Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G

Percentage Accurate: 84.7% → 98.2%

Time: 11.7s

Alternatives: 9

Speedup: 8.7×

• could not determine a ground truth

  1. x = 3.952853191924873e+186
  2. y = 9.132515288075727e+40
  3. z = -2.893092385656932e-255

Specification

Math

\[\begin{array}{l} \\ x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))

C

double code(double x, double y, double z) {
	return x + (exp((y * log((y / (z + y))))) / 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 + (exp((y * log((y / (z + y))))) / y)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + Float64(exp(Float64(y * log(Float64(y / Float64(z + y))))) / y))
end

MATLAB

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

Wolfram

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

Initial Program: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))

C

double code(double x, double y, double z) {
	return x + (exp((y * log((y / (z + y))))) / 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 + (exp((y * log((y / (z + y))))) / y)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + Float64(exp(Float64(y * log(Float64(y / Float64(z + y))))) / y))
end

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \mathbf{elif}\;y \leq 10^{-13}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+47)
   (+ x (/ 1.0 (* y (exp z))))
   (if (<= y 1e-13) (+ x (/ 1.0 y)) (+ x (/ (exp (- z)) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+47) {
		tmp = x + (1.0 / (y * exp(z)));
	} else if (y <= 1e-13) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (exp(-z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.1d+47)) then
        tmp = x + (1.0d0 / (y * exp(z)))
    else if (y <= 1d-13) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (exp(-z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+47) {
		tmp = x + (1.0 / (y * Math.exp(z)));
	} else if (y <= 1e-13) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (Math.exp(-z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+47:
		tmp = x + (1.0 / (y * math.exp(z)))
	elif y <= 1e-13:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (math.exp(-z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+47)
		tmp = Float64(x + Float64(1.0 / Float64(y * exp(z))));
	elseif (y <= 1e-13)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.1e+47)
		tmp = x + (1.0 / (y * exp(z)));
	elseif (y <= 1e-13)
		tmp = x + (1.0 / y);
	else
		tmp = x + (exp(-z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+47], N[(x + N[(1.0 / N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-13], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000001e47

   1. Initial program 84.3%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

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

      1. div-inv N/A

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

      2. exp-neg N/A

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

      3. frac-times N/A

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

      4. metadata-eval N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. exp-lowering-exp.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   if -4.1000000000000001e47 < y < 1e-13

   1. Initial program 87.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 99.2

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

   5. Simplified 99.2%

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

   if 1e-13 < y

   1. Initial program 77.7%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

      \[\leadsto x + \frac{\color{blue}{e^{-z}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \mathbf{elif}\;y \leq 10^{-13}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{e^{-z}}{y}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ (exp (- z)) y))))
   (if (<= y -4.1e+47) t_0 (if (<= y 7e-9) (+ x (/ 1.0 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (exp(-z) / y);
	double tmp;
	if (y <= -4.1e+47) {
		tmp = t_0;
	} else if (y <= 7e-9) {
		tmp = x + (1.0 / y);
	} else {
		tmp = t_0;
	}
	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 + (exp(-z) / y)
    if (y <= (-4.1d+47)) then
        tmp = t_0
    else if (y <= 7d-9) then
        tmp = x + (1.0d0 / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (Math.exp(-z) / y);
	double tmp;
	if (y <= -4.1e+47) {
		tmp = t_0;
	} else if (y <= 7e-9) {
		tmp = x + (1.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (math.exp(-z) / y)
	tmp = 0
	if y <= -4.1e+47:
		tmp = t_0
	elif y <= 7e-9:
		tmp = x + (1.0 / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(exp(Float64(-z)) / y))
	tmp = 0.0
	if (y <= -4.1e+47)
		tmp = t_0;
	elseif (y <= 7e-9)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (exp(-z) / y);
	tmp = 0.0;
	if (y <= -4.1e+47)
		tmp = t_0;
	elseif (y <= 7e-9)
		tmp = x + (1.0 / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+47], t$95$0, If[LessEqual[y, 7e-9], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1000000000000001e47 or 6.9999999999999998e-9 < y

   1. Initial program 80.5%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

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

   if -4.1000000000000001e47 < y < 6.9999999999999998e-9

   1. Initial program 87.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 99.2

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

   5. Simplified 99.2%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1150:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1150.0) (/ (exp (- z)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1150.0) {
		tmp = exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1150.0d0)) then
        tmp = exp(-z) / y
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1150.0) {
		tmp = Math.exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1150.0:
		tmp = math.exp(-z) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1150.0)
		tmp = Float64(exp(Float64(-z)) / y);
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1150.0)
		tmp = exp(-z) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1150.0], N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1150

   1. Initial program 44.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 65.3

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

   5. Simplified 65.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{e^{\mathsf{neg}\left(z\right)}}{y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{e^{\mathsf{neg}\left(z\right)}}{y}} \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \frac{\color{blue}{e^{\mathsf{neg}\left(z\right)}}}{y} \]

      3. neg-lowering-neg.f64 65.3

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

   8. Simplified 65.3%

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

   if -1150 < z

   1. Initial program 93.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 94.5

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

   5. Simplified 94.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, -0.16666666666666666, 0.5\right), -1\right), 1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+104)
   (+ x (/ (fma z (fma z (fma z -0.16666666666666666 0.5) -1.0) 1.0) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+104) {
		tmp = x + (fma(z, fma(z, fma(z, -0.16666666666666666, 0.5), -1.0), 1.0) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+104)
		tmp = Float64(x + Float64(fma(z, fma(z, fma(z, -0.16666666666666666, 0.5), -1.0), 1.0) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+104], N[(x + N[(N[(z * N[(z * N[(z * -0.16666666666666666 + 0.5), $MachinePrecision] + -1.0), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e104

   1. Initial program 49.9%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 70.5

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto x + \frac{\color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}}{y} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right) + 1}}{y} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z, z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1, 1\right)}}{y} \]

      3. sub-neg N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(z, \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

      4. metadata-eval N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(z, z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{-1}, 1\right)}{y} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, \frac{1}{2} + \frac{-1}{6} \cdot z, -1\right)}, 1\right)}{y} \]

      6. +-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{\frac{-1}{6} \cdot z + \frac{1}{2}}, -1\right), 1\right)}{y} \]

      7. *-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{z \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

      8. accelerator-lowering-fma.f64 70.5

         \[\leadsto x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   8. Simplified 70.5%

      \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   if -1.0499999999999999e104 < z

   1. Initial program 87.4%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 89.1

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

   5. Simplified 89.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, -0.16666666666666666, 0.5\right), -1\right), 1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+154) (/ (* z (* z 0.5)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+154) {
		tmp = (z * (z * 0.5)) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.9d+154)) then
        tmp = (z * (z * 0.5d0)) / y
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+154) {
		tmp = (z * (z * 0.5)) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+154:
		tmp = (z * (z * 0.5)) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+154)
		tmp = Float64(Float64(z * Float64(z * 0.5)) / y);
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+154)
		tmp = (z * (z * 0.5)) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+154], N[(N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e154

   1. Initial program 55.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, z \cdot \left(\frac{1}{2} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right) - \frac{1}{y}, x + \frac{1}{y}\right)} \]

   5. Simplified 23.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \frac{0.5}{y} + \frac{0.5}{y \cdot y}, \frac{-1}{y}\right), \frac{1}{y} + x\right)} \]

   6. Taylor expanded in z around inf

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

   8. Simplified 23.8%

      \[\leadsto \color{blue}{z \cdot \frac{\mathsf{fma}\left(z, 0.5 + \frac{0.5}{y}, -1\right)}{y}} \]

   9. Taylor expanded in y around inf

      \[\leadsto z \cdot \color{blue}{\frac{\frac{1}{2} \cdot z - 1}{y}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto z \cdot \color{blue}{\frac{\frac{1}{2} \cdot z - 1}{y}} \]

       2. sub-neg N/A

          \[\leadsto z \cdot \frac{\color{blue}{\frac{1}{2} \cdot z + \left(\mathsf{neg}\left(1\right)\right)}}{y} \]

       3. metadata-eval N/A

          \[\leadsto z \cdot \frac{\frac{1}{2} \cdot z + \color{blue}{-1}}{y} \]

       4. *-commutative N/A

          \[\leadsto z \cdot \frac{\color{blue}{z \cdot \frac{1}{2}} + -1}{y} \]

       5. accelerator-lowering-fma.f64 24.7

          \[\leadsto z \cdot \frac{\color{blue}{\mathsf{fma}\left(z, 0.5, -1\right)}}{y} \]

   11. Simplified 24.7%

       \[\leadsto z \cdot \color{blue}{\frac{\mathsf{fma}\left(z, 0.5, -1\right)}{y}} \]

   12. Taylor expanded in z around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{z}^{2}}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot {z}^{2}}{y}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot {z}^{2}}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{\color{blue}{{z}^{2} \cdot \frac{1}{2}}}{y} \]

       4. unpow2 N/A

          \[\leadsto \frac{\color{blue}{\left(z \cdot z\right)} \cdot \frac{1}{2}}{y} \]

       5. associate-*l* N/A

          \[\leadsto \frac{\color{blue}{z \cdot \left(z \cdot \frac{1}{2}\right)}}{y} \]

       6. *-commutative N/A

          \[\leadsto \frac{z \cdot \color{blue}{\left(\frac{1}{2} \cdot z\right)}}{y} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z \cdot \left(\frac{1}{2} \cdot z\right)}}{y} \]

       8. *-commutative N/A

          \[\leadsto \frac{z \cdot \color{blue}{\left(z \cdot \frac{1}{2}\right)}}{y} \]

       9. *-lowering-*.f64 80.9

          \[\leadsto \frac{z \cdot \color{blue}{\left(z \cdot 0.5\right)}}{y} \]

   14. Simplified 80.9%

       \[\leadsto \color{blue}{\frac{z \cdot \left(z \cdot 0.5\right)}{y}} \]

   if -1.8999999999999999e154 < z

   1. Initial program 84.9%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 86.5

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

   5. Simplified 86.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\mathsf{fma}\left(y, z, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5e-9) (+ x (/ 1.0 y)) (+ x (/ 1.0 (fma y z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e-9) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / fma(y, z, y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5e-9)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / fma(y, z, y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5e-9], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y * z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.0000000000000001e-9

   1. Initial program 86.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. /-lowering-/.f64 88.7

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

   5. Simplified 88.7%

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

   if 5.0000000000000001e-9 < y

   1. Initial program 77.7%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. exp-lowering-exp.f64 N/A

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

      2. mul-1-neg N/A

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

      3. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

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

      1. div-inv N/A

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

      2. exp-neg N/A

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

      3. frac-times N/A

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

      4. metadata-eval N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. exp-lowering-exp.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 76.9

         \[\leadsto x + \frac{1}{\color{blue}{\mathsf{fma}\left(y, z, y\right)}} \]

   10. Simplified 76.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\mathsf{fma}\left(y, z, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.1% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.2e-15) x (if (<= y 3.5e+16) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e-15) {
		tmp = x;
	} else if (y <= 3.5e+16) {
		tmp = 1.0 / 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 (y <= (-9.2d-15)) then
        tmp = x
    else if (y <= 3.5d+16) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e-15) {
		tmp = x;
	} else if (y <= 3.5e+16) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.2e-15:
		tmp = x
	elif y <= 3.5e+16:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.2e-15)
		tmp = x;
	elseif (y <= 3.5e+16)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.2e-15)
		tmp = x;
	elseif (y <= 3.5e+16)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.2e-15], x, If[LessEqual[y, 3.5e+16], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999961e-15 or 3.5e16 < y

   1. Initial program 81.6%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.0%

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

   if -9.19999999999999961e-15 < y < 3.5e16

   1. Initial program 85.8%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 82.0

         \[\leadsto \color{blue}{\frac{1}{y}} \]

   5. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 84.2% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ 1.0 y)))

C

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

Java

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

Python

def code(x, y, z):
	return x + (1.0 / y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

   \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

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

   3. /-lowering-/.f64 82.7

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

5. Simplified 82.7%

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

6. Final simplification 82.7%

   \[\leadsto x + \frac{1}{y} \]
7. Add Preprocessing

Alternative 9: 49.3% accurate, 234.0× 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 83.1%

   \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 49.6%

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

Developer Target 1: 91.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z + y} < 7.11541576 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< (/ y (+ z y)) 7.11541576e-315)
   (+ x (/ (exp (/ -1.0 z)) y))
   (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (exp((-1.0 / z)) / y);
	} else {
		tmp = x + (exp(log(pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y / (z + y)) < 7.11541576d-315) then
        tmp = x + (exp(((-1.0d0) / z)) / y)
    else
        tmp = x + (exp(log(((y / (y + z)) ** y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (Math.exp((-1.0 / z)) / y);
	} else {
		tmp = x + (Math.exp(Math.log(Math.pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y / (z + y)) < 7.11541576e-315:
		tmp = x + (math.exp((-1.0 / z)) / y)
	else:
		tmp = x + (math.exp(math.log(math.pow((y / (y + z)), y))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y / Float64(z + y)) < 7.11541576e-315)
		tmp = Float64(x + Float64(exp(Float64(-1.0 / z)) / y));
	else
		tmp = Float64(x + Float64(exp(log((Float64(y / Float64(y + z)) ^ y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y / (z + y)) < 7.11541576e-315)
		tmp = x + (exp((-1.0 / z)) / y);
	else
		tmp = x + (exp(log(((y / (y + z)) ^ y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision], 7.11541576e-315], N[(x + N[(N[Exp[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Exp[N[Log[N[Power[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ y (+ z y)) 17788539399477/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (exp (/ -1 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

  (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))