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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.0×

• 57.5% 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: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{x - z}\\ \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- x z))))
   (if (<= y 7.5e-7)
     t_0
     (if (<= y 1.7e+20)
       (* (pow y y) (exp x))
       (if (<= y 2.4e+126) t_0 (pow y y))))))

C

double code(double x, double y, double z) {
	double t_0 = exp((x - z));
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_0;
	} else if (y <= 1.7e+20) {
		tmp = pow(y, y) * exp(x);
	} else if (y <= 2.4e+126) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = exp((x - z))
    if (y <= 7.5d-7) then
        tmp = t_0
    else if (y <= 1.7d+20) then
        tmp = (y ** y) * exp(x)
    else if (y <= 2.4d+126) then
        tmp = t_0
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.exp((x - z));
	double tmp;
	if (y <= 7.5e-7) {
		tmp = t_0;
	} else if (y <= 1.7e+20) {
		tmp = Math.pow(y, y) * Math.exp(x);
	} else if (y <= 2.4e+126) {
		tmp = t_0;
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp((x - z))
	tmp = 0
	if y <= 7.5e-7:
		tmp = t_0
	elif y <= 1.7e+20:
		tmp = math.pow(y, y) * math.exp(x)
	elif y <= 2.4e+126:
		tmp = t_0
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(x - z))
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = t_0;
	elseif (y <= 1.7e+20)
		tmp = Float64((y ^ y) * exp(x));
	elseif (y <= 2.4e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp((x - z));
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = t_0;
	elseif (y <= 1.7e+20)
		tmp = (y ^ y) * exp(x);
	elseif (y <= 2.4e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 7.5e-7], t$95$0, If[LessEqual[y, 1.7e+20], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+126], t$95$0, N[Power[y, y], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5000000000000002e-7 or 1.7e20 < y < 2.40000000000000012e126

   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 88.0%

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

      4. *-commutative 88.0%

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

      5. exp-to-pow 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around 0 94.5%

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

   if 7.5000000000000002e-7 < y < 1.7e20

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. exp-sum 99.8%

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

      4. *-commutative 99.8%

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

      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

   5. Taylor expanded in z around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 2.40000000000000012e126 < 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 58.0%

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

      4. *-commutative 58.0%

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

      5. exp-to-pow 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in x around 0 73.9%

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

      1. exp-to-pow 73.9%

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

      2. *-commutative 73.9%

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

      3. prod-exp 95.7%

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

      4. +-commutative 95.7%

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

      5. unsub-neg 95.7%

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

      6. div-exp 73.9%

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

      7. *-commutative 73.9%

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

      8. exp-to-pow 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 92.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;e^{x - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+126}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{x - z}\\ \mathbf{if}\;y \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- x z))))
   (if (<= y 3.8e-24)
     t_0
     (if (<= y 1.9e+20)
       (/ (pow y y) (exp z))
       (if (<= y 3.6e+126) t_0 (pow y y))))))

C

double code(double x, double y, double z) {
	double t_0 = exp((x - z));
	double tmp;
	if (y <= 3.8e-24) {
		tmp = t_0;
	} else if (y <= 1.9e+20) {
		tmp = pow(y, y) / exp(z);
	} else if (y <= 3.6e+126) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = exp((x - z))
    if (y <= 3.8d-24) then
        tmp = t_0
    else if (y <= 1.9d+20) then
        tmp = (y ** y) / exp(z)
    else if (y <= 3.6d+126) then
        tmp = t_0
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.exp((x - z));
	double tmp;
	if (y <= 3.8e-24) {
		tmp = t_0;
	} else if (y <= 1.9e+20) {
		tmp = Math.pow(y, y) / Math.exp(z);
	} else if (y <= 3.6e+126) {
		tmp = t_0;
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp((x - z))
	tmp = 0
	if y <= 3.8e-24:
		tmp = t_0
	elif y <= 1.9e+20:
		tmp = math.pow(y, y) / math.exp(z)
	elif y <= 3.6e+126:
		tmp = t_0
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(x - z))
	tmp = 0.0
	if (y <= 3.8e-24)
		tmp = t_0;
	elseif (y <= 1.9e+20)
		tmp = Float64((y ^ y) / exp(z));
	elseif (y <= 3.6e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp((x - z));
	tmp = 0.0;
	if (y <= 3.8e-24)
		tmp = t_0;
	elseif (y <= 1.9e+20)
		tmp = (y ^ y) / exp(z);
	elseif (y <= 3.6e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 3.8e-24], t$95$0, If[LessEqual[y, 1.9e+20], N[(N[Power[y, y], $MachinePrecision] / N[Exp[z], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+126], t$95$0, N[Power[y, y], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.80000000000000026e-24 or 1.9e20 < y < 3.6e126

   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 87.6%

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

      4. *-commutative 87.6%

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

      5. exp-to-pow 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 94.3%

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

   if 3.80000000000000026e-24 < y < 1.9e20

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. exp-sum 99.9%

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

      4. *-commutative 99.9%

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

      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

   5. Taylor expanded in x around 0 100.0%

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

      1. exp-to-pow 99.9%

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

      2. *-commutative 99.9%

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

      3. prod-exp 99.9%

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

      4. +-commutative 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-exp 99.9%

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

      7. *-commutative 99.9%

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

      8. exp-to-pow 100.0%

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

   7. Simplified 100.0%

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

   if 3.6e126 < 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 58.0%

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

      4. *-commutative 58.0%

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

      5. exp-to-pow 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in x around 0 73.9%

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

      1. exp-to-pow 73.9%

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

      2. *-commutative 73.9%

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

      3. prod-exp 95.7%

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

      4. +-commutative 95.7%

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

      5. unsub-neg 95.7%

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

      6. div-exp 73.9%

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

      7. *-commutative 73.9%

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

      8. exp-to-pow 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 92.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;e^{x - z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+126}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{x - z}\\ \mathbf{if}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;{y}^{y} \cdot t\_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- x z))))
   (if (<= y 1.7e+20) (* (pow y y) t_0) (if (<= y 6e+126) t_0 (pow y y)))))

C

double code(double x, double y, double z) {
	double t_0 = exp((x - z));
	double tmp;
	if (y <= 1.7e+20) {
		tmp = pow(y, y) * t_0;
	} else if (y <= 6e+126) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = exp((x - z))
    if (y <= 1.7d+20) then
        tmp = (y ** y) * t_0
    else if (y <= 6d+126) then
        tmp = t_0
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.exp((x - z));
	double tmp;
	if (y <= 1.7e+20) {
		tmp = Math.pow(y, y) * t_0;
	} else if (y <= 6e+126) {
		tmp = t_0;
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp((x - z))
	tmp = 0
	if y <= 1.7e+20:
		tmp = math.pow(y, y) * t_0
	elif y <= 6e+126:
		tmp = t_0
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(x - z))
	tmp = 0.0
	if (y <= 1.7e+20)
		tmp = Float64((y ^ y) * t_0);
	elseif (y <= 6e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp((x - z));
	tmp = 0.0;
	if (y <= 1.7e+20)
		tmp = (y ^ y) * t_0;
	elseif (y <= 6e+126)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 1.7e+20], N[(N[Power[y, y], $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[y, 6e+126], t$95$0, N[Power[y, y], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.7e20

   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 1.7e20 < y < 6.0000000000000005e126

   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 47.5%

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

      4. *-commutative 47.5%

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

      5. exp-to-pow 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in y around 0 75.9%

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

   if 6.0000000000000005e126 < 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 58.0%

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

      4. *-commutative 58.0%

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

      5. exp-to-pow 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in x around 0 73.9%

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

      1. exp-to-pow 73.9%

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

      2. *-commutative 73.9%

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

      3. prod-exp 95.7%

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

      4. +-commutative 95.7%

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

      5. unsub-neg 95.7%

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

      6. div-exp 73.9%

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

      7. *-commutative 73.9%

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

      8. exp-to-pow 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 92.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+126}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7} \lor \neg \left(y \leq 4.9 \cdot 10^{+20}\right) \land y \leq 4.1 \cdot 10^{+126}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 7.5e-7) (and (not (<= y 4.9e+20)) (<= y 4.1e+126)))
   (exp (- x z))
   (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 7.5e-7) || (!(y <= 4.9e+20) && (y <= 4.1e+126))) {
		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-7) .or. (.not. (y <= 4.9d+20)) .and. (y <= 4.1d+126)) 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-7) || (!(y <= 4.9e+20) && (y <= 4.1e+126))) {
		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-7) or (not (y <= 4.9e+20) and (y <= 4.1e+126)):
		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-7) || (!(y <= 4.9e+20) && (y <= 4.1e+126)))
		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-7) || (~((y <= 4.9e+20)) && (y <= 4.1e+126)))
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 7.5e-7], And[N[Not[LessEqual[y, 4.9e+20]], $MachinePrecision], LessEqual[y, 4.1e+126]]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000002e-7 or 4.9e20 < y < 4.1000000000000001e126

   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 88.0%

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

      4. *-commutative 88.0%

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

      5. exp-to-pow 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around 0 94.5%

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

   if 7.5000000000000002e-7 < y < 4.9e20 or 4.1000000000000001e126 < 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 64.2%

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

      4. *-commutative 64.2%

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

      5. exp-to-pow 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in x around 0 77.8%

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

      1. exp-to-pow 77.8%

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

      2. *-commutative 77.8%

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

      3. prod-exp 96.3%

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

      4. +-commutative 96.3%

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

      5. unsub-neg 96.3%

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

      6. div-exp 77.8%

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

      7. *-commutative 77.8%

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

      8. exp-to-pow 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around 0 92.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7} \lor \neg \left(y \leq 4.9 \cdot 10^{+20}\right) \land y \leq 4.1 \cdot 10^{+126}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 7.5e-7) (exp (- z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-7) {
		tmp = exp(-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-7) then
        tmp = exp(-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-7) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-7:
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-7)
		tmp = exp(Float64(-z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.5e-7)
		tmp = exp(-z);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-7], N[Exp[(-z)], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000002e-7

   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

   5. Taylor expanded in x around 0 66.2%

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

      1. exp-to-pow 66.2%

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

      2. *-commutative 66.2%

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

      3. prod-exp 66.2%

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

      4. +-commutative 66.2%

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

      5. unsub-neg 66.2%

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

      6. div-exp 66.2%

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

      7. *-commutative 66.2%

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

      8. exp-to-pow 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in y around 0 66.2%

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

      1. rec-exp 66.2%

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

   10. Simplified 66.2%

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

   if 7.5000000000000002e-7 < 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 58.7%

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

      4. *-commutative 58.7%

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

      5. exp-to-pow 58.7%

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

   3. Simplified 58.7%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. exp-to-pow 67.0%

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

      2. *-commutative 67.0%

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

      3. prod-exp 91.0%

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

      4. +-commutative 91.0%

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

      5. unsub-neg 91.0%

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

      6. div-exp 67.0%

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

      7. *-commutative 67.0%

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

      8. exp-to-pow 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in z around 0 79.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{-z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Exp[(-z)], $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 80.5%

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

   4. *-commutative 80.5%

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

   5. exp-to-pow 80.5%

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

3. Simplified 80.5%

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

5. Taylor expanded in x around 0 66.6%

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

   1. exp-to-pow 66.6%

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

   2. *-commutative 66.6%

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

   3. prod-exp 77.9%

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

   4. +-commutative 77.9%

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

   5. unsub-neg 77.9%

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

   6. div-exp 66.6%

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

   7. *-commutative 66.6%

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

   8. exp-to-pow 66.6%

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

7. Simplified 66.6%

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

8. Taylor expanded in y around 0 53.3%

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

   1. rec-exp 53.3%

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

10. Simplified 53.3%

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

11. Final simplification 53.3%

    \[\leadsto e^{-z} \]
12. 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 2024059 
(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)))