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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 10

Speedup: 1.0×

• 58.4% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.6e+17) (exp (- x z)) (exp (- (* y (log y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+17) {
		tmp = exp((x - z));
	} else {
		tmp = exp(((y * log(y)) - 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 (y <= 4.6d+17) then
        tmp = exp((x - z))
    else
        tmp = exp(((y * log(y)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+17) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp(((y * Math.log(y)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.6e+17:
		tmp = math.exp((x - z))
	else:
		tmp = math.exp(((y * math.log(y)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e+17)
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(Float64(y * log(y)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.6e+17)
		tmp = exp((x - z));
	else
		tmp = exp(((y * log(y)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e+17], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.2%

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

   if 4.6e17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.2%

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

Alternative 3: 73.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.76:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-181}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-221}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.76)
   (exp (- z))
   (if (<= z -2.25e-181)
     (pow y y)
     (if (<= z -1.6e-221)
       (exp x)
       (if (<= z 1.25e-31) (pow y y) (if (<= z 2.1e+17) (exp x) 0.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.76) {
		tmp = exp(-z);
	} else if (z <= -2.25e-181) {
		tmp = pow(y, y);
	} else if (z <= -1.6e-221) {
		tmp = exp(x);
	} else if (z <= 1.25e-31) {
		tmp = pow(y, y);
	} else if (z <= 2.1e+17) {
		tmp = exp(x);
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-0.76d0)) then
        tmp = exp(-z)
    else if (z <= (-2.25d-181)) then
        tmp = y ** y
    else if (z <= (-1.6d-221)) then
        tmp = exp(x)
    else if (z <= 1.25d-31) then
        tmp = y ** y
    else if (z <= 2.1d+17) then
        tmp = exp(x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.76) {
		tmp = Math.exp(-z);
	} else if (z <= -2.25e-181) {
		tmp = Math.pow(y, y);
	} else if (z <= -1.6e-221) {
		tmp = Math.exp(x);
	} else if (z <= 1.25e-31) {
		tmp = Math.pow(y, y);
	} else if (z <= 2.1e+17) {
		tmp = Math.exp(x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.76:
		tmp = math.exp(-z)
	elif z <= -2.25e-181:
		tmp = math.pow(y, y)
	elif z <= -1.6e-221:
		tmp = math.exp(x)
	elif z <= 1.25e-31:
		tmp = math.pow(y, y)
	elif z <= 2.1e+17:
		tmp = math.exp(x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.76)
		tmp = exp(Float64(-z));
	elseif (z <= -2.25e-181)
		tmp = y ^ y;
	elseif (z <= -1.6e-221)
		tmp = exp(x);
	elseif (z <= 1.25e-31)
		tmp = y ^ y;
	elseif (z <= 2.1e+17)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.76)
		tmp = exp(-z);
	elseif (z <= -2.25e-181)
		tmp = y ^ y;
	elseif (z <= -1.6e-221)
		tmp = exp(x);
	elseif (z <= 1.25e-31)
		tmp = y ^ y;
	elseif (z <= 2.1e+17)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.76], N[Exp[(-z)], $MachinePrecision], If[LessEqual[z, -2.25e-181], N[Power[y, y], $MachinePrecision], If[LessEqual[z, -1.6e-221], N[Exp[x], $MachinePrecision], If[LessEqual[z, 1.25e-31], N[Power[y, y], $MachinePrecision], If[LessEqual[z, 2.1e+17], N[Exp[x], $MachinePrecision], 0.0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.76000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in y around 0 94.2%

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

      1. neg-mul-1 94.2%

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

   6. Simplified 94.2%

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

   if -0.76000000000000001 < z < -2.2499999999999999e-181 or -1.60000000000000008e-221 < z < 1.25e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. exp-sum 85.0%

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

      3. *-commutative 85.0%

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

      4. exp-to-pow 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around 0 76.9%

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

   if -2.2499999999999999e-181 < z < -1.60000000000000008e-221 or 1.25e-31 < z < 2.1e17

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 76.2%

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

      4. exp-diff 71.4%

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

      5. associate-/r/ 71.4%

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

      6. *-commutative 71.4%

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

      7. exp-to-pow 71.4%

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

      8. div-exp 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 90.7%

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

   6. Taylor expanded in z around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. remove-double-div 87.0%

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

   8. Simplified 87.0%

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

   if 2.1e17 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 75.9%

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

      4. exp-diff 46.6%

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

      5. associate-/r/ 46.6%

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

      6. *-commutative 46.6%

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

      7. exp-to-pow 46.6%

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

      8. div-exp 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around 0 83.0%

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

   6. Taylor expanded in z around 0 33.0%

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

   8. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{0} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+32) (exp (- z)) (if (<= z 1.4e+18) (exp x) 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+32) {
		tmp = exp(-z);
	} else if (z <= 1.4e+18) {
		tmp = exp(x);
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-3.6d+32)) then
        tmp = exp(-z)
    else if (z <= 1.4d+18) then
        tmp = exp(x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+32) {
		tmp = Math.exp(-z);
	} else if (z <= 1.4e+18) {
		tmp = Math.exp(x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e+32:
		tmp = math.exp(-z)
	elif z <= 1.4e+18:
		tmp = math.exp(x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+32)
		tmp = exp(Float64(-z));
	elseif (z <= 1.4e+18)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+32)
		tmp = exp(-z);
	elseif (z <= 1.4e+18)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+32], N[Exp[(-z)], $MachinePrecision], If[LessEqual[z, 1.4e+18], N[Exp[x], $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5999999999999997e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.8%

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

   4. Taylor expanded in y around 0 96.8%

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

      1. neg-mul-1 96.8%

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

   6. Simplified 96.8%

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

   if -3.5999999999999997e32 < z < 1.4e18

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 84.6%

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

      4. exp-diff 83.8%

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

      5. associate-/r/ 83.8%

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

      6. *-commutative 83.8%

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

      7. exp-to-pow 83.8%

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

      8. div-exp 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in y around 0 69.7%

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

   6. Taylor expanded in z around 0 64.9%

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

      1. exp-neg 64.9%

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

      2. remove-double-div 64.9%

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

   8. Simplified 64.9%

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

   if 1.4e18 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 75.9%

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

      4. exp-diff 46.6%

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

      5. associate-/r/ 46.6%

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

      6. *-commutative 46.6%

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

      7. exp-to-pow 46.6%

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

      8. div-exp 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around 0 83.0%

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

   6. Taylor expanded in z around 0 33.0%

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

   8. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 90.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+45}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.65e+45) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.65e+45) {
		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 <= 1.65d+45) 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 <= 1.65e+45) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.65e+45:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.65e+45)
		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 <= 1.65e+45)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.65e+45], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.65e45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.0%

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

   if 1.65e45 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. exp-sum 71.2%

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

      3. *-commutative 71.2%

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

      4. exp-to-pow 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in x around 0 87.8%

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

Alternative 6: 60.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+17}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.45e+17) (exp x) 0.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.45e+17) {
		tmp = exp(x);
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= 1.45d+17) then
        tmp = exp(x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.45e+17) {
		tmp = Math.exp(x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.45e+17:
		tmp = math.exp(x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.45e+17)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.45e+17)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.45e+17], N[Exp[x], $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if z < 1.45e17

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 84.3%

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

      4. exp-diff 83.8%

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

      5. associate-/r/ 83.8%

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

      6. *-commutative 83.8%

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

      7. exp-to-pow 83.8%

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

      8. div-exp 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around 0 79.2%

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

   6. Taylor expanded in z around 0 55.3%

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

      1. exp-neg 55.3%

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

      2. remove-double-div 55.3%

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

   8. Simplified 55.3%

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

   if 1.45e17 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 75.9%

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

      4. exp-diff 46.6%

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

      5. associate-/r/ 46.6%

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

      6. *-commutative 46.6%

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

      7. exp-to-pow 46.6%

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

      8. div-exp 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around 0 83.0%

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

   6. Taylor expanded in z around 0 33.0%

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

   8. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 41.6% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 6.2e-13) (+ 1.0 (* x (+ 1.0 (* x 0.5)))) 0.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.2e-13) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= 6.2d-13) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.2e-13) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 6.2e-13:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 6.2e-13)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 6.2e-13)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 6.2e-13], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if z < 6.1999999999999998e-13

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 85.3%

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

      4. exp-diff 85.3%

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

      5. associate-/r/ 85.2%

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

      6. *-commutative 85.2%

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

      7. exp-to-pow 85.2%

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

      8. div-exp 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 78.3%

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

   6. Taylor expanded in z around 0 53.8%

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

   7. Taylor expanded in x around 0 38.9%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto 1 + x \cdot \left(1 + \color{blue}{x \cdot 0.5}\right) \]

   9. Simplified 38.9%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot 0.5\right)} \]

   if 6.1999999999999998e-13 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 74.2%

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

      4. exp-diff 46.9%

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

      5. associate-/r/ 46.9%

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

      6. *-commutative 46.9%

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

      7. exp-to-pow 46.9%

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

      8. div-exp 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in y around 0 85.1%

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

   6. Taylor expanded in z around 0 39.9%

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

   8. Applied egg-rr 68.7%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 30.7% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 8.2e-61) (+ x 1.0) 0.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.2e-61) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= 8.2d-61) then
        tmp = x + 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.2e-61) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 8.2e-61:
		tmp = x + 1.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8.2e-61)
		tmp = Float64(x + 1.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 8.2e-61)
		tmp = x + 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8.2e-61], N[(x + 1.0), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if z < 8.19999999999999998e-61

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 85.4%

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

      4. exp-diff 85.4%

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

      5. associate-/r/ 85.4%

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

      6. *-commutative 85.4%

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

      7. exp-to-pow 85.4%

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

      8. div-exp 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 79.8%

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

   6. Taylor expanded in z around 0 54.7%

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

   7. Taylor expanded in x around 0 22.1%

      \[\leadsto \color{blue}{1 + x} \]

   if 8.19999999999999998e-61 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 74.6%

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

      4. exp-diff 49.3%

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

      5. associate-/r/ 49.3%

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

      6. *-commutative 49.3%

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

      7. exp-to-pow 49.3%

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

      8. div-exp 64.8%

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

   3. Simplified 64.8%

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

   5. Taylor expanded in y around 0 80.6%

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

   6. Taylor expanded in z around 0 38.7%

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

   8. Applied egg-rr 64.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 30.3% accurate, 34.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9 \cdot 10^{-109}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 9e-109) 1.0 0.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 9e-109) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= 9d-109) then
        tmp = 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 9e-109) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 9e-109:
		tmp = 1.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 9e-109)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 9e-109)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 9e-109], 1.0, 0.0]

Derivation

1. Split input into 2 regimes

2. if z < 9.0000000000000002e-109

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 85.2%

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

      4. exp-diff 85.2%

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

      5. associate-/r/ 85.2%

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

      6. *-commutative 85.2%

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

      7. exp-to-pow 85.2%

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

      8. div-exp 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 79.9%

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

   6. Taylor expanded in z around 0 53.5%

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

   7. Taylor expanded in x around 0 20.4%

      \[\leadsto \color{blue}{1} \]

   if 9.0000000000000002e-109 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 76.3%

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

      4. exp-diff 53.7%

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

      5. associate-/r/ 53.7%

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

      6. *-commutative 53.7%

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

      7. exp-to-pow 53.7%

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

      8. div-exp 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in y around 0 80.4%

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

   6. Taylor expanded in z around 0 43.1%

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

   8. Applied egg-rr 57.0%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 30.1% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. exp-sum 82.4%

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

   4. exp-diff 75.4%

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

   5. associate-/r/ 75.4%

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

   6. *-commutative 75.4%

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

   7. exp-to-pow 75.4%

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

   8. div-exp 83.6%

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

3. Simplified 83.6%

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

5. Taylor expanded in y around 0 80.0%

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

6. Taylor expanded in z around 0 50.2%

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

8. Applied egg-rr 24.9%

   \[\leadsto \color{blue}{0} \]
9. 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 2024107 
(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)))