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

Percentage Accurate: 95.1% → 99.9%

Time: 12.7s

Alternatives: 13

Speedup: 5.8×

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: 95.1% 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, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 100.0%

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

   if 0.0 < (exp.f64 z)

   1. Initial program 97.4%

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

      1. remove-double-neg 97.4%

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

      2. distribute-frac-neg 97.4%

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

      3. unsub-neg 97.4%

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

      4. distribute-frac-neg 97.4%

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

      5. distribute-neg-frac2 97.4%

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

      6. neg-sub0 97.4%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 97.4%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 97.4%

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

      9. +-commutative 97.4%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 2:\\ \;\;\;\;x - \frac{y}{\left(x \cdot y + z \cdot \left(z \cdot \left(z \cdot -0.18806319451591877 - 0.5641895835477563\right) - 1.1283791670955126\right)\right) - 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 x))
   (if (<= (exp z) 2.0)
     (-
      x
      (/
       y
       (-
        (+
         (* x y)
         (*
          z
          (-
           (* z (- (* z -0.18806319451591877) 0.5641895835477563))
           1.1283791670955126)))
        1.1283791670955126)))
     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) <= 2.0) {
		tmp = x - (y / (((x * y) + (z * ((z * ((z * -0.18806319451591877) - 0.5641895835477563)) - 1.1283791670955126))) - 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 (exp(z) <= 0.0d0) then
        tmp = x + ((-1.0d0) / x)
    else if (exp(z) <= 2.0d0) then
        tmp = x - (y / (((x * y) + (z * ((z * ((z * (-0.18806319451591877d0)) - 0.5641895835477563d0)) - 1.1283791670955126d0))) - 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 (Math.exp(z) <= 0.0) {
		tmp = x + (-1.0 / x);
	} else if (Math.exp(z) <= 2.0) {
		tmp = x - (y / (((x * y) + (z * ((z * ((z * -0.18806319451591877) - 0.5641895835477563)) - 1.1283791670955126))) - 1.1283791670955126));
	} 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) <= 2.0:
		tmp = x - (y / (((x * y) + (z * ((z * ((z * -0.18806319451591877) - 0.5641895835477563)) - 1.1283791670955126))) - 1.1283791670955126))
	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) <= 2.0)
		tmp = Float64(x - Float64(y / Float64(Float64(Float64(x * y) + Float64(z * Float64(Float64(z * Float64(Float64(z * -0.18806319451591877) - 0.5641895835477563)) - 1.1283791670955126))) - 1.1283791670955126)));
	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) <= 2.0)
		tmp = x - (y / (((x * y) + (z * ((z * ((z * -0.18806319451591877) - 0.5641895835477563)) - 1.1283791670955126))) - 1.1283791670955126));
	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], 2.0], N[(x - N[(y / N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(N[(z * N[(N[(z * -0.18806319451591877), $MachinePrecision] - 0.5641895835477563), $MachinePrecision]), $MachinePrecision] - 1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 100.0%

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

   if 0.0 < (exp.f64 z) < 2

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   if 2 < (exp.f64 z)

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;e^{z} \leq 2:\\ \;\;\;\;x - \frac{y}{\left(x \cdot y + z \cdot \left(z \cdot \left(z \cdot -0.18806319451591877 - 0.5641895835477563\right) - 1.1283791670955126\right)\right) - 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y}\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{+249}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y (- (* (exp z) 1.1283791670955126) (* x y))))))
   (if (<= t_0 5e+249) 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 <= 5e+249) {
		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 <= 5d+249) 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 <= 5e+249) {
		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 <= 5e+249:
		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 <= 5e+249)
		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 <= 5e+249)
		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, 5e+249], t$95$0, N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y)))) < 4.9999999999999996e249

   1. Initial program 99.5%

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

   if 4.9999999999999996e249 < (+.f64 x (/.f64 y (-.f64 (*.f64 #s(literal 5641895835477563/5000000000000000 binary64) (exp.f64 z)) (*.f64 x y))))

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y} \leq 5 \cdot 10^{+249}:\\ \;\;\;\;x + \frac{y}{e^{z} \cdot 1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\left(z \cdot \left(1.1283791670955126 - z \cdot -0.5641895835477563\right) - x \cdot y\right) + 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -16200000000.0)
   (+ x (/ -1.0 x))
   (if (<= z 7.2e-25)
     (+
      x
      (/
       y
       (+
        (- (* z (- 1.1283791670955126 (* z -0.5641895835477563))) (* x y))
        1.1283791670955126)))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x + (y / (((z * (1.1283791670955126 - (z * -0.5641895835477563))) - (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 (z <= (-16200000000.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 7.2d-25) then
        tmp = x + (y / (((z * (1.1283791670955126d0 - (z * (-0.5641895835477563d0)))) - (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 (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x + (y / (((z * (1.1283791670955126 - (z * -0.5641895835477563))) - (x * y)) + 1.1283791670955126));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -16200000000.0:
		tmp = x + (-1.0 / x)
	elif z <= 7.2e-25:
		tmp = x + (y / (((z * (1.1283791670955126 - (z * -0.5641895835477563))) - (x * y)) + 1.1283791670955126))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 7.2e-25)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(z * Float64(1.1283791670955126 - Float64(z * -0.5641895835477563))) - Float64(x * y)) + 1.1283791670955126)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -16200000000.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 7.2e-25)
		tmp = x + (y / (((z * (1.1283791670955126 - (z * -0.5641895835477563))) - (x * y)) + 1.1283791670955126));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -16200000000.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-25], N[(x + N[(y / N[(N[(N[(z * N[(1.1283791670955126 - N[(z * -0.5641895835477563), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] + 1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62e10

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.62e10 < z < 7.1999999999999998e-25

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.8%

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

   if 7.1999999999999998e-25 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\left(z \cdot \left(1.1283791670955126 - z \cdot -0.5641895835477563\right) - x \cdot y\right) + 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.5% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - \left(x \cdot y + z \cdot -1.1283791670955126\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -16200000000.0)
   (+ x (/ -1.0 x))
   (if (<= z 7.2e-25)
     (+ x (/ y (- 1.1283791670955126 (+ (* x y) (* z -1.1283791670955126)))))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x + (y / (1.1283791670955126 - ((x * y) + (z * -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 (z <= (-16200000000.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 7.2d-25) then
        tmp = x + (y / (1.1283791670955126d0 - ((x * y) + (z * (-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 (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x + (y / (1.1283791670955126 - ((x * y) + (z * -1.1283791670955126))));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -16200000000.0:
		tmp = x + (-1.0 / x)
	elif z <= 7.2e-25:
		tmp = x + (y / (1.1283791670955126 - ((x * y) + (z * -1.1283791670955126))))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 7.2e-25)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(Float64(x * y) + Float64(z * -1.1283791670955126)))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -16200000000.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 7.2e-25)
		tmp = x + (y / (1.1283791670955126 - ((x * y) + (z * -1.1283791670955126))));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -16200000000.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-25], N[(x + N[(y / N[(1.1283791670955126 - N[(N[(x * y), $MachinePrecision] + N[(z * -1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62e10

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.62e10 < z < 7.1999999999999998e-25

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 7.1999999999999998e-25 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - \left(x \cdot y + z \cdot -1.1283791670955126\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;x - 0.8862269254527579 \cdot \left(z \cdot y - y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))))
   (if (<= z -16200000000.0)
     t_0
     (if (<= z 2.6e-166)
       (- x (* 0.8862269254527579 (- (* z y) y)))
       (if (<= z 2.8e-47) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double tmp;
	if (z <= -16200000000.0) {
		tmp = t_0;
	} else if (z <= 2.6e-166) {
		tmp = x - (0.8862269254527579 * ((z * y) - y));
	} else if (z <= 2.8e-47) {
		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) :: tmp
    t_0 = x + ((-1.0d0) / x)
    if (z <= (-16200000000.0d0)) then
        tmp = t_0
    else if (z <= 2.6d-166) then
        tmp = x - (0.8862269254527579d0 * ((z * y) - y))
    else if (z <= 2.8d-47) 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 tmp;
	if (z <= -16200000000.0) {
		tmp = t_0;
	} else if (z <= 2.6e-166) {
		tmp = x - (0.8862269254527579 * ((z * y) - y));
	} else if (z <= 2.8e-47) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	tmp = 0
	if z <= -16200000000.0:
		tmp = t_0
	elif z <= 2.6e-166:
		tmp = x - (0.8862269254527579 * ((z * y) - y))
	elif z <= 2.8e-47:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(-1.0 / x))
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = t_0;
	elseif (z <= 2.6e-166)
		tmp = Float64(x - Float64(0.8862269254527579 * Float64(Float64(z * y) - y)));
	elseif (z <= 2.8e-47)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (-1.0 / x);
	tmp = 0.0;
	if (z <= -16200000000.0)
		tmp = t_0;
	elseif (z <= 2.6e-166)
		tmp = x - (0.8862269254527579 * ((z * y) - y));
	elseif (z <= 2.8e-47)
		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]}, If[LessEqual[z, -16200000000.0], t$95$0, If[LessEqual[z, 2.6e-166], N[(x - N[(0.8862269254527579 * N[(N[(z * y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-47], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62e10 or 2.59999999999999989e-166 < z < 2.79999999999999993e-47

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf 94.1%

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

   if -1.62e10 < z < 2.59999999999999989e-166

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto x - \color{blue}{-0.8862269254527579 \cdot \frac{y}{e^{z}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in z around 0 74.9%

      \[\leadsto x - \frac{-0.8862269254527579 \cdot y}{\color{blue}{1 + z}} \]
   9. Step-by-step derivation

      1. +-commutative 74.9%

         \[\leadsto x - \frac{-0.8862269254527579 \cdot y}{\color{blue}{z + 1}} \]

   10. Simplified 74.9%

       \[\leadsto x - \frac{-0.8862269254527579 \cdot y}{\color{blue}{z + 1}} \]

   11. Taylor expanded in z around 0 74.9%

       \[\leadsto x - \color{blue}{\left(-0.8862269254527579 \cdot y + 0.8862269254527579 \cdot \left(y \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. +-commutative 74.9%

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

       2. metadata-eval 74.9%

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

       3. cancel-sign-sub-inv 74.9%

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

       4. distribute-lft-out-- 74.9%

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

   13. Simplified 74.9%

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

   if 2.79999999999999993e-47 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 95.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;x - 0.8862269254527579 \cdot \left(z \cdot y - y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{y}{-1.1283791670955126}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))))
   (if (<= z -7.2e-24)
     t_0
     (if (<= z 5e-168)
       (- x (/ y -1.1283791670955126))
       (if (<= z 4.8e-47) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double tmp;
	if (z <= -7.2e-24) {
		tmp = t_0;
	} else if (z <= 5e-168) {
		tmp = x - (y / -1.1283791670955126);
	} else if (z <= 4.8e-47) {
		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) :: tmp
    t_0 = x + ((-1.0d0) / x)
    if (z <= (-7.2d-24)) then
        tmp = t_0
    else if (z <= 5d-168) then
        tmp = x - (y / (-1.1283791670955126d0))
    else if (z <= 4.8d-47) 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 tmp;
	if (z <= -7.2e-24) {
		tmp = t_0;
	} else if (z <= 5e-168) {
		tmp = x - (y / -1.1283791670955126);
	} else if (z <= 4.8e-47) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	tmp = 0
	if z <= -7.2e-24:
		tmp = t_0
	elif z <= 5e-168:
		tmp = x - (y / -1.1283791670955126)
	elif z <= 4.8e-47:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(-1.0 / x))
	tmp = 0.0
	if (z <= -7.2e-24)
		tmp = t_0;
	elseif (z <= 5e-168)
		tmp = Float64(x - Float64(y / -1.1283791670955126));
	elseif (z <= 4.8e-47)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (-1.0 / x);
	tmp = 0.0;
	if (z <= -7.2e-24)
		tmp = t_0;
	elseif (z <= 5e-168)
		tmp = x - (y / -1.1283791670955126);
	elseif (z <= 4.8e-47)
		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]}, If[LessEqual[z, -7.2e-24], t$95$0, If[LessEqual[z, 5e-168], N[(x - N[(y / -1.1283791670955126), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-47], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000002e-24 or 5.00000000000000001e-168 < z < 4.7999999999999999e-47

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 91.4%

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

   if -7.2000000000000002e-24 < z < 5.00000000000000001e-168

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 74.7%

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

   if 4.7999999999999999e-47 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 95.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{y}{-1.1283791670955126}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{-1}{x}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-163}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ -1.0 x))))
   (if (<= z -7.2e-24)
     t_0
     (if (<= z 3.2e-163)
       (- x (* y -0.8862269254527579))
       (if (<= z 5.4e-47) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (-1.0 / x);
	double tmp;
	if (z <= -7.2e-24) {
		tmp = t_0;
	} else if (z <= 3.2e-163) {
		tmp = x - (y * -0.8862269254527579);
	} else if (z <= 5.4e-47) {
		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) :: tmp
    t_0 = x + ((-1.0d0) / x)
    if (z <= (-7.2d-24)) then
        tmp = t_0
    else if (z <= 3.2d-163) then
        tmp = x - (y * (-0.8862269254527579d0))
    else if (z <= 5.4d-47) 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 tmp;
	if (z <= -7.2e-24) {
		tmp = t_0;
	} else if (z <= 3.2e-163) {
		tmp = x - (y * -0.8862269254527579);
	} else if (z <= 5.4e-47) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (-1.0 / x)
	tmp = 0
	if z <= -7.2e-24:
		tmp = t_0
	elif z <= 3.2e-163:
		tmp = x - (y * -0.8862269254527579)
	elif z <= 5.4e-47:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(-1.0 / x))
	tmp = 0.0
	if (z <= -7.2e-24)
		tmp = t_0;
	elseif (z <= 3.2e-163)
		tmp = Float64(x - Float64(y * -0.8862269254527579));
	elseif (z <= 5.4e-47)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (-1.0 / x);
	tmp = 0.0;
	if (z <= -7.2e-24)
		tmp = t_0;
	elseif (z <= 3.2e-163)
		tmp = x - (y * -0.8862269254527579);
	elseif (z <= 5.4e-47)
		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]}, If[LessEqual[z, -7.2e-24], t$95$0, If[LessEqual[z, 3.2e-163], N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-47], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000002e-24 or 3.19999999999999988e-163 < z < 5.3999999999999996e-47

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 91.4%

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

   if -7.2000000000000002e-24 < z < 3.19999999999999988e-163

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around 0 74.6%

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

      1. *-commutative 74.6%

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

   8. Simplified 74.6%

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

   if 5.3999999999999996e-47 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 95.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-163}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+232}:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e+232)
   (/ -1.0 x)
   (if (<= z -2.15e+26)
     x
     (if (<= z 5.5e-25) (- x (* y -0.8862269254527579)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+232) {
		tmp = -1.0 / x;
	} else if (z <= -2.15e+26) {
		tmp = x;
	} else if (z <= 5.5e-25) {
		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 (z <= (-5.5d+232)) then
        tmp = (-1.0d0) / x
    else if (z <= (-2.15d+26)) then
        tmp = x
    else if (z <= 5.5d-25) 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 (z <= -5.5e+232) {
		tmp = -1.0 / x;
	} else if (z <= -2.15e+26) {
		tmp = x;
	} else if (z <= 5.5e-25) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e+232:
		tmp = -1.0 / x
	elif z <= -2.15e+26:
		tmp = x
	elif z <= 5.5e-25:
		tmp = x - (y * -0.8862269254527579)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e+232)
		tmp = Float64(-1.0 / x);
	elseif (z <= -2.15e+26)
		tmp = x;
	elseif (z <= 5.5e-25)
		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 (z <= -5.5e+232)
		tmp = -1.0 / x;
	elseif (z <= -2.15e+26)
		tmp = x;
	elseif (z <= 5.5e-25)
		tmp = x - (y * -0.8862269254527579);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e+232], N[(-1.0 / x), $MachinePrecision], If[LessEqual[z, -2.15e+26], x, If[LessEqual[z, 5.5e-25], N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999997e232

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 65.3%

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

   if -5.49999999999999997e232 < z < -2.1499999999999999e26 or 5.50000000000000004e-25 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 87.8%

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

   if -2.1499999999999999e26 < z < 5.50000000000000004e-25

   1. Initial program 98.4%

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

      1. remove-double-neg 98.4%

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

      2. distribute-frac-neg 98.4%

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

      3. unsub-neg 98.4%

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

      4. distribute-frac-neg 98.4%

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

      5. distribute-neg-frac2 98.4%

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

      6. neg-sub0 98.4%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 98.4%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 98.4%

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

      9. +-commutative 98.4%

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

      10. fma-define 98.4%

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

      11. *-commutative 98.4%

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

      12. distribute-rgt-neg-in 98.4%

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

      13. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 97.5%

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

   6. Taylor expanded in y around 0 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

      \[\leadsto x - \color{blue}{y \cdot -0.8862269254527579} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 98.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y}{x \cdot y - 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -16200000000.0)
   (+ x (/ -1.0 x))
   (if (<= z 7.2e-25) (- x (/ y (- (* x y) 1.1283791670955126))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x - (y / ((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 (z <= (-16200000000.0d0)) then
        tmp = x + ((-1.0d0) / x)
    else if (z <= 7.2d-25) then
        tmp = x - (y / ((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 (z <= -16200000000.0) {
		tmp = x + (-1.0 / x);
	} else if (z <= 7.2e-25) {
		tmp = x - (y / ((x * y) - 1.1283791670955126));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -16200000000.0:
		tmp = x + (-1.0 / x)
	elif z <= 7.2e-25:
		tmp = x - (y / ((x * y) - 1.1283791670955126))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = Float64(x + Float64(-1.0 / x));
	elseif (z <= 7.2e-25)
		tmp = Float64(x - Float64(y / Float64(Float64(x * y) - 1.1283791670955126)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -16200000000.0)
		tmp = x + (-1.0 / x);
	elseif (z <= 7.2e-25)
		tmp = x - (y / ((x * y) - 1.1283791670955126));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -16200000000.0], N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-25], N[(x - N[(y / N[(N[(x * y), $MachinePrecision] - 1.1283791670955126), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62e10

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.62e10 < z < 7.1999999999999998e-25

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. distribute-neg-frac2 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 99.9%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. *-commutative 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.0%

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

   if 7.1999999999999998e-25 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;x + \frac{-1}{x}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y}{x \cdot y - 1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-221}:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e-28)
   x
   (if (<= x -1.4e-221)
     (/ -1.0 x)
     (if (<= x 8e-215) (* y 0.8862269254527579) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-28) {
		tmp = x;
	} else if (x <= -1.4e-221) {
		tmp = -1.0 / x;
	} else if (x <= 8e-215) {
		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 <= (-7d-28)) then
        tmp = x
    else if (x <= (-1.4d-221)) then
        tmp = (-1.0d0) / x
    else if (x <= 8d-215) 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 <= -7e-28) {
		tmp = x;
	} else if (x <= -1.4e-221) {
		tmp = -1.0 / x;
	} else if (x <= 8e-215) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7e-28:
		tmp = x
	elif x <= -1.4e-221:
		tmp = -1.0 / x
	elif x <= 8e-215:
		tmp = y * 0.8862269254527579
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e-28)
		tmp = x;
	elseif (x <= -1.4e-221)
		tmp = Float64(-1.0 / x);
	elseif (x <= 8e-215)
		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 <= -7e-28)
		tmp = x;
	elseif (x <= -1.4e-221)
		tmp = -1.0 / x;
	elseif (x <= 8e-215)
		tmp = y * 0.8862269254527579;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e-28], x, If[LessEqual[x, -1.4e-221], N[(-1.0 / x), $MachinePrecision], If[LessEqual[x, 8e-215], N[(y * 0.8862269254527579), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999999e-28 or 8.00000000000000033e-215 < x

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 84.0%

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

   if -6.9999999999999999e-28 < x < -1.4000000000000001e-221

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 46.2%

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

   4. Taylor expanded in x around 0 46.2%

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

   if -1.4000000000000001e-221 < x < 8.00000000000000033e-215

   1. Initial program 91.4%

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

      1. remove-double-neg 91.4%

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

      2. distribute-frac-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. distribute-frac-neg 91.4%

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

      5. distribute-neg-frac2 91.4%

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

      6. neg-sub0 91.2%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 91.2%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 91.7%

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

      9. +-commutative 91.7%

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

      10. fma-define 91.7%

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

      11. *-commutative 91.7%

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

      12. distribute-rgt-neg-in 91.7%

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

      13. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around 0 59.4%

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

   6. Taylor expanded in x around 0 52.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-221}:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-213) x (if (<= x 5.5e-215) (* y 0.8862269254527579) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-213) {
		tmp = x;
	} else if (x <= 5.5e-215) {
		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 <= (-1.6d-213)) then
        tmp = x
    else if (x <= 5.5d-215) 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 <= -1.6e-213) {
		tmp = x;
	} else if (x <= 5.5e-215) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-213:
		tmp = x
	elif x <= 5.5e-215:
		tmp = y * 0.8862269254527579
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-213)
		tmp = x;
	elseif (x <= 5.5e-215)
		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 <= -1.6e-213)
		tmp = x;
	elseif (x <= 5.5e-215)
		tmp = y * 0.8862269254527579;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-213], x, If[LessEqual[x, 5.5e-215], N[(y * 0.8862269254527579), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999986e-213 or 5.50000000000000004e-215 < x

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -1.59999999999999986e-213 < x < 5.50000000000000004e-215

   1. Initial program 90.1%

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

      1. remove-double-neg 90.1%

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

      2. distribute-frac-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. distribute-frac-neg 90.1%

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

      5. distribute-neg-frac2 90.1%

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

      6. neg-sub0 89.7%

         \[\leadsto x - \frac{y}{\color{blue}{0 - \left(1.1283791670955126 \cdot e^{z} - x \cdot y\right)}} \]

      7. associate--r- 89.7%

         \[\leadsto x - \frac{y}{\color{blue}{\left(0 - 1.1283791670955126 \cdot e^{z}\right) + x \cdot y}} \]

      8. neg-sub0 90.3%

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

      9. +-commutative 90.3%

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

      10. fma-define 90.3%

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

      11. *-commutative 90.3%

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

      12. distribute-rgt-neg-in 90.3%

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

      13. metadata-eval 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around 0 62.1%

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

   6. Taylor expanded in x around 0 51.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.7% 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 94.9%

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

3. Taylor expanded in x around inf 65.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

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

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