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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 5

Speedup: 1.0×

• 52.4% 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. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-z}\\ \mathbf{if}\;y \leq 1.62 \cdot 10^{-255}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-199}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-46}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 11000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- z))))
   (if (<= y 1.62e-255)
     t_0
     (if (<= y 9.2e-199)
       (exp x)
       (if (<= y 5.4e-181)
         t_0
         (if (<= y 5e-46) (exp x) (if (<= y 11000000.0) t_0 (pow y y))))))))

C

double code(double x, double y, double z) {
	double t_0 = exp(-z);
	double tmp;
	if (y <= 1.62e-255) {
		tmp = t_0;
	} else if (y <= 9.2e-199) {
		tmp = exp(x);
	} else if (y <= 5.4e-181) {
		tmp = t_0;
	} else if (y <= 5e-46) {
		tmp = exp(x);
	} else if (y <= 11000000.0) {
		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(-z)
    if (y <= 1.62d-255) then
        tmp = t_0
    else if (y <= 9.2d-199) then
        tmp = exp(x)
    else if (y <= 5.4d-181) then
        tmp = t_0
    else if (y <= 5d-46) then
        tmp = exp(x)
    else if (y <= 11000000.0d0) 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(-z);
	double tmp;
	if (y <= 1.62e-255) {
		tmp = t_0;
	} else if (y <= 9.2e-199) {
		tmp = Math.exp(x);
	} else if (y <= 5.4e-181) {
		tmp = t_0;
	} else if (y <= 5e-46) {
		tmp = Math.exp(x);
	} else if (y <= 11000000.0) {
		tmp = t_0;
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp(-z)
	tmp = 0
	if y <= 1.62e-255:
		tmp = t_0
	elif y <= 9.2e-199:
		tmp = math.exp(x)
	elif y <= 5.4e-181:
		tmp = t_0
	elif y <= 5e-46:
		tmp = math.exp(x)
	elif y <= 11000000.0:
		tmp = t_0
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(-z))
	tmp = 0.0
	if (y <= 1.62e-255)
		tmp = t_0;
	elseif (y <= 9.2e-199)
		tmp = exp(x);
	elseif (y <= 5.4e-181)
		tmp = t_0;
	elseif (y <= 5e-46)
		tmp = exp(x);
	elseif (y <= 11000000.0)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp(-z);
	tmp = 0.0;
	if (y <= 1.62e-255)
		tmp = t_0;
	elseif (y <= 9.2e-199)
		tmp = exp(x);
	elseif (y <= 5.4e-181)
		tmp = t_0;
	elseif (y <= 5e-46)
		tmp = exp(x);
	elseif (y <= 11000000.0)
		tmp = t_0;
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[(-z)], $MachinePrecision]}, If[LessEqual[y, 1.62e-255], t$95$0, If[LessEqual[y, 9.2e-199], N[Exp[x], $MachinePrecision], If[LessEqual[y, 5.4e-181], t$95$0, If[LessEqual[y, 5e-46], N[Exp[x], $MachinePrecision], If[LessEqual[y, 11000000.0], t$95$0, N[Power[y, y], $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.6200000000000001e-255 or 9.2000000000000005e-199 < y < 5.3999999999999999e-181 or 4.99999999999999992e-46 < y < 1.1e7

   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 98.2%

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

      4. *-commutative 98.2%

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

      5. exp-to-pow 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. exp-neg 84.6%

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

      2. associate-*l/ 84.6%

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

      3. *-lft-identity 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around 0 84.1%

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

      1. rec-exp 84.1%

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

   9. Simplified 84.1%

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

   if 1.6200000000000001e-255 < y < 9.2000000000000005e-199 or 5.3999999999999999e-181 < y < 4.99999999999999992e-46

   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. Taylor expanded in z around 0 76.5%

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

   5. Taylor expanded in y around 0 76.5%

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

   if 1.1e7 < 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 62.9%

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

      4. *-commutative 62.9%

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

      5. exp-to-pow 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around 0 76.0%

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

   5. Taylor expanded in x around 0 84.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{-255}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-199}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-181}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-46}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 11000000:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]

Alternative 3: 72.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+43}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-16}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e+43) (exp x) (if (<= x 1.2e-16) (exp (- z)) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+43) {
		tmp = exp(x);
	} else if (x <= 1.2e-16) {
		tmp = exp(-z);
	} 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) :: tmp
    if (x <= (-3.7d+43)) then
        tmp = exp(x)
    else if (x <= 1.2d-16) then
        tmp = exp(-z)
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+43) {
		tmp = Math.exp(x);
	} else if (x <= 1.2e-16) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e+43:
		tmp = math.exp(x)
	elif x <= 1.2e-16:
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e+43)
		tmp = exp(x);
	elseif (x <= 1.2e-16)
		tmp = exp(Float64(-z));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.7e+43)
		tmp = exp(x);
	elseif (x <= 1.2e-16)
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e+43], N[Exp[x], $MachinePrecision], If[LessEqual[x, 1.2e-16], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000001e43 or 1.20000000000000002e-16 < 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 80.4%

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

      4. *-commutative 80.4%

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

      5. exp-to-pow 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in z around 0 78.7%

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

   5. Taylor expanded in y around 0 85.1%

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

   if -3.7000000000000001e43 < x < 1.20000000000000002e-16

   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 84.7%

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

      4. *-commutative 84.7%

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

      5. exp-to-pow 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in x around 0 85.4%

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

      1. exp-neg 85.4%

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

      2. associate-*l/ 85.4%

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

      3. *-lft-identity 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in y around 0 63.3%

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

      1. rec-exp 63.3%

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

   9. Simplified 63.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+43}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-16}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]

Alternative 4: 89.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 36000000000:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 36000000000.0) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 36000000000.0) {
		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 <= 36000000000.0d0) 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 <= 36000000000.0) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 36000000000.0:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 36000000000.0)
		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 <= 36000000000.0)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 36000000000.0], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.6e10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.8%

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

   if 3.6e10 < 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 63.2%

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

      4. *-commutative 63.2%

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

      5. exp-to-pow 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in z around 0 76.5%

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

   5. Taylor expanded in x around 0 85.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 36000000000:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]

Alternative 5: 52.2% 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 82.8%

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

   4. *-commutative 82.8%

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

   5. exp-to-pow 82.8%

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

3. Simplified 82.8%

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

4. Taylor expanded in z around 0 68.6%

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

5. Taylor expanded in y around 0 47.9%

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

6. Final simplification 47.9%

   \[\leadsto e^{x} \]

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 2023221 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

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