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

Percentage Accurate: 95.3% → 99.4%

Time: 6.9s

Alternatives: 9

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: 95.3% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1.000000000001:\\ \;\;\;\;x + \frac{y}{\left(1.1283791670955126 + 1.1283791670955126 \cdot z\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (if (<= (exp z) 1.000000000001)
     (+ x (/ y (- (+ 1.1283791670955126 (* 1.1283791670955126 z)) (* 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) <= 1.000000000001) {
		tmp = x + (y / ((1.1283791670955126 + (1.1283791670955126 * z)) - (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) <= 1.000000000001d0) then
        tmp = x + (y / ((1.1283791670955126d0 + (1.1283791670955126d0 * z)) - (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) <= 1.000000000001) {
		tmp = x + (y / ((1.1283791670955126 + (1.1283791670955126 * z)) - (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) <= 1.000000000001:
		tmp = x + (y / ((1.1283791670955126 + (1.1283791670955126 * z)) - (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) <= 1.000000000001)
		tmp = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 + Float64(1.1283791670955126 * z)) - 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) <= 1.000000000001)
		tmp = x + (y / ((1.1283791670955126 + (1.1283791670955126 * z)) - (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], 1.000000000001], N[(x + N[(y / N[(N[(1.1283791670955126 + N[(1.1283791670955126 * z), $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 82.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 82.1%

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

      2. associate-/l* 82.3%

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

      3. div-sub 82.3%

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

      4. associate-*r/ 82.3%

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

      5. /-rgt-identity 82.3%

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

      6. metadata-eval 82.3%

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

      7. associate-/l* 82.3%

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

      8. *-commutative 82.3%

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

      9. neg-mul-1 82.3%

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

      10. associate-/l* 82.3%

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

      11. associate-*r* 82.3%

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

      12. *-commutative 82.3%

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

      13. neg-mul-1 82.3%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   if 0.0 < (exp.f64 z) < 1.0000000000010001

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   if 1.0000000000010001 < (exp.f64 z)

   1. Initial program 94.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 94.1%

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

      2. associate-/l* 94.1%

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

      3. div-sub 94.1%

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

      4. associate-*r/ 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. metadata-eval 94.1%

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

      7. associate-/l* 94.1%

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

      8. *-commutative 94.1%

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

      9. neg-mul-1 94.1%

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

      10. associate-/l* 94.1%

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

      11. associate-*r* 94.1%

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

      12. *-commutative 94.1%

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

      13. neg-mul-1 94.1%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 68.2%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 1.000000000001:\\ \;\;\;\;x + \frac{y}{\left(1.1283791670955126 + 1.1283791670955126 \cdot z\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 94.3%

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

   2. associate-/l* 94.3%

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

   3. div-sub 94.3%

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

   4. associate-*r/ 94.3%

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

   5. /-rgt-identity 94.3%

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

   6. metadata-eval 94.3%

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

   7. associate-/l* 94.3%

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

   8. *-commutative 94.3%

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

   9. neg-mul-1 94.3%

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

   10. associate-/l* 94.3%

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

   11. associate-*r* 94.3%

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

   12. *-commutative 94.3%

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

   13. neg-mul-1 94.3%

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

   14. associate-/l* 99.9%

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

   15. *-inverses 99.9%

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

   16. /-rgt-identity 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 99.4% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -340:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{1}{\frac{1.1283791670955126 + 1.1283791670955126 \cdot z}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -340.0)
   (+ x (/ -1.0 x))
   (if (<= z 1.35e-12)
     (+ x (/ 1.0 (- (/ (+ 1.1283791670955126 (* 1.1283791670955126 z)) y) x)))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -340.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		tmp = x + (1.0 / (((1.1283791670955126 + (1.1283791670955126 * z)) / 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 <= (-340.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 1.35d-12) then
        tmp = x + (1.0d0 / (((1.1283791670955126d0 + (1.1283791670955126d0 * z)) / 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 <= -340.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		tmp = x + (1.0 / (((1.1283791670955126 + (1.1283791670955126 * z)) / y) - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -340.0:
		tmp = x + (-1.0 / x)
	elif z <= 1.35e-12:
		tmp = x + (1.0 / (((1.1283791670955126 + (1.1283791670955126 * z)) / y) - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -340.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1.35e-12)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(1.1283791670955126 + Float64(1.1283791670955126 * z)) / y) - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -340.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 1.35e-12)
		tmp = x + (1.0 / (((1.1283791670955126 + (1.1283791670955126 * z)) / y) - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -340.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-12], N[(x + N[(1.0 / N[(N[(N[(1.1283791670955126 + N[(1.1283791670955126 * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -340

   1. Initial program 82.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 82.1%

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

      2. associate-/l* 82.3%

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

      3. div-sub 82.3%

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

      4. associate-*r/ 82.3%

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

      5. /-rgt-identity 82.3%

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

      6. metadata-eval 82.3%

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

      7. associate-/l* 82.3%

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

      8. *-commutative 82.3%

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

      9. neg-mul-1 82.3%

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

      10. associate-/l* 82.3%

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

      11. associate-*r* 82.3%

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

      12. *-commutative 82.3%

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

      13. neg-mul-1 82.3%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -340 < z < 1.3499999999999999e-12

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 99.9%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. associate-*r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-/l* 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/l* 99.9%

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

      11. associate-*r* 99.9%

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

      12. *-commutative 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

   if 1.3499999999999999e-12 < z

   1. Initial program 94.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 94.1%

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

      2. associate-/l* 94.1%

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

      3. div-sub 94.1%

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

      4. associate-*r/ 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. metadata-eval 94.1%

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

      7. associate-/l* 94.1%

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

      8. *-commutative 94.1%

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

      9. neg-mul-1 94.1%

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

      10. associate-/l* 94.1%

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

      11. associate-*r* 94.1%

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

      12. *-commutative 94.1%

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

      13. neg-mul-1 94.1%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 68.2%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -340:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{1}{\frac{1.1283791670955126 + 1.1283791670955126 \cdot z}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 84.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ t_1 := x + y \cdot 0.8862269254527579\\ \mathbf{if}\;z \leq -56:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))) (t_1 (+ x (* y 0.8862269254527579))))
   (if (<= z -56.0)
     t_0
     (if (<= z -4.3e-201)
       t_1
       (if (<= z 8.2e-212) t_0 (if (<= z 1.22e-152) t_1 x))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double t_1 = x + (y * 0.8862269254527579);
	double tmp;
	if (z <= -56.0) {
		tmp = t_0;
	} else if (z <= -4.3e-201) {
		tmp = t_1;
	} else if (z <= 8.2e-212) {
		tmp = t_0;
	} else if (z <= 1.22e-152) {
		tmp = t_1;
	} 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 * 0.8862269254527579d0)
    if (z <= (-56.0d0)) then
        tmp = t_0
    else if (z <= (-4.3d-201)) then
        tmp = t_1
    else if (z <= 8.2d-212) then
        tmp = t_0
    else if (z <= 1.22d-152) then
        tmp = t_1
    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 * 0.8862269254527579);
	double tmp;
	if (z <= -56.0) {
		tmp = t_0;
	} else if (z <= -4.3e-201) {
		tmp = t_1;
	} else if (z <= 8.2e-212) {
		tmp = t_0;
	} else if (z <= 1.22e-152) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	t_1 = x + (y * 0.8862269254527579)
	tmp = 0
	if z <= -56.0:
		tmp = t_0
	elif z <= -4.3e-201:
		tmp = t_1
	elif z <= 8.2e-212:
		tmp = t_0
	elif z <= 1.22e-152:
		tmp = t_1
	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 * 0.8862269254527579))
	tmp = 0.0
	if (z <= -56.0)
		tmp = t_0;
	elseif (z <= -4.3e-201)
		tmp = t_1;
	elseif (z <= 8.2e-212)
		tmp = t_0;
	elseif (z <= 1.22e-152)
		tmp = t_1;
	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 * 0.8862269254527579);
	tmp = 0.0;
	if (z <= -56.0)
		tmp = t_0;
	elseif (z <= -4.3e-201)
		tmp = t_1;
	elseif (z <= 8.2e-212)
		tmp = t_0;
	elseif (z <= 1.22e-152)
		tmp = t_1;
	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 * 0.8862269254527579), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -56.0], t$95$0, If[LessEqual[z, -4.3e-201], t$95$1, If[LessEqual[z, 8.2e-212], t$95$0, If[LessEqual[z, 1.22e-152], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -56 or -4.2999999999999997e-201 < z < 8.20000000000000028e-212

   1. Initial program 89.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 89.7%

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

      2. associate-/l* 89.8%

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

      3. div-sub 89.8%

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

      4. associate-*r/ 89.8%

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

      5. /-rgt-identity 89.8%

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

      6. metadata-eval 89.8%

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

      7. associate-/l* 89.8%

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

      8. *-commutative 89.8%

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

      9. neg-mul-1 89.8%

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

      10. associate-/l* 89.8%

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

      11. associate-*r* 89.8%

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

      12. *-commutative 89.8%

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

      13. neg-mul-1 89.8%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 89.5%

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

   if -56 < z < -4.2999999999999997e-201 or 8.20000000000000028e-212 < z < 1.22000000000000009e-152

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 99.9%

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

      2. associate-/l* 99.8%

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

      3. div-sub 99.8%

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

      4. associate-*r/ 99.8%

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

      5. /-rgt-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-/l* 99.8%

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

      8. *-commutative 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/l* 99.8%

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

      11. associate-*r* 99.8%

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

      12. *-commutative 99.8%

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

      13. neg-mul-1 99.8%

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

      14. associate-/l* 99.8%

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

      15. *-inverses 99.8%

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

      16. /-rgt-identity 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in y around 0 87.8%

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

      1. *-commutative 87.8%

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

   7. Simplified 87.8%

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

   if 1.22000000000000009e-152 < z

   1. Initial program 95.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 95.7%

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

      2. associate-/l* 95.7%

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

      3. div-sub 95.7%

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

      4. associate-*r/ 95.7%

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

      5. /-rgt-identity 95.7%

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

      6. metadata-eval 95.7%

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

      7. associate-/l* 95.7%

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

      8. *-commutative 95.7%

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

      9. neg-mul-1 95.7%

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

      10. associate-/l* 95.7%

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

      11. associate-*r* 95.7%

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

      12. *-commutative 95.7%

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

      13. neg-mul-1 95.7%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 76.6%

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

   5. Taylor expanded in y around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around inf 93.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -56:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-201}:\\ \;\;\;\;x + y \cdot 0.8862269254527579\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-212}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-152}:\\ \;\;\;\;x + y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 83.7% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ t_1 := x + \frac{y}{1.1283791670955126}\\ \mathbf{if}\;z \leq -59:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-203}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))) (t_1 (+ x (/ y 1.1283791670955126))))
   (if (<= z -59.0)
     t_0
     (if (<= z -3.4e-201)
       t_1
       (if (<= z 1.75e-203) t_0 (if (<= z 1.72e-155) t_1 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 <= -59.0) {
		tmp = t_0;
	} else if (z <= -3.4e-201) {
		tmp = t_1;
	} else if (z <= 1.75e-203) {
		tmp = t_0;
	} else if (z <= 1.72e-155) {
		tmp = t_1;
	} 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 <= (-59.0d0)) then
        tmp = t_0
    else if (z <= (-3.4d-201)) then
        tmp = t_1
    else if (z <= 1.75d-203) then
        tmp = t_0
    else if (z <= 1.72d-155) then
        tmp = t_1
    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 <= -59.0) {
		tmp = t_0;
	} else if (z <= -3.4e-201) {
		tmp = t_1;
	} else if (z <= 1.75e-203) {
		tmp = t_0;
	} else if (z <= 1.72e-155) {
		tmp = t_1;
	} 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 <= -59.0:
		tmp = t_0
	elif z <= -3.4e-201:
		tmp = t_1
	elif z <= 1.75e-203:
		tmp = t_0
	elif z <= 1.72e-155:
		tmp = t_1
	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 <= -59.0)
		tmp = t_0;
	elseif (z <= -3.4e-201)
		tmp = t_1;
	elseif (z <= 1.75e-203)
		tmp = t_0;
	elseif (z <= 1.72e-155)
		tmp = t_1;
	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 <= -59.0)
		tmp = t_0;
	elseif (z <= -3.4e-201)
		tmp = t_1;
	elseif (z <= 1.75e-203)
		tmp = t_0;
	elseif (z <= 1.72e-155)
		tmp = t_1;
	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, -59.0], t$95$0, If[LessEqual[z, -3.4e-201], t$95$1, If[LessEqual[z, 1.75e-203], t$95$0, If[LessEqual[z, 1.72e-155], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -59 or -3.39999999999999985e-201 < z < 1.7500000000000001e-203

   1. Initial program 89.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 89.7%

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

      2. associate-/l* 89.8%

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

      3. div-sub 89.8%

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

      4. associate-*r/ 89.8%

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

      5. /-rgt-identity 89.8%

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

      6. metadata-eval 89.8%

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

      7. associate-/l* 89.8%

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

      8. *-commutative 89.8%

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

      9. neg-mul-1 89.8%

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

      10. associate-/l* 89.8%

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

      11. associate-*r* 89.8%

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

      12. *-commutative 89.8%

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

      13. neg-mul-1 89.8%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 89.5%

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

   if -59 < z < -3.39999999999999985e-201 or 1.7500000000000001e-203 < z < 1.71999999999999991e-155

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 99.9%

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

      2. associate-/l* 99.8%

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

      3. div-sub 99.8%

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

      4. associate-*r/ 99.8%

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

      5. /-rgt-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-/l* 99.8%

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

      8. *-commutative 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/l* 99.8%

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

      11. associate-*r* 99.8%

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

      12. *-commutative 99.8%

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

      13. neg-mul-1 99.8%

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

      14. associate-/l* 99.8%

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

      15. *-inverses 99.8%

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

      16. /-rgt-identity 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in y around 0 87.8%

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

      1. *-commutative 87.8%

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

   7. Simplified 87.8%

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

      1. metadata-eval 87.8%

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

      2. div-inv 87.9%

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

   9. Applied egg-rr 87.9%

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

   if 1.71999999999999991e-155 < z

   1. Initial program 95.7%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 95.7%

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

      2. associate-/l* 95.7%

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

      3. div-sub 95.7%

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

      4. associate-*r/ 95.7%

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

      5. /-rgt-identity 95.7%

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

      6. metadata-eval 95.7%

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

      7. associate-/l* 95.7%

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

      8. *-commutative 95.7%

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

      9. neg-mul-1 95.7%

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

      10. associate-/l* 95.7%

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

      11. associate-*r* 95.7%

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

      12. *-commutative 95.7%

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

      13. neg-mul-1 95.7%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 76.6%

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

   5. Taylor expanded in y around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around inf 93.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -59:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-203}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-155}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 99.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{1}{\frac{1.1283791670955126}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -140.0)
   (+ x (/ -1.0 x))
   (if (<= z 1.35e-12) (+ x (/ 1.0 (- (/ 1.1283791670955126 y) x))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -140.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		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 <= (-140.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 1.35d-12) 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 <= -140.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		tmp = x + (1.0 / ((1.1283791670955126 / y) - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -140.0:
		tmp = x + (-1.0 / x)
	elif z <= 1.35e-12:
		tmp = x + (1.0 / ((1.1283791670955126 / y) - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -140.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1.35e-12)
		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 <= -140.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 1.35e-12)
		tmp = x + (1.0 / ((1.1283791670955126 / y) - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -140.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-12], 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 < -140

   1. Initial program 82.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 82.1%

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

      2. associate-/l* 82.3%

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

      3. div-sub 82.3%

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

      4. associate-*r/ 82.3%

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

      5. /-rgt-identity 82.3%

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

      6. metadata-eval 82.3%

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

      7. associate-/l* 82.3%

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

      8. *-commutative 82.3%

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

      9. neg-mul-1 82.3%

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

      10. associate-/l* 82.3%

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

      11. associate-*r* 82.3%

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

      12. *-commutative 82.3%

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

      13. neg-mul-1 82.3%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -140 < z < 1.3499999999999999e-12

   1. Initial program 99.9%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 99.9%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. associate-*r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-/l* 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/l* 99.9%

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

      11. associate-*r* 99.9%

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

      12. *-commutative 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.8%

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

   if 1.3499999999999999e-12 < z

   1. Initial program 94.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 94.1%

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

      2. associate-/l* 94.1%

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

      3. div-sub 94.1%

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

      4. associate-*r/ 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. metadata-eval 94.1%

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

      7. associate-/l* 94.1%

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

      8. *-commutative 94.1%

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

      9. neg-mul-1 94.1%

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

      10. associate-/l* 94.1%

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

      11. associate-*r* 94.1%

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

      12. *-commutative 94.1%

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

      13. neg-mul-1 94.1%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 68.2%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{1}{\frac{1.1283791670955126}{y} - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 99.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -195.0)
   (+ x (/ -1.0 x))
   (if (<= z 1.35e-12) (+ x (/ y (- 1.1283791670955126 (* x y)))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		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 <= (-195.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 1.35d-12) 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 <= -195.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 1.35e-12) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -195.0:
		tmp = x + (-1.0 / x)
	elif z <= 1.35e-12:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -195.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 1.35e-12)
		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 <= -195.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 1.35e-12)
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -195.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-12], 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 < -195

   1. Initial program 82.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 82.1%

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

      2. associate-/l* 82.3%

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

      3. div-sub 82.3%

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

      4. associate-*r/ 82.3%

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

      5. /-rgt-identity 82.3%

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

      6. metadata-eval 82.3%

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

      7. associate-/l* 82.3%

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

      8. *-commutative 82.3%

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

      9. neg-mul-1 82.3%

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

      10. associate-/l* 82.3%

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

      11. associate-*r* 82.3%

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

      12. *-commutative 82.3%

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

      13. neg-mul-1 82.3%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -195 < z < 1.3499999999999999e-12

   1. Initial program 99.9%

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

   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%

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

   if 1.3499999999999999e-12 < z

   1. Initial program 94.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 94.1%

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

      2. associate-/l* 94.1%

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

      3. div-sub 94.1%

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

      4. associate-*r/ 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. metadata-eval 94.1%

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

      7. associate-/l* 94.1%

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

      8. *-commutative 94.1%

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

      9. neg-mul-1 94.1%

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

      10. associate-/l* 94.1%

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

      11. associate-*r* 94.1%

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

      12. *-commutative 94.1%

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

      13. neg-mul-1 94.1%

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

      14. associate-/l* 100.0%

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

      15. *-inverses 100.0%

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

      16. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 68.2%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 72.1% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.6e+37) x (if (<= y 4.7e+42) (+ x (* y 0.8862269254527579)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+37) {
		tmp = x;
	} else if (y <= 4.7e+42) {
		tmp = x + (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 (y <= (-1.6d+37)) then
        tmp = x
    else if (y <= 4.7d+42) then
        tmp = x + (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 (y <= -1.6e+37) {
		tmp = x;
	} else if (y <= 4.7e+42) {
		tmp = x + (y * 0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.6e+37:
		tmp = x
	elif y <= 4.7e+42:
		tmp = x + (y * 0.8862269254527579)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e+37)
		tmp = x;
	elseif (y <= 4.7e+42)
		tmp = Float64(x + Float64(y * 0.8862269254527579));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.6e+37)
		tmp = x;
	elseif (y <= 4.7e+42)
		tmp = x + (y * 0.8862269254527579);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.6e+37], x, If[LessEqual[y, 4.7e+42], N[(x + N[(y * 0.8862269254527579), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000007e37 or 4.69999999999999986e42 < y

   1. Initial program 96.0%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 96.0%

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

      2. associate-/l* 96.0%

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

      3. div-sub 96.0%

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

      4. associate-*r/ 96.0%

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

      5. /-rgt-identity 96.0%

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

      6. metadata-eval 96.0%

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

      7. associate-/l* 96.0%

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

      8. *-commutative 96.0%

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

      9. neg-mul-1 96.0%

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

      10. associate-/l* 96.0%

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

      11. associate-*r* 96.0%

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

      12. *-commutative 96.0%

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

      13. neg-mul-1 96.0%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 82.6%

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

   5. Taylor expanded in y around 0 34.2%

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

      1. *-commutative 34.2%

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

   7. Simplified 34.2%

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

   8. Taylor expanded in x around inf 72.5%

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

   if -1.60000000000000007e37 < y < 4.69999999999999986e42

   1. Initial program 93.1%

      \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
   2. Step-by-step derivation

      1. *-lft-identity 93.1%

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

      2. associate-/l* 93.1%

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

      3. div-sub 93.1%

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

      4. associate-*r/ 93.1%

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

      5. /-rgt-identity 93.1%

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

      6. metadata-eval 93.1%

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

      7. associate-/l* 93.1%

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

      8. *-commutative 93.1%

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

      9. neg-mul-1 93.1%

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

      10. associate-/l* 93.1%

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

      11. associate-*r* 93.1%

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

      12. *-commutative 93.1%

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

      13. neg-mul-1 93.1%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 82.7%

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

   5. Taylor expanded in y around 0 82.5%

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

      1. *-commutative 82.5%

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

   7. Simplified 82.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 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 94.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 94.3%

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

   2. associate-/l* 94.3%

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

   3. div-sub 94.3%

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

   4. associate-*r/ 94.3%

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

   5. /-rgt-identity 94.3%

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

   6. metadata-eval 94.3%

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

   7. associate-/l* 94.3%

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

   8. *-commutative 94.3%

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

   9. neg-mul-1 94.3%

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

   10. associate-/l* 94.3%

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

   11. associate-*r* 94.3%

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

   12. *-commutative 94.3%

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

   13. neg-mul-1 94.3%

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

   14. associate-/l* 99.9%

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

   15. *-inverses 99.9%

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

   16. /-rgt-identity 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around 0 82.6%

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

5. Taylor expanded in y around 0 63.2%

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

   1. *-commutative 63.2%

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

7. Simplified 63.2%

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

8. Taylor expanded in x around inf 73.0%

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

9. Final simplification 73.0%

   \[\leadsto x \]

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 2023334 
(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)))))