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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 5

Speedup: 1.0×

• 58.0% 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. Final simplification 100.0%

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

Alternative 2: 74.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-z}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+16}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- z))))
   (if (<= x -3e+16)
     (exp x)
     (if (<= x 4.9e-214)
       t_0
       (if (<= x 8.2e-151) (pow y y) (if (<= x 650.0) t_0 (exp x)))))))

C

double code(double x, double y, double z) {
	double t_0 = exp(-z);
	double tmp;
	if (x <= -3e+16) {
		tmp = exp(x);
	} else if (x <= 4.9e-214) {
		tmp = t_0;
	} else if (x <= 8.2e-151) {
		tmp = pow(y, y);
	} else if (x <= 650.0) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = exp(-z)
    if (x <= (-3d+16)) then
        tmp = exp(x)
    else if (x <= 4.9d-214) then
        tmp = t_0
    else if (x <= 8.2d-151) then
        tmp = y ** y
    else if (x <= 650.0d0) then
        tmp = t_0
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.exp(-z);
	double tmp;
	if (x <= -3e+16) {
		tmp = Math.exp(x);
	} else if (x <= 4.9e-214) {
		tmp = t_0;
	} else if (x <= 8.2e-151) {
		tmp = Math.pow(y, y);
	} else if (x <= 650.0) {
		tmp = t_0;
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp(-z)
	tmp = 0
	if x <= -3e+16:
		tmp = math.exp(x)
	elif x <= 4.9e-214:
		tmp = t_0
	elif x <= 8.2e-151:
		tmp = math.pow(y, y)
	elif x <= 650.0:
		tmp = t_0
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(-z))
	tmp = 0.0
	if (x <= -3e+16)
		tmp = exp(x);
	elseif (x <= 4.9e-214)
		tmp = t_0;
	elseif (x <= 8.2e-151)
		tmp = y ^ y;
	elseif (x <= 650.0)
		tmp = t_0;
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp(-z);
	tmp = 0.0;
	if (x <= -3e+16)
		tmp = exp(x);
	elseif (x <= 4.9e-214)
		tmp = t_0;
	elseif (x <= 8.2e-151)
		tmp = y ^ y;
	elseif (x <= 650.0)
		tmp = t_0;
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[(-z)], $MachinePrecision]}, If[LessEqual[x, -3e+16], N[Exp[x], $MachinePrecision], If[LessEqual[x, 4.9e-214], t$95$0, If[LessEqual[x, 8.2e-151], N[Power[y, y], $MachinePrecision], If[LessEqual[x, 650.0], t$95$0, N[Exp[x], $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e16 or 650 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 60.7%

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

      4. exp-diff 57.8%

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

      5. associate-/r/ 57.8%

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

      6. *-commutative 57.8%

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

      7. exp-to-pow 57.8%

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

      8. div-exp 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-rgt-identity 69.0%

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

      2. associate-*l/ 69.0%

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

      3. associate-/l* 69.0%

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

      4. exp-neg 69.0%

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

      5. remove-double-div 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in y around 0 84.7%

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

   if -3e16 < x < 4.89999999999999968e-214 or 8.2000000000000002e-151 < x < 650

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 97.3%

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

      4. exp-diff 83.6%

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

      5. associate-/r/ 83.6%

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

      6. *-commutative 83.6%

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

      7. exp-to-pow 83.6%

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

      8. div-exp 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in y around 0 78.1%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. rec-exp 77.7%

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

   8. Simplified 77.7%

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

   if 4.89999999999999968e-214 < x < 8.2000000000000002e-151

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 100.0%

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

      4. exp-diff 81.8%

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

      5. associate-/r/ 81.8%

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

      6. *-commutative 81.8%

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

      7. exp-to-pow 81.8%

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

      8. div-exp 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. *-rgt-identity 100.0%

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

      2. associate-*l/ 100.0%

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

      3. associate-/l* 100.0%

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

      4. exp-neg 100.0%

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

      5. remove-double-div 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+16}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-214}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+14} \lor \neg \left(x \leq 1450\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e+14) (not (<= x 1450.0))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e+14) || !(x <= 1450.0)) {
		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 <= (-2.1d+14)) .or. (.not. (x <= 1450.0d0))) 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 <= -2.1e+14) || !(x <= 1450.0)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e+14) or not (x <= 1450.0):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e+14) || !(x <= 1450.0))
		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 <= -2.1e+14) || ~((x <= 1450.0)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e+14], N[Not[LessEqual[x, 1450.0]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e14 or 1450 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 60.7%

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

      4. exp-diff 57.8%

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

      5. associate-/r/ 57.8%

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

      6. *-commutative 57.8%

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

      7. exp-to-pow 57.8%

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

      8. div-exp 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-rgt-identity 69.0%

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

      2. associate-*l/ 69.0%

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

      3. associate-/l* 69.0%

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

      4. exp-neg 69.0%

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

      5. remove-double-div 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in y around 0 84.7%

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

   if -2.1e14 < x < 1450

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 97.5%

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

      4. exp-diff 83.5%

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

      5. associate-/r/ 83.5%

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

      6. *-commutative 83.5%

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

      7. exp-to-pow 83.5%

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

      8. div-exp 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 74.5%

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

   6. Taylor expanded in x around 0 74.1%

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

      1. rec-exp 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+14} \lor \neg \left(x \leq 1450\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+166}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.35e+166) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.35e+166) {
		tmp = exp((x - z));
	} 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 <= 1.35d+166) then
        tmp = exp((x - z))
    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 <= 1.35e+166) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.35e+166:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.35e+166)
		tmp = exp(Float64(x - z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.35e+166)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.35e+166], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.35000000000000006e166

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 80.1%

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

      4. exp-diff 73.5%

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

      5. associate-/r/ 73.5%

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

      6. *-commutative 73.5%

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

      7. exp-to-pow 73.5%

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

      8. div-exp 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around 0 94.2%

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

      1. exp-diff 80.9%

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

      2. associate-/r/ 80.9%

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

      3. associate-*l/ 80.9%

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

      4. metadata-eval 80.9%

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

      5. associate-/r/ 80.9%

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

      6. remove-double-div 80.9%

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

      7. div-exp 94.2%

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

   7. Simplified 94.2%

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

   if 1.35000000000000006e166 < y

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 71.7%

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

      4. exp-diff 58.3%

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

      5. associate-/r/ 58.3%

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

      6. *-commutative 58.3%

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

      7. exp-to-pow 58.3%

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

      8. div-exp 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in z around 0 70.0%

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

      1. *-rgt-identity 70.0%

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

      2. associate-*l/ 70.0%

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

      3. associate-/l* 70.0%

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

      4. exp-neg 70.0%

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

      5. remove-double-div 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in x around 0 90.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+166}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	return math.exp(x)

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Exp[x], $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. exp-sum 78.1%

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

   4. exp-diff 69.9%

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

   5. associate-/r/ 69.9%

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

   6. *-commutative 69.9%

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

   7. exp-to-pow 69.9%

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

   8. div-exp 78.9%

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

3. Simplified 78.9%

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

5. Taylor expanded in z around 0 65.4%

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

   1. *-rgt-identity 65.4%

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

   2. associate-*l/ 65.4%

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

   3. associate-/l* 65.4%

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

   4. exp-neg 65.4%

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

   5. remove-double-div 65.4%

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

7. Simplified 65.4%

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

8. Taylor expanded in y around 0 57.6%

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

9. Final simplification 57.6%

   \[\leadsto e^{x} \]
10. Add Preprocessing

Developer target: 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 2024077 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

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

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