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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 5

Speedup: 1.0×

• 58.1% 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: 73.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-z}\\ \mathbf{if}\;z \leq -0.00011:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-186}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- z))))
   (if (<= z -0.00011)
     t_0
     (if (<= z 2e-186) (pow y y) (if (<= z 3.6e+47) (exp x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = exp(-z);
	double tmp;
	if (z <= -0.00011) {
		tmp = t_0;
	} else if (z <= 2e-186) {
		tmp = pow(y, y);
	} else if (z <= 3.6e+47) {
		tmp = exp(x);
	} 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 = exp(-z)
    if (z <= (-0.00011d0)) then
        tmp = t_0
    else if (z <= 2d-186) then
        tmp = y ** y
    else if (z <= 3.6d+47) then
        tmp = exp(x)
    else
        tmp = t_0
    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 (z <= -0.00011) {
		tmp = t_0;
	} else if (z <= 2e-186) {
		tmp = Math.pow(y, y);
	} else if (z <= 3.6e+47) {
		tmp = Math.exp(x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp(-z)
	tmp = 0
	if z <= -0.00011:
		tmp = t_0
	elif z <= 2e-186:
		tmp = math.pow(y, y)
	elif z <= 3.6e+47:
		tmp = math.exp(x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(-z))
	tmp = 0.0
	if (z <= -0.00011)
		tmp = t_0;
	elseif (z <= 2e-186)
		tmp = y ^ y;
	elseif (z <= 3.6e+47)
		tmp = exp(x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp(-z);
	tmp = 0.0;
	if (z <= -0.00011)
		tmp = t_0;
	elseif (z <= 2e-186)
		tmp = y ^ y;
	elseif (z <= 3.6e+47)
		tmp = exp(x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[(-z)], $MachinePrecision]}, If[LessEqual[z, -0.00011], t$95$0, If[LessEqual[z, 2e-186], N[Power[y, y], $MachinePrecision], If[LessEqual[z, 3.6e+47], N[Exp[x], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000004e-4 or 3.60000000000000008e47 < z

   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 75.6%

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

      4. *-commutative 75.6%

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

      5. exp-to-pow 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in x around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. exp-to-pow 68.6%

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

      3. *-commutative 68.6%

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

      4. prod-exp 89.1%

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

      5. unsub-neg 89.1%

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

      6. div-exp 68.6%

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

      7. *-commutative 68.6%

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

      8. exp-to-pow 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in y around 0 85.3%

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

      1. rec-exp 85.3%

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

   10. Simplified 85.3%

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

   if -1.10000000000000004e-4 < z < 1.9999999999999998e-186

   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 87.0%

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

      4. *-commutative 87.0%

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

      5. exp-to-pow 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{{y}^{y}} \]

   if 1.9999999999999998e-186 < z < 3.60000000000000008e47

   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 88.5%

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

      4. *-commutative 88.5%

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

      5. exp-to-pow 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around 0 85.9%

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

      1. *-commutative 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in y around 0 78.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00011:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-186}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51} \lor \neg \left(x \leq 255\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+51) (not (<= x 255.0))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+51) || !(x <= 255.0)) {
		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 <= (-5.5d+51)) .or. (.not. (x <= 255.0d0))) 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 <= -5.5e+51) || !(x <= 255.0)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+51) or not (x <= 255.0):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+51) || !(x <= 255.0))
		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 <= -5.5e+51) || ~((x <= 255.0)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+51], N[Not[LessEqual[x, 255.0]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e51 or 255 < 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 77.6%

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

      4. *-commutative 77.6%

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

      5. exp-to-pow 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in z around 0 70.2%

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

      1. *-commutative 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in y around 0 85.3%

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

   if -5.5e51 < x < 255

   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 84.6%

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

      4. *-commutative 84.6%

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

      5. exp-to-pow 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in x around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. exp-to-pow 86.4%

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

      3. *-commutative 86.4%

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

      4. prod-exp 99.8%

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

      5. unsub-neg 99.8%

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

      6. div-exp 86.3%

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

      7. *-commutative 86.3%

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

      8. exp-to-pow 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in y around 0 75.8%

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

      1. rec-exp 75.8%

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

   10. Simplified 75.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51} \lor \neg \left(x \leq 255\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e+43) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e+43) {
		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 <= 7.5d+43) 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 <= 7.5e+43) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e+43:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e+43)
		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 <= 7.5e+43)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e+43], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.49999999999999967e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.2%

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

   if 7.49999999999999967e43 < y

   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 69.4%

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

      4. *-commutative 69.4%

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

      5. exp-to-pow 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around 0 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x around 0 84.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
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. +-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 81.6%

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

   4. *-commutative 81.6%

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

   5. exp-to-pow 81.6%

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

3. Simplified 81.6%

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

5. Taylor expanded in z around 0 68.1%

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

   1. *-commutative 68.1%

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

7. Simplified 68.1%

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

8. Taylor expanded in y around 0 52.6%

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

9. Final simplification 52.6%

   \[\leadsto e^{x} \]
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 2024096 
(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)))