower-exp.f64 61.0

      \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{e^{z}}}, 0.8862269254527579, x\right) \]

8. Applied rewrites 61.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{e^{z}}, 0.8862269254527579, x\right)} \]

9. Taylor expanded in z around 0

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

11. Applied rewrites 61.1%

    \[\leadsto \mathsf{fma}\left(0.8862269254527579, \color{blue}{y}, x\right) \]
12. Add Preprocessing

Alternative 14: 14.5% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ 0.8862269254527579 \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.8862269254527579 y))

C

double code(double x, double y, double z) {
	return 0.8862269254527579 * 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 = 0.8862269254527579d0 * y
end function

Java

public static double code(double x, double y, double z) {
	return 0.8862269254527579 * y;
}

Python

def code(x, y, z):
	return 0.8862269254527579 * y

Julia

function code(x, y, z)
	return Float64(0.8862269254527579 * y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.8862269254527579 * y;
end

Wolfram

code[x_, y_, z_] := N[(0.8862269254527579 * y), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot \frac{5000000000000000}{5641895835477563}} \]

   3. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{e^{z}}} \cdot \frac{5000000000000000}{5641895835477563} \]

   4. lower-exp.f64 16.9

      \[\leadsto \frac{y}{\color{blue}{e^{z}}} \cdot 0.8862269254527579 \]

5. Applied rewrites 16.9%

   \[\leadsto \color{blue}{\frac{y}{e^{z}} \cdot 0.8862269254527579} \]

6. Taylor expanded in z around 0

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

8. Applied rewrites 15.8%

   \[\leadsto \left(y - z \cdot y\right) \cdot 0.8862269254527579 \]

9. Taylor expanded in z around 0

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

11. Applied rewrites 15.4%

    \[\leadsto 0.8862269254527579 \cdot \color{blue}{y} \]
12. 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 2025008 
(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)))))