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

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 6

Speedup: 1.0×

• 51.1% 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. Final simplification 100.0%

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

Alternative 2: 94.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-303}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{t_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 -1e-303) (exp (- x z)) (exp (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= -1e-303) {
		tmp = exp((x - z));
	} else {
		tmp = exp((t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = y * log(y)
    if (t_0 <= (-1d-303)) then
        tmp = exp((x - z))
    else
        tmp = exp((t_0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (t_0 <= -1e-303) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp((t_0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= -1e-303:
		tmp = math.exp((x - z))
	else:
		tmp = math.exp((t_0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= -1e-303)
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(t_0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= -1e-303)
		tmp = exp((x - z));
	else
		tmp = exp((t_0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-303], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(t$95$0 - z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < -9.99999999999999931e-304

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -9.99999999999999931e-304 < (*.f64 y (log.f64 y))

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq -1 \cdot 10^{-303}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \]

Alternative 3: 73.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-z}\\ \mathbf{if}\;y \leq 7.1 \cdot 10^{-211}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.7:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- z))))
   (if (<= y 7.1e-211)
     (exp x)
     (if (<= y 1.15e-154)
       t_0
       (if (<= y 2.5e-116)
         (exp x)
         (if (<= y 1.58e-96)
           t_0
           (if (<= y 6.7) (exp x) (if (<= y 1.85e+28) t_0 (pow y y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = exp(-z);
	double tmp;
	if (y <= 7.1e-211) {
		tmp = exp(x);
	} else if (y <= 1.15e-154) {
		tmp = t_0;
	} else if (y <= 2.5e-116) {
		tmp = exp(x);
	} else if (y <= 1.58e-96) {
		tmp = t_0;
	} else if (y <= 6.7) {
		tmp = exp(x);
	} else if (y <= 1.85e+28) {
		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 <= 7.1d-211) then
        tmp = exp(x)
    else if (y <= 1.15d-154) then
        tmp = t_0
    else if (y <= 2.5d-116) then
        tmp = exp(x)
    else if (y <= 1.58d-96) then
        tmp = t_0
    else if (y <= 6.7d0) then
        tmp = exp(x)
    else if (y <= 1.85d+28) 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 <= 7.1e-211) {
		tmp = Math.exp(x);
	} else if (y <= 1.15e-154) {
		tmp = t_0;
	} else if (y <= 2.5e-116) {
		tmp = Math.exp(x);
	} else if (y <= 1.58e-96) {
		tmp = t_0;
	} else if (y <= 6.7) {
		tmp = Math.exp(x);
	} else if (y <= 1.85e+28) {
		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 <= 7.1e-211:
		tmp = math.exp(x)
	elif y <= 1.15e-154:
		tmp = t_0
	elif y <= 2.5e-116:
		tmp = math.exp(x)
	elif y <= 1.58e-96:
		tmp = t_0
	elif y <= 6.7:
		tmp = math.exp(x)
	elif y <= 1.85e+28:
		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 <= 7.1e-211)
		tmp = exp(x);
	elseif (y <= 1.15e-154)
		tmp = t_0;
	elseif (y <= 2.5e-116)
		tmp = exp(x);
	elseif (y <= 1.58e-96)
		tmp = t_0;
	elseif (y <= 6.7)
		tmp = exp(x);
	elseif (y <= 1.85e+28)
		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 <= 7.1e-211)
		tmp = exp(x);
	elseif (y <= 1.15e-154)
		tmp = t_0;
	elseif (y <= 2.5e-116)
		tmp = exp(x);
	elseif (y <= 1.58e-96)
		tmp = t_0;
	elseif (y <= 6.7)
		tmp = exp(x);
	elseif (y <= 1.85e+28)
		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, 7.1e-211], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1.15e-154], t$95$0, If[LessEqual[y, 2.5e-116], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1.58e-96], t$95$0, If[LessEqual[y, 6.7], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1.85e+28], t$95$0, N[Power[y, y], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.09999999999999987e-211 or 1.15e-154 < y < 2.5000000000000001e-116 or 1.5800000000000001e-96 < y < 6.70000000000000018

   1. Initial program 100.0%

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

      1. exp-diff 90.0%

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

      2. +-commutative 90.0%

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

      3. exp-sum 90.0%

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

      4. associate-*r/ 90.0%

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

      5. *-commutative 90.0%

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

      6. exp-to-pow 90.0%

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

      7. exp-diff 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 83.0%

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

      1. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in y around 0 83.0%

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

   if 7.09999999999999987e-211 < y < 1.15e-154 or 2.5000000000000001e-116 < y < 1.5800000000000001e-96 or 6.70000000000000018 < y < 1.85e28

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 79.8%

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

      1. mul-1-neg 79.8%

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

   4. Simplified 79.8%

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

   if 1.85e28 < y

   1. Initial program 100.0%

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

      1. exp-diff 78.8%

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

      2. +-commutative 78.8%

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

      3. exp-sum 59.3%

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

      4. associate-*r/ 59.3%

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

      5. *-commutative 59.3%

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

      6. exp-to-pow 59.3%

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

      7. exp-diff 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x around 0 87.5%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.1 \cdot 10^{-211}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-96}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 6.7:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+28}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]

Alternative 4: 73.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700 \lor \neg \left(z \leq 5.5 \cdot 10^{+86}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -700.0) (not (<= z 5.5e+86))) (exp (- z)) (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -700.0) || !(z <= 5.5e+86)) {
		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 ((z <= (-700.0d0)) .or. (.not. (z <= 5.5d+86))) 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 ((z <= -700.0) || !(z <= 5.5e+86)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -700.0) or not (z <= 5.5e+86):
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -700.0) || !(z <= 5.5e+86))
		tmp = exp(Float64(-z));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -700.0) || ~((z <= 5.5e+86)))
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -700.0], N[Not[LessEqual[z, 5.5e+86]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -700 or 5.5000000000000002e86 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. mul-1-neg 87.2%

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

   4. Simplified 87.2%

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

   if -700 < z < 5.5000000000000002e86

   1. Initial program 100.0%

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

      1. exp-diff 91.5%

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

      2. +-commutative 91.5%

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

      3. exp-sum 79.4%

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

      4. associate-*r/ 79.4%

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

      5. *-commutative 79.4%

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

      6. exp-to-pow 79.4%

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

      7. exp-diff 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in z around 0 83.7%

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

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around 0 68.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700 \lor \neg \left(z \leq 5.5 \cdot 10^{+86}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]

Alternative 5: 89.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e+141) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e+141) {
		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 <= 1.6d+141) 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 <= 1.6e+141) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e+141:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e+141)
		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 <= 1.6e+141)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e+141], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.60000000000000009e141

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.2%

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

   if 1.60000000000000009e141 < y

   1. Initial program 100.0%

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

      1. exp-diff 80.8%

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

      2. +-commutative 80.8%

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

      3. exp-sum 61.6%

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

      4. associate-*r/ 61.6%

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

      5. *-commutative 61.6%

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

      6. exp-to-pow 61.6%

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

      7. exp-diff 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. *-commutative 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in x around 0 96.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]

Alternative 6: 53.3% 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. exp-diff 82.0%

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

   2. +-commutative 82.0%

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

   3. exp-sum 72.7%

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

   4. associate-*r/ 72.7%

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

   5. *-commutative 72.7%

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

   6. exp-to-pow 72.7%

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

   7. exp-diff 84.0%

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

3. Simplified 84.0%

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

4. Taylor expanded in z around 0 70.3%

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

   1. *-commutative 70.3%

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

6. Simplified 70.3%

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

7. Taylor expanded in y around 0 54.0%

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

8. Final simplification 54.0%

   \[\leadsto e^{x} \]

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 2023301 
(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)))