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

Percentage Accurate: 95.3% → 99.3%

Time: 7.3s

Alternatives: 8

Speedup: 0.5×

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

real(8) function code(x, y, z)
    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: 95.3% 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

real(8) function code(x, y, z)
    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: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(1.1283791670955126, z, 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (if (<= (exp z) 1.0)
     (+ x (/ y (- (fma 1.1283791670955126 z 1.1283791670955126) (* x y))))
     (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else if (exp(z) <= 1.0) {
		tmp = x + (y / (fma(1.1283791670955126, z, 1.1283791670955126) - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Exp[z], $MachinePrecision], 1.0], N[(x + N[(y / N[(N[(1.1283791670955126 * z + 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 86.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 0.0 < (exp.f64 z) < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if 1 < (exp.f64 z)

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 42.4

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

   5. Applied rewrites 42.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 100.0%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (if (<= (exp z) 1.0) (+ x (/ y (- 1.1283791670955126 (* x y)))) (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else if (exp(z) <= 1.0) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (exp(z) <= 0.0d0) then
        tmp = x + ((-1.0d0) / x)
    else if (exp(z) <= 1.0d0) then
        tmp = x + (y / (1.1283791670955126d0 - (x * y)))
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (Math.exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else if (Math.exp(z) <= 1.0) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if math.exp(z) <= 0.0:
		tmp = x + (-1.0 / x)
	elif math.exp(z) <= 1.0:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = 1.0 * x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Exp[z], $MachinePrecision], 1.0], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 86.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 0.0 < (exp.f64 z) < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 99.7%

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

   if 1 < (exp.f64 z)

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 42.4

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

   5. Applied rewrites 42.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 100.0%

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

Alternative 3: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (exp(z) <= 0.0d0) then
        tmp = x + ((-1.0d0) / x)
    else
        tmp = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (Math.exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if math.exp(z) <= 0.0:
		tmp = x + (-1.0 / x)
	else:
		tmp = x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 86.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 0.0 < (exp.f64 z)

   1. Initial program 98.4%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.8862269254527579, z, 0.8862269254527579\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -820.0)
   (/ -1.0 x)
   (if (<= z 5e-155)
     (+ x (* (fma -0.8862269254527579 z 0.8862269254527579) y))
     (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -820.0) {
		tmp = -1.0 / x;
	} else if (z <= 5e-155) {
		tmp = x + (fma(-0.8862269254527579, z, 0.8862269254527579) * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -820.0)
		tmp = Float64(-1.0 / x);
	elseif (z <= 5e-155)
		tmp = Float64(x + Float64(fma(-0.8862269254527579, z, 0.8862269254527579) * y));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -820.0], N[(-1.0 / x), $MachinePrecision], If[LessEqual[z, 5e-155], N[(x + N[(N[(-0.8862269254527579 * z + 0.8862269254527579), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -820

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.9%

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

   if -820 < z < 4.9999999999999999e-155

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-/r* N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.4%

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

   if 4.9999999999999999e-155 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 95.1%

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

Alternative 5: 72.0% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-105} \lor \neg \left(z \leq 5 \cdot 10^{-155}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e-105) (not (<= z 5e-155)))
   (* 1.0 x)
   (+ x (* 0.8862269254527579 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-105) || !(z <= 5e-155)) {
		tmp = 1.0 * x;
	} else {
		tmp = x + (0.8862269254527579 * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.8d-105)) .or. (.not. (z <= 5d-155))) then
        tmp = 1.0d0 * x
    else
        tmp = x + (0.8862269254527579d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-105) || !(z <= 5e-155)) {
		tmp = 1.0 * x;
	} else {
		tmp = x + (0.8862269254527579 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e-105) or not (z <= 5e-155):
		tmp = 1.0 * x
	else:
		tmp = x + (0.8862269254527579 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e-105) || !(z <= 5e-155))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e-105) || ~((z <= 5e-155)))
		tmp = 1.0 * x;
	else
		tmp = x + (0.8862269254527579 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e-105], N[Not[LessEqual[z, 5e-155]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e-105 or 4.9999999999999999e-155 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.1%

      \[\leadsto 1 \cdot x \]

   if -3.7999999999999998e-105 < z < 4.9999999999999999e-155

   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

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-/r* N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 80.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 80.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-105} \lor \neg \left(z \leq 5 \cdot 10^{-155}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e-76)
   (+ x (/ -1.0 x))
   (if (<= z 5e-155) (+ x (* 0.8862269254527579 y)) (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e-76) {
		tmp = x + (-1.0 / x);
	} else if (z <= 5e-155) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.6d-76)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 5d-155) then
        tmp = x + (0.8862269254527579d0 * y)
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e-76) {
		tmp = x + (-1.0 / x);
	} else if (z <= 5e-155) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e-76:
		tmp = x + (-1.0 / x)
	elif z <= 5e-155:
		tmp = x + (0.8862269254527579 * y)
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e-76)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 5e-155)
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e-76)
		tmp = x + (-1.0 / x);
	elseif (z <= 5e-155)
		tmp = x + (0.8862269254527579 * y);
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e-76], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-155], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000002e-76

   1. Initial program 89.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   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 94.8

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

   5. Applied rewrites 94.8%

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

   if -5.6000000000000002e-76 < z < 4.9999999999999999e-155

   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

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-/r* N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 79.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 79.6%

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

   if 4.9999999999999999e-155 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 95.1%

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

Alternative 7: 73.1% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x + 0.8862269254527579 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -820.0)
   (/ -1.0 x)
   (if (<= z 5e-155) (+ x (* 0.8862269254527579 y)) (* 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -820.0) {
		tmp = -1.0 / x;
	} else if (z <= 5e-155) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-820.0d0)) then
        tmp = (-1.0d0) / x
    else if (z <= 5d-155) then
        tmp = x + (0.8862269254527579d0 * y)
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -820.0) {
		tmp = -1.0 / x;
	} else if (z <= 5e-155) {
		tmp = x + (0.8862269254527579 * y);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -820.0:
		tmp = -1.0 / x
	elif z <= 5e-155:
		tmp = x + (0.8862269254527579 * y)
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -820.0)
		tmp = Float64(-1.0 / x);
	elseif (z <= 5e-155)
		tmp = Float64(x + Float64(0.8862269254527579 * y));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -820.0)
		tmp = -1.0 / x;
	elseif (z <= 5e-155)
		tmp = x + (0.8862269254527579 * y);
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -820.0], N[(-1.0 / x), $MachinePrecision], If[LessEqual[z, 5e-155], N[(x + N[(0.8862269254527579 * y), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -820

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.9%

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

   if -820 < z < 4.9999999999999999e-155

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-/r* N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 75.2%

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

   if 4.9999999999999999e-155 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 95.1%

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

Alternative 8: 68.9% accurate, 21.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. unpow2 N/A

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

   6. lower-*.f64 58.2

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

5. Applied rewrites 58.2%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 71.0%

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

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    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 2024326 
(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)))))