Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.6s

Alternatives: 15

Speedup: 1.0×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 90.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+69}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+69)
   (exp x)
   (if (<= x 1.3e-22) (exp (- (* y (log y)) z)) (* (pow y y) (exp x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+69) {
		tmp = exp(x);
	} else if (x <= 1.3e-22) {
		tmp = exp(((y * log(y)) - z));
	} else {
		tmp = pow(y, y) * exp(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 <= (-4.6d+69)) then
        tmp = exp(x)
    else if (x <= 1.3d-22) then
        tmp = exp(((y * log(y)) - z))
    else
        tmp = (y ** y) * exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+69) {
		tmp = Math.exp(x);
	} else if (x <= 1.3e-22) {
		tmp = Math.exp(((y * Math.log(y)) - z));
	} else {
		tmp = Math.pow(y, y) * Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+69:
		tmp = math.exp(x)
	elif x <= 1.3e-22:
		tmp = math.exp(((y * math.log(y)) - z))
	else:
		tmp = math.pow(y, y) * math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+69)
		tmp = exp(x);
	elseif (x <= 1.3e-22)
		tmp = exp(Float64(Float64(y * log(y)) - z));
	else
		tmp = Float64((y ^ y) * exp(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+69)
		tmp = exp(x);
	elseif (x <= 1.3e-22)
		tmp = exp(((y * log(y)) - z));
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+69], N[Exp[x], $MachinePrecision], If[LessEqual[x, 1.3e-22], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.60000000000000033e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.6%

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

   if -4.60000000000000033e69 < x < 1.3e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.2%

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

   if 1.3e-22 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 90.1%

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

      4. *-commutative 90.1%

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

      5. exp-to-pow 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 87.5%

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

Alternative 3: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8400000000 \lor \neg \left(z \leq 2 \cdot 10^{+74}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8400000000.0) (not (<= z 2e+74)))
   (exp (- z))
   (* (pow y y) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8400000000.0) || !(z <= 2e+74)) {
		tmp = exp(-z);
	} else {
		tmp = pow(y, y) * exp(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 <= (-8400000000.0d0)) .or. (.not. (z <= 2d+74))) then
        tmp = exp(-z)
    else
        tmp = (y ** y) * exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8400000000.0) || !(z <= 2e+74)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y) * Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8400000000.0) or not (z <= 2e+74):
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y) * math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8400000000.0) || !(z <= 2e+74))
		tmp = exp(Float64(-z));
	else
		tmp = Float64((y ^ y) * exp(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8400000000.0) || ~((z <= 2e+74)))
		tmp = exp(-z);
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8400000000.0], N[Not[LessEqual[z, 2e+74]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4e9 or 1.9999999999999999e74 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.2%

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

      1. neg-mul-1 81.2%

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

   5. Simplified 81.2%

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

   if -8.4e9 < z < 1.9999999999999999e74

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 84.2%

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

      4. *-commutative 84.2%

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

      5. exp-to-pow 84.2%

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

   3. Simplified 84.2%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 84.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8400000000 \lor \neg \left(z \leq 2 \cdot 10^{+74}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+68}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z}}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.35e+68)
   (exp x)
   (if (<= x 4.4e-23) (/ (pow y y) (exp z)) (* (pow y y) (exp x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.35e+68) {
		tmp = exp(x);
	} else if (x <= 4.4e-23) {
		tmp = pow(y, y) / exp(z);
	} else {
		tmp = pow(y, y) * exp(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 <= (-3.35d+68)) then
        tmp = exp(x)
    else if (x <= 4.4d-23) then
        tmp = (y ** y) / exp(z)
    else
        tmp = (y ** y) * exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.35e+68) {
		tmp = Math.exp(x);
	} else if (x <= 4.4e-23) {
		tmp = Math.pow(y, y) / Math.exp(z);
	} else {
		tmp = Math.pow(y, y) * Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.35e+68:
		tmp = math.exp(x)
	elif x <= 4.4e-23:
		tmp = math.pow(y, y) / math.exp(z)
	else:
		tmp = math.pow(y, y) * math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.35e+68)
		tmp = exp(x);
	elseif (x <= 4.4e-23)
		tmp = Float64((y ^ y) / exp(z));
	else
		tmp = Float64((y ^ y) * exp(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.35e+68)
		tmp = exp(x);
	elseif (x <= 4.4e-23)
		tmp = (y ^ y) / exp(z);
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.35e+68], N[Exp[x], $MachinePrecision], If[LessEqual[x, 4.4e-23], N[(N[Power[y, y], $MachinePrecision] / N[Exp[z], $MachinePrecision]), $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3499999999999999e68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.6%

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

   if -3.3499999999999999e68 < x < 4.3999999999999999e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.2%

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

      1. exp-diff 81.1%

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

      2. *-commutative 81.1%

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

      3. exp-to-pow 81.1%

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

   5. Simplified 81.1%

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

   if 4.3999999999999999e-23 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 90.1%

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

      4. *-commutative 90.1%

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

      5. exp-to-pow 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 87.5%

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

Alternative 5: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-14}:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.4e-14) (* (pow y y) (exp (- x z))) (exp (- (* y (log y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.4e-14) {
		tmp = pow(y, y) * exp((x - z));
	} else {
		tmp = exp(((y * log(y)) - z));
	}
	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 <= 4.4d-14) then
        tmp = (y ** y) * exp((x - z))
    else
        tmp = exp(((y * log(y)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.4e-14) {
		tmp = Math.pow(y, y) * Math.exp((x - z));
	} else {
		tmp = Math.exp(((y * Math.log(y)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.4e-14:
		tmp = math.pow(y, y) * math.exp((x - z))
	else:
		tmp = math.exp(((y * math.log(y)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.4e-14)
		tmp = Float64((y ^ y) * exp(Float64(x - z)));
	else
		tmp = exp(Float64(Float64(y * log(y)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.4e-14)
		tmp = (y ^ y) * exp((x - z));
	else
		tmp = exp(((y * log(y)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.4e-14], N[(N[Power[y, y], $MachinePrecision] * N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.4000000000000002e-14

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 100.0%

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

      4. *-commutative 100.0%

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

      5. exp-to-pow 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{{y}^{y} \cdot e^{x - z}} \]
   4. Add Preprocessing

   if 4.4000000000000002e-14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.7%

      \[\leadsto \color{blue}{e^{y \cdot \log y - z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 72.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+28} \lor \neg \left(x \leq 1.3 \cdot 10^{-22}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e+28) (not (<= x 1.3e-22))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+28) || !(x <= 1.3e-22)) {
		tmp = exp(x);
	} else {
		tmp = exp(-z);
	}
	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 <= (-1.2d+28)) .or. (.not. (x <= 1.3d-22))) then
        tmp = exp(x)
    else
        tmp = exp(-z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+28) || !(x <= 1.3e-22)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e+28) or not (x <= 1.3e-22):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e+28) || !(x <= 1.3e-22))
		tmp = exp(x);
	else
		tmp = exp(Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e+28) || ~((x <= 1.3e-22)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e+28], N[Not[LessEqual[x, 1.3e-22]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999991e28 or 1.3e-22 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.9%

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

   if -1.19999999999999991e28 < x < 1.3e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. neg-mul-1 60.7%

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

   5. Simplified 60.7%

      \[\leadsto e^{\color{blue}{-z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+28} \lor \neg \left(x \leq 1.3 \cdot 10^{-22}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{-228}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 3400000000000:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.4e-228)
   (exp (- z))
   (if (<= y 3400000000000.0) (exp x) (pow y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.4e-228) {
		tmp = exp(-z);
	} else if (y <= 3400000000000.0) {
		tmp = exp(x);
	} else {
		tmp = pow(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 <= 3.4d-228) then
        tmp = exp(-z)
    else if (y <= 3400000000000.0d0) then
        tmp = exp(x)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.4e-228) {
		tmp = Math.exp(-z);
	} else if (y <= 3400000000000.0) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.4e-228:
		tmp = math.exp(-z)
	elif y <= 3400000000000.0:
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.4e-228)
		tmp = exp(Float64(-z));
	elseif (y <= 3400000000000.0)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.4e-228)
		tmp = exp(-z);
	elseif (y <= 3400000000000.0)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.4e-228], N[Exp[(-z)], $MachinePrecision], If[LessEqual[y, 3400000000000.0], N[Exp[x], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.39999999999999991e-228

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. neg-mul-1 75.6%

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

   5. Simplified 75.6%

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

   if 3.39999999999999991e-228 < y < 3.4e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.2%

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

   if 3.4e12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.7%

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

   4. Taylor expanded in z around 0 80.9%

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

Alternative 8: 58.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28} \lor \neg \left(x \leq 1.02 \cdot 10^{-54}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+28) (not (<= x 1.02e-54)))
   (exp x)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+28) || !(x <= 1.02e-54)) {
		tmp = exp(x);
	} else {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	}
	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) :: tmp
    if ((x <= (-1.05d+28)) .or. (.not. (x <= 1.02d-54))) then
        tmp = exp(x)
    else
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+28) || !(x <= 1.02e-54)) {
		tmp = Math.exp(x);
	} else {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+28) or not (x <= 1.02e-54):
		tmp = math.exp(x)
	else:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+28) || !(x <= 1.02e-54))
		tmp = exp(x);
	else
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+28) || ~((x <= 1.02e-54)))
		tmp = exp(x);
	else
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+28], N[Not[LessEqual[x, 1.02e-54]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999995e28 or 1.01999999999999999e-54 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.0%

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

   if -1.04999999999999995e28 < x < 1.01999999999999999e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 59.2%

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

      1. neg-mul-1 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in z around 0 35.4%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28} \lor \neg \left(x \leq 1.02 \cdot 10^{-54}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.0% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+129} \lor \neg \left(z \leq 4.3 \cdot 10^{+136}\right):\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.9e+129) (not (<= z 4.3e+136)))
   (+ 1.0 (* z (* z 0.5)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.9e+129) || !(z <= 4.3e+136)) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	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 <= (-4.9d+129)) .or. (.not. (z <= 4.3d+136))) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.9e+129) || !(z <= 4.3e+136)) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.9e+129) or not (z <= 4.3e+136):
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.9e+129) || !(z <= 4.3e+136))
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.9e+129) || ~((z <= 4.3e+136)))
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.9e+129], N[Not[LessEqual[z, 4.3e+136]], $MachinePrecision]], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e129 or 4.2999999999999999e136 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in z around 0 52.5%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   7. Taylor expanded in z around inf 52.5%

      \[\leadsto 1 + z \cdot \color{blue}{\left(0.5 \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto 1 + z \cdot \color{blue}{\left(z \cdot 0.5\right)} \]

   9. Simplified 52.5%

      \[\leadsto 1 + z \cdot \color{blue}{\left(z \cdot 0.5\right)} \]

   if -4.9e129 < z < 4.2999999999999999e136

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.6%

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

   4. Taylor expanded in x around 0 26.4%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+129} \lor \neg \left(z \leq 4.3 \cdot 10^{+136}\right):\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.8% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 3.8e+31)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e+31) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	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 <= 3.8d+31) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e+31) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.8e+31:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.8e+31)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.8e+31)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.8e+31], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.8000000000000001e31

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 47.7%

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

      1. neg-mul-1 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in z around 0 25.7%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   if 3.8000000000000001e31 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.5%

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

   4. Taylor expanded in x around 0 68.5%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]

   5. Taylor expanded in x around inf 68.5%

      \[\leadsto 1 + x \cdot \left(1 + x \cdot \color{blue}{\left(0.16666666666666666 \cdot x\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.3% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+153}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.55e+153)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+153) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	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 <= 1.55d+153) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+153) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.55e+153:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.55e+153)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.55e+153)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.55e+153], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55e153

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 48.6%

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

      1. neg-mul-1 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in z around 0 24.1%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   if 1.55e153 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.1%

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

   4. Taylor expanded in x around 0 88.5%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+153}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.1% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ 1 + z \cdot \left(z \cdot 0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (* z (* z 0.5))))

C

double code(double x, double y, double z) {
	return 1.0 + (z * (z * 0.5));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (z * (z * 0.5d0))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (z * (z * 0.5));
}

Python

def code(x, y, z):
	return 1.0 + (z * (z * 0.5))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(z * Float64(z * 0.5)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (z * (z * 0.5));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 47.6%

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

   1. neg-mul-1 47.6%

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

5. Simplified 47.6%

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

6. Taylor expanded in z around 0 24.9%

   \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

7. Taylor expanded in z around inf 24.6%

   \[\leadsto 1 + z \cdot \color{blue}{\left(0.5 \cdot z\right)} \]
8. Step-by-step derivation

   1. *-commutative 24.6%

      \[\leadsto 1 + z \cdot \color{blue}{\left(z \cdot 0.5\right)} \]

9. Simplified 24.6%

   \[\leadsto 1 + z \cdot \color{blue}{\left(z \cdot 0.5\right)} \]
10. Add Preprocessing

Alternative 13: 14.9% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 79.1%

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

   1. exp-diff 66.1%

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

   2. *-commutative 66.1%

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

   3. exp-to-pow 66.1%

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

5. Simplified 66.1%

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

6. Taylor expanded in z around 0 41.7%

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

   1. +-commutative 41.7%

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

8. Simplified 41.7%

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

9. Taylor expanded in y around 0 10.8%

   \[\leadsto \frac{\color{blue}{1}}{z + 1} \]
10. Add Preprocessing

Alternative 14: 15.1% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 50.9%

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

4. Taylor expanded in x around 0 10.8%

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

5. Final simplification 10.8%

   \[\leadsto x + 1 \]
6. Add Preprocessing

Alternative 15: 14.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 50.9%

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

4. Taylor expanded in x around 0 10.6%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (exp (+ (- x z) (* (log y) y))))

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