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

Percentage Accurate: 95.8% → 99.9%

Time: 8.9s

Alternatives: 11

Speedup: 8.5×

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: 95.8% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - (-1.0 / ((exp(z) * (1.1283791670955126 / y)) - 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) / ((exp(z) * (1.1283791670955126d0 / y)) - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.2%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x - \frac{-1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}} \]

4. Final simplification 99.9%

   \[\leadsto x - \frac{-1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x} \]

Alternative 2: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y}\\ \mathbf{if}\;t_0 \leq 10^{+273}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y (- (* (exp z) 1.1283791670955126) (* x y))))))
   (if (<= t_0 1e+273) t_0 (+ x (/ -1.0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / ((exp(z) * 1.1283791670955126) - (x * y)));
	double tmp;
	if (t_0 <= 1e+273) {
		tmp = t_0;
	} else {
		tmp = x + (-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) :: t_0
    real(8) :: tmp
    t_0 = x + (y / ((exp(z) * 1.1283791670955126d0) - (x * y)))
    if (t_0 <= 1d+273) then
        tmp = t_0
    else
        tmp = x + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y / ((Math.exp(z) * 1.1283791670955126) - (x * y)));
	double tmp;
	if (t_0 <= 1e+273) {
		tmp = t_0;
	} else {
		tmp = x + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / ((math.exp(z) * 1.1283791670955126) - (x * y)))
	tmp = 0
	if t_0 <= 1e+273:
		tmp = t_0
	else:
		tmp = x + (-1.0 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / Float64(Float64(exp(z) * 1.1283791670955126) - Float64(x * y))))
	tmp = 0.0
	if (t_0 <= 1e+273)
		tmp = t_0;
	else
		tmp = Float64(x + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / ((exp(z) * 1.1283791670955126) - (x * y)));
	tmp = 0.0;
	if (t_0 <= 1e+273)
		tmp = t_0;
	else
		tmp = x + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / N[(N[(N[Exp[z], $MachinePrecision] * 1.1283791670955126), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+273], t$95$0, N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 y (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))) < 9.99999999999999945e272

   1. Initial program 99.4%

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

   if 9.99999999999999945e272 < (+.f64 x (/.f64 y (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))

   1. Initial program 54.6%

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

   2. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y} \leq 10^{+273}:\\ \;\;\;\;x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{x}\\ \end{array} \]

Alternative 3: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1.0005:\\ \;\;\;\;x + \frac{y}{\left(1.1283791670955126 + z \cdot 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (if (<= (exp z) 1.0005)
     (+ x (/ y (- (+ 1.1283791670955126 (* z 1.1283791670955126)) (* x y))))
     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) <= 1.0005) {
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	} else {
		tmp = 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) <= 1.0005d0) then
        tmp = x + (y / ((1.1283791670955126d0 + (z * 1.1283791670955126d0)) - (x * y)))
    else
        tmp = 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) <= 1.0005) {
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	} else {
		tmp = 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) <= 1.0005:
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)))
	else:
		tmp = 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) <= 1.0005)
		tmp = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 + Float64(z * 1.1283791670955126)) - Float64(x * y))));
	else
		tmp = 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) <= 1.0005)
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	else
		tmp = 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], 1.0005], N[(x + N[(y / N[(N[(1.1283791670955126 + N[(z * 1.1283791670955126), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 100.0%

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

   if 0.0 < (exp.f64 z) < 1.00049999999999994

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   if 1.00049999999999994 < (exp.f64 z)

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1.0005:\\ \;\;\;\;x + \frac{y}{\left(1.1283791670955126 + z \cdot 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 84.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ t_1 := x + \frac{y}{1.1283791670955126}\\ \mathbf{if}\;z \leq -14.2:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.3 \cdot 10^{-305}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))) (t_1 (+ x (/ y 1.1283791670955126))))
   (if (<= z -14.2)
     t_0
     (if (<= z -6.8e-228)
       t_1
       (if (<= z 8.3e-305)
         t_0
         (if (<= z 1e-118) t_1 (if (<= z 1.28e-8) t_0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double t_1 = x + (y / 1.1283791670955126);
	double tmp;
	if (z <= -14.2) {
		tmp = t_0;
	} else if (z <= -6.8e-228) {
		tmp = t_1;
	} else if (z <= 8.3e-305) {
		tmp = t_0;
	} else if (z <= 1e-118) {
		tmp = t_1;
	} else if (z <= 1.28e-8) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + ((-1.0d0) / x)
    t_1 = x + (y / 1.1283791670955126d0)
    if (z <= (-14.2d0)) then
        tmp = t_0
    else if (z <= (-6.8d-228)) then
        tmp = t_1
    else if (z <= 8.3d-305) then
        tmp = t_0
    else if (z <= 1d-118) then
        tmp = t_1
    else if (z <= 1.28d-8) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double t_1 = x + (y / 1.1283791670955126);
	double tmp;
	if (z <= -14.2) {
		tmp = t_0;
	} else if (z <= -6.8e-228) {
		tmp = t_1;
	} else if (z <= 8.3e-305) {
		tmp = t_0;
	} else if (z <= 1e-118) {
		tmp = t_1;
	} else if (z <= 1.28e-8) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	t_1 = x + (y / 1.1283791670955126)
	tmp = 0
	if z <= -14.2:
		tmp = t_0
	elif z <= -6.8e-228:
		tmp = t_1
	elif z <= 8.3e-305:
		tmp = t_0
	elif z <= 1e-118:
		tmp = t_1
	elif z <= 1.28e-8:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(-1.0 / x))
	t_1 = Float64(x + Float64(y / 1.1283791670955126))
	tmp = 0.0
	if (z <= -14.2)
		tmp = t_0;
	elseif (z <= -6.8e-228)
		tmp = t_1;
	elseif (z <= 8.3e-305)
		tmp = t_0;
	elseif (z <= 1e-118)
		tmp = t_1;
	elseif (z <= 1.28e-8)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (-1.0 / x);
	t_1 = x + (y / 1.1283791670955126);
	tmp = 0.0;
	if (z <= -14.2)
		tmp = t_0;
	elseif (z <= -6.8e-228)
		tmp = t_1;
	elseif (z <= 8.3e-305)
		tmp = t_0;
	elseif (z <= 1e-118)
		tmp = t_1;
	elseif (z <= 1.28e-8)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y / 1.1283791670955126), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -14.2], t$95$0, If[LessEqual[z, -6.8e-228], t$95$1, If[LessEqual[z, 8.3e-305], t$95$0, If[LessEqual[z, 1e-118], t$95$1, If[LessEqual[z, 1.28e-8], t$95$0, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -14.199999999999999 or -6.79999999999999981e-228 < z < 8.3000000000000002e-305 or 9.99999999999999985e-119 < z < 1.28000000000000005e-8

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 90.4%

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

   if -14.199999999999999 < z < -6.79999999999999981e-228 or 8.3000000000000002e-305 < z < 9.99999999999999985e-119

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto x + \color{blue}{\frac{y}{1.1283791670955126 - x \cdot y}} \]
   3. Step-by-step derivation

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 78.6%

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

   if 1.28000000000000005e-8 < z

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14.2:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-228}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{elif}\;z \leq 8.3 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 10^{-118}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 81.9% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+28} \lor \neg \left(y \leq 4.8 \cdot 10^{+56}\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 + z \cdot 1.1283791670955126}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.95e+28) (not (<= y 4.8e+56)))
   (+ x (/ -1.0 x))
   (+ x (/ y (+ 1.1283791670955126 (* z 1.1283791670955126))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.95e+28) || !(y <= 4.8e+56)) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (1.1283791670955126 + (z * 1.1283791670955126)));
	}
	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 ((y <= (-1.95d+28)) .or. (.not. (y <= 4.8d+56))) then
        tmp = x + ((-1.0d0) / x)
    else
        tmp = x + (y / (1.1283791670955126d0 + (z * 1.1283791670955126d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.95e+28) || !(y <= 4.8e+56)) {
		tmp = x + (-1.0 / x);
	} else {
		tmp = x + (y / (1.1283791670955126 + (z * 1.1283791670955126)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.95e+28) or not (y <= 4.8e+56):
		tmp = x + (-1.0 / x)
	else:
		tmp = x + (y / (1.1283791670955126 + (z * 1.1283791670955126)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.95e+28) || !(y <= 4.8e+56))
		tmp = Float64(x + Float64(-1.0 / x));
	else
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 + Float64(z * 1.1283791670955126))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.95e+28) || ~((y <= 4.8e+56)))
		tmp = x + (-1.0 / x);
	else
		tmp = x + (y / (1.1283791670955126 + (z * 1.1283791670955126)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.95e+28], N[Not[LessEqual[y, 4.8e+56]], $MachinePrecision]], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.1283791670955126 + N[(z * 1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9499999999999999e28 or 4.80000000000000027e56 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 80.2%

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

   if -1.9499999999999999e28 < y < 4.80000000000000027e56

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 89.3%

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

      1. *-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 88.5%

      \[\leadsto x + \color{blue}{\frac{y}{1.1283791670955126 + 1.1283791670955126 \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+28} \lor \neg \left(y \leq 4.8 \cdot 10^{+56}\right):\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 + z \cdot 1.1283791670955126}\\ \end{array} \]

Alternative 6: 99.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.00058:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -700.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.00058) (+ x (/ y (- 1.1283791670955126 (* x y)))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -700.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.00058) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = 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 <= (-700.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 0.00058d0) then
        tmp = x + (y / (1.1283791670955126d0 - (x * y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -700.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.00058) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -700.0:
		tmp = x + (-1.0 / x)
	elif z <= 0.00058:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -700.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.00058)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(x * y))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -700.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 0.00058)
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -700.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00058], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -700

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -700 < z < 5.8e-4

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.5%

      \[\leadsto x + \color{blue}{\frac{y}{1.1283791670955126 - x \cdot y}} \]
   3. Step-by-step derivation

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   if 5.8e-4 < z

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.00058:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 99.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.00058:\\ \;\;\;\;x - \frac{-1}{\frac{1.1283791670955126}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -700.0)
   (+ x (/ -1.0 x))
   (if (<= z 0.00058) (- x (/ -1.0 (- (/ 1.1283791670955126 y) x))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -700.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.00058) {
		tmp = x - (-1.0 / ((1.1283791670955126 / y) - x));
	} else {
		tmp = 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 <= (-700.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 0.00058d0) then
        tmp = x - ((-1.0d0) / ((1.1283791670955126d0 / y) - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -700.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 0.00058) {
		tmp = x - (-1.0 / ((1.1283791670955126 / y) - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -700.0:
		tmp = x + (-1.0 / x)
	elif z <= 0.00058:
		tmp = x - (-1.0 / ((1.1283791670955126 / y) - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -700.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 0.00058)
		tmp = Float64(x - Float64(-1.0 / Float64(Float64(1.1283791670955126 / y) - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -700.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 0.00058)
		tmp = x - (-1.0 / ((1.1283791670955126 / y) - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -700.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00058], N[(x - N[(-1.0 / N[(N[(1.1283791670955126 / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -700

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -700 < z < 5.8e-4

   1. Initial program 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{-1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}} \]

   4. Taylor expanded in z around 0 99.5%

      \[\leadsto x - \color{blue}{\frac{-1}{1.1283791670955126 \cdot \frac{1}{y} - x}} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x - \frac{-1}{\color{blue}{\frac{1.1283791670955126 \cdot 1}{y}} - x} \]

      2. metadata-eval 99.6%

         \[\leadsto x - \frac{-1}{\frac{\color{blue}{1.1283791670955126}}{y} - x} \]

   6. Simplified 99.6%

      \[\leadsto x - \color{blue}{\frac{-1}{\frac{1.1283791670955126}{y} - x}} \]

   if 5.8e-4 < z

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 0.00058:\\ \;\;\;\;x - \frac{-1}{\frac{1.1283791670955126}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 73.0% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-152}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e-26) x (if (<= x 7e-152) (+ x (/ y 1.1283791670955126)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-26) {
		tmp = x;
	} else if (x <= 7e-152) {
		tmp = x + (y / 1.1283791670955126);
	} else {
		tmp = 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 (x <= (-2.4d-26)) then
        tmp = x
    else if (x <= 7d-152) then
        tmp = x + (y / 1.1283791670955126d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-26) {
		tmp = x;
	} else if (x <= 7e-152) {
		tmp = x + (y / 1.1283791670955126);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e-26:
		tmp = x
	elif x <= 7e-152:
		tmp = x + (y / 1.1283791670955126)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e-26)
		tmp = x;
	elseif (x <= 7e-152)
		tmp = Float64(x + Float64(y / 1.1283791670955126));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e-26)
		tmp = x;
	elseif (x <= 7e-152)
		tmp = x + (y / 1.1283791670955126);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e-26], x, If[LessEqual[x, 7e-152], N[(x + N[(y / 1.1283791670955126), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e-26 or 7.0000000000000002e-152 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{x} \]

   if -2.4000000000000001e-26 < x < 7.0000000000000002e-152

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 68.9%

      \[\leadsto x + \color{blue}{\frac{y}{1.1283791670955126 - x \cdot y}} \]
   3. Step-by-step derivation

      1. *-commutative 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in y around 0 52.0%

      \[\leadsto x + \frac{y}{\color{blue}{1.1283791670955126}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-152}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 68.5% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-155}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-27) x (if (<= x 1.75e-155) (* y 0.8862269254527579) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-27) {
		tmp = x;
	} else if (x <= 1.75e-155) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = 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 (x <= (-2.6d-27)) then
        tmp = x
    else if (x <= 1.75d-155) then
        tmp = y * 0.8862269254527579d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-27) {
		tmp = x;
	} else if (x <= 1.75e-155) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-27:
		tmp = x
	elif x <= 1.75e-155:
		tmp = y * 0.8862269254527579
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-27)
		tmp = x;
	elseif (x <= 1.75e-155)
		tmp = Float64(y * 0.8862269254527579);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-27)
		tmp = x;
	elseif (x <= 1.75e-155)
		tmp = y * 0.8862269254527579;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-27], x, If[LessEqual[x, 1.75e-155], N[(y * 0.8862269254527579), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000017e-27 or 1.75000000000000008e-155 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{x} \]

   if -2.60000000000000017e-27 < x < 1.75000000000000008e-155

   1. Initial program 92.9%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{-1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}} \]

   4. Taylor expanded in z around 0 68.9%

      \[\leadsto x - \color{blue}{\frac{-1}{1.1283791670955126 \cdot \frac{1}{y} - x}} \]
   5. Step-by-step derivation

      1. associate-*r/ 68.9%

         \[\leadsto x - \frac{-1}{\color{blue}{\frac{1.1283791670955126 \cdot 1}{y}} - x} \]

      2. metadata-eval 68.9%

         \[\leadsto x - \frac{-1}{\frac{\color{blue}{1.1283791670955126}}{y} - x} \]

   6. Simplified 68.9%

      \[\leadsto x - \color{blue}{\frac{-1}{\frac{1.1283791670955126}{y} - x}} \]

   7. Taylor expanded in x around 0 41.1%

      \[\leadsto \color{blue}{0.8862269254527579 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{y \cdot 0.8862269254527579} \]

   9. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot 0.8862269254527579} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-155}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 68.5% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-27) x (if (<= x 1.3e-154) (/ y 1.1283791670955126) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-27) {
		tmp = x;
	} else if (x <= 1.3e-154) {
		tmp = y / 1.1283791670955126;
	} else {
		tmp = 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 (x <= (-2.6d-27)) then
        tmp = x
    else if (x <= 1.3d-154) then
        tmp = y / 1.1283791670955126d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-27) {
		tmp = x;
	} else if (x <= 1.3e-154) {
		tmp = y / 1.1283791670955126;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-27:
		tmp = x
	elif x <= 1.3e-154:
		tmp = y / 1.1283791670955126
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-27)
		tmp = x;
	elseif (x <= 1.3e-154)
		tmp = Float64(y / 1.1283791670955126);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-27)
		tmp = x;
	elseif (x <= 1.3e-154)
		tmp = y / 1.1283791670955126;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-27], x, If[LessEqual[x, 1.3e-154], N[(y / 1.1283791670955126), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000017e-27 or 1.3e-154 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{x} \]

   if -2.60000000000000017e-27 < x < 1.3e-154

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around 0 58.5%

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

   6. Taylor expanded in x around 0 41.1%

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

   7. Taylor expanded in z around 0 41.2%

      \[\leadsto \frac{y}{\color{blue}{1.1283791670955126}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 69.4% accurate, 111.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.2%

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

2. Taylor expanded in x around inf 66.0%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 66.0%

   \[\leadsto x \]

Developer target: 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 2023308 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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