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

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 15

Speedup: 1.0×

• 59.2% 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: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-30} \lor \neg \left(z \leq 3 \cdot 10^{+107}\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.38e-30) (not (<= z 3e+107)))
   (exp (- x z))
   (* (pow y y) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.38e-30) || !(z <= 3e+107)) {
		tmp = exp((x - z));
	} else {
		tmp = pow(y, y) * 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 <= (-1.38d-30)) .or. (.not. (z <= 3d+107))) then
        tmp = exp((x - z))
    else
        tmp = (y ** y) * exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.38e-30) || !(z <= 3e+107)) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y) * Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.38e-30) or not (z <= 3e+107):
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y) * math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.38e-30) || !(z <= 3e+107))
		tmp = exp(Float64(x - z));
	else
		tmp = Float64((y ^ y) * exp(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.38e-30) || ~((z <= 3e+107)))
		tmp = exp((x - z));
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.38e-30], N[Not[LessEqual[z, 3e+107]], $MachinePrecision]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.38000000000000008e-30 or 3.00000000000000023e107 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

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

   if -1.38000000000000008e-30 < z < 3.00000000000000023e107

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. exp-sum 87.3%

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

      3. *-commutative 87.3%

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

      4. exp-to-pow 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-30} \lor \neg \left(z \leq 3 \cdot 10^{+107}\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.0165:\\ \;\;\;\;\frac{{y}^{y}}{e^{z - x}}\\ \mathbf{else}:\\ \;\;\;\;e^{x - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.0165) (/ (pow y y) (exp (- z x))) (exp (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0165) {
		tmp = pow(y, y) / exp((z - x));
	} else {
		tmp = exp((x - 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 (z <= 0.0165d0) then
        tmp = (y ** y) / exp((z - x))
    else
        tmp = exp((x - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0165) {
		tmp = Math.pow(y, y) / Math.exp((z - x));
	} else {
		tmp = Math.exp((x - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.0165:
		tmp = math.pow(y, y) / math.exp((z - x))
	else:
		tmp = math.exp((x - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.0165)
		tmp = Float64((y ^ y) / exp(Float64(z - x)));
	else
		tmp = exp(Float64(x - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.0165)
		tmp = (y ^ y) / exp((z - x));
	else
		tmp = exp((x - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.0165], N[(N[Power[y, y], $MachinePrecision] / N[Exp[N[(z - x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.016500000000000001

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. exp-sum 86.6%

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

      4. exp-diff 86.6%

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

      5. associate-/r/ 86.6%

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

      6. *-commutative 86.6%

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

      7. exp-to-pow 86.6%

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

      8. div-exp 92.0%

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

   3. Simplified 92.0%

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

   if 0.016500000000000001 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.3%

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

Alternative 4: 73.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-z}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-122}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-306}:\\ \;\;\;\;{y}^{y}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-244}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;{y}^{y}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- z))))
   (if (<= x -1.35e+69)
     (exp x)
     (if (<= x -2.25e-122)
       t_0
       (if (<= x -1.2e-306)
         (pow y y)
         (if (<= x 2.1e-244) t_0 (if (<= x 7.2e-6) (pow y y) (exp x))))))))

C

double code(double x, double y, double z) {
	double t_0 = exp(-z);
	double tmp;
	if (x <= -1.35e+69) {
		tmp = exp(x);
	} else if (x <= -2.25e-122) {
		tmp = t_0;
	} else if (x <= -1.2e-306) {
		tmp = pow(y, y);
	} else if (x <= 2.1e-244) {
		tmp = t_0;
	} else if (x <= 7.2e-6) {
		tmp = pow(y, y);
	} 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) :: t_0
    real(8) :: tmp
    t_0 = exp(-z)
    if (x <= (-1.35d+69)) then
        tmp = exp(x)
    else if (x <= (-2.25d-122)) then
        tmp = t_0
    else if (x <= (-1.2d-306)) then
        tmp = y ** y
    else if (x <= 2.1d-244) then
        tmp = t_0
    else if (x <= 7.2d-6) then
        tmp = y ** y
    else
        tmp = exp(x)
    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 (x <= -1.35e+69) {
		tmp = Math.exp(x);
	} else if (x <= -2.25e-122) {
		tmp = t_0;
	} else if (x <= -1.2e-306) {
		tmp = Math.pow(y, y);
	} else if (x <= 2.1e-244) {
		tmp = t_0;
	} else if (x <= 7.2e-6) {
		tmp = Math.pow(y, y);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp(-z)
	tmp = 0
	if x <= -1.35e+69:
		tmp = math.exp(x)
	elif x <= -2.25e-122:
		tmp = t_0
	elif x <= -1.2e-306:
		tmp = math.pow(y, y)
	elif x <= 2.1e-244:
		tmp = t_0
	elif x <= 7.2e-6:
		tmp = math.pow(y, y)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(-z))
	tmp = 0.0
	if (x <= -1.35e+69)
		tmp = exp(x);
	elseif (x <= -2.25e-122)
		tmp = t_0;
	elseif (x <= -1.2e-306)
		tmp = y ^ y;
	elseif (x <= 2.1e-244)
		tmp = t_0;
	elseif (x <= 7.2e-6)
		tmp = y ^ y;
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp(-z);
	tmp = 0.0;
	if (x <= -1.35e+69)
		tmp = exp(x);
	elseif (x <= -2.25e-122)
		tmp = t_0;
	elseif (x <= -1.2e-306)
		tmp = y ^ y;
	elseif (x <= 2.1e-244)
		tmp = t_0;
	elseif (x <= 7.2e-6)
		tmp = y ^ y;
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[(-z)], $MachinePrecision]}, If[LessEqual[x, -1.35e+69], N[Exp[x], $MachinePrecision], If[LessEqual[x, -2.25e-122], t$95$0, If[LessEqual[x, -1.2e-306], N[Power[y, y], $MachinePrecision], If[LessEqual[x, 2.1e-244], t$95$0, If[LessEqual[x, 7.2e-6], N[Power[y, y], $MachinePrecision], N[Exp[x], $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3499999999999999e69 or 7.19999999999999967e-6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.5%

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

   4. Taylor expanded in z around 0 88.1%

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

   if -1.3499999999999999e69 < x < -2.2499999999999999e-122 or -1.2e-306 < x < 2.10000000000000002e-244

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. neg-mul-1 72.9%

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

   5. Simplified 72.9%

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

   if -2.2499999999999999e-122 < x < -1.2e-306 or 2.10000000000000002e-244 < x < 7.19999999999999967e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. exp-sum 79.9%

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

      3. *-commutative 79.9%

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

      4. exp-to-pow 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in x around 0 79.9%

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

Alternative 5: 62.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 72000000000000 \lor \neg \left(z \leq 1.62 \cdot 10^{+111}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.02e+103)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (or (<= z 72000000000000.0) (not (<= z 1.62e+111))) (exp x) (exp z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 72000000000000.0) || !(z <= 1.62e+111)) {
		tmp = exp(x);
	} else {
		tmp = exp(z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.02d+103)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if ((z <= 72000000000000.0d0) .or. (.not. (z <= 1.62d+111))) then
        tmp = exp(x)
    else
        tmp = exp(z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+103) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 72000000000000.0) || !(z <= 1.62e+111)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.02e+103:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif (z <= 72000000000000.0) or not (z <= 1.62e+111):
		tmp = math.exp(x)
	else:
		tmp = math.exp(z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.02e+103)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif ((z <= 72000000000000.0) || !(z <= 1.62e+111))
		tmp = exp(x);
	else
		tmp = exp(z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.02e+103)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif ((z <= 72000000000000.0) || ~((z <= 1.62e+111)))
		tmp = exp(x);
	else
		tmp = exp(z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.02e+103], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 72000000000000.0], N[Not[LessEqual[z, 1.62e+111]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[z], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.01999999999999991e103

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. neg-mul-1 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in z around 0 89.6%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 89.6%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 89.6%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 89.6%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -1.01999999999999991e103 < z < 7.2e13 or 1.61999999999999999e111 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.5%

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

   4. Taylor expanded in z around 0 60.5%

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

   if 7.2e13 < z < 1.61999999999999999e111

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 36.0%

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

      1. neg-mul-1 36.0%

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

   5. Simplified 36.0%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 65.5%

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

      3. sqr-neg 65.5%

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

      4. sqrt-unprod 65.5%

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

      5. add-sqr-sqrt 65.5%

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

      6. expm1-log1p-u 65.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{z}\right)\right)} \]

      7. expm1-undefine 65.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{z}\right)} - 1} \]

   7. Applied egg-rr 65.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(e^{z}\right)} - 1} \]
   8. Step-by-step derivation

      1. log1p-undefine 65.5%

         \[\leadsto e^{\color{blue}{\log \left(1 + e^{z}\right)}} - 1 \]

      2. rem-exp-log 65.5%

         \[\leadsto \color{blue}{\left(1 + e^{z}\right)} - 1 \]

      3. associate-+r- 65.5%

         \[\leadsto \color{blue}{1 + \left(e^{z} - 1\right)} \]

      4. expm1-undefine 65.5%

         \[\leadsto 1 + \color{blue}{\mathsf{expm1}\left(z\right)} \]

      5. rem-exp-log 65.5%

         \[\leadsto \color{blue}{e^{\log \left(1 + \mathsf{expm1}\left(z\right)\right)}} \]

      6. log1p-define 65.5%

         \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right)\right)}} \]

      7. log1p-expm1 65.5%

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

   9. Simplified 65.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+103}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 72000000000000 \lor \neg \left(z \leq 1.62 \cdot 10^{+111}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+70} \lor \neg \left(x \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+70) (not (<= x 1.7e+22))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+70) || !(x <= 1.7e+22)) {
		tmp = exp(x);
	} else {
		tmp = exp(-z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.05d+70)) .or. (.not. (x <= 1.7d+22))) then
        tmp = exp(x)
    else
        tmp = exp(-z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+70) || !(x <= 1.7e+22)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+70) or not (x <= 1.7e+22):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+70) || !(x <= 1.7e+22))
		tmp = exp(x);
	else
		tmp = exp(Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+70) || ~((x <= 1.7e+22)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+70], N[Not[LessEqual[x, 1.7e+22]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000004e70 or 1.7e22 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.2%

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

   4. Taylor expanded in z around 0 90.6%

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

   if -1.05000000000000004e70 < x < 1.7e22

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 68.2%

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

      1. neg-mul-1 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+70} \lor \neg \left(x \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{+129}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.4e+129) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.4e+129) {
		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 <= 8.4d+129) 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 <= 8.4e+129) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.4e+129:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.4e+129)
		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 <= 8.4e+129)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.4e+129], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.39999999999999986e129

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 90.9%

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

   if 8.39999999999999986e129 < 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 92.7%

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

      1. +-commutative 92.7%

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

      2. exp-sum 77.7%

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

      3. *-commutative 77.7%

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

      4. exp-to-pow 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 86.8%

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

Alternative 8: 61.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.05 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.05e+102)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.05e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} 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 <= (-4.05d+102)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    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 <= -4.05e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.05e+102:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.05e+102)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.05e+102)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.05e+102], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.05000000000000019e102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. neg-mul-1 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in z around 0 89.6%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 89.6%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 89.6%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 89.6%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -4.05000000000000019e102 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.6%

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

   4. Taylor expanded in z around 0 58.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.05 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.8% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+101}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+101)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+101) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	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 <= (-1.8d+101)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+101) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+101:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+101)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+101)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+101], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000015e101

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.4%

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

      1. neg-mul-1 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around 0 87.4%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 87.4%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 87.4%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -1.80000000000000015e101 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.6%

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

   4. Taylor expanded in z around 0 58.2%

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

   5. Taylor expanded in x around 0 32.6%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.6%

         \[\leadsto 1 + x \cdot \left(1 + x \cdot \left(0.5 + \color{blue}{x \cdot 0.16666666666666666}\right)\right) \]

   7. Simplified 32.6%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+101}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.7% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+101}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.36e+101)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.36e+101) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	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 <= (-1.36d+101)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.36e+101) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.36e+101:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.36e+101)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.36e+101)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.36e+101], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35999999999999998e101

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.4%

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

      1. neg-mul-1 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around 0 87.4%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   7. Taylor expanded in z around inf 87.4%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(-0.16666666666666666 \cdot z\right)} - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   9. Simplified 87.4%

      \[\leadsto 1 + z \cdot \left(z \cdot \color{blue}{\left(z \cdot -0.16666666666666666\right)} - 1\right) \]

   if -1.35999999999999998e101 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.6%

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

   4. Taylor expanded in z around 0 58.2%

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

   5. Taylor expanded in x around 0 29.1%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+101}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+152}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8e+152) (+ 1.0 (* z (+ (* z 0.5) -1.0))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8e+152) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	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 <= 8d+152) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 8e+152) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 8e+152:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8e+152)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 8e+152)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8e+152], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.0000000000000004e152

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 57.1%

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

      1. neg-mul-1 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in z around 0 27.9%

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

   if 8.0000000000000004e152 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.5%

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

   6. Taylor expanded in x around inf 88.5%

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

      1. *-commutative 88.5%

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

   8. Simplified 88.5%

      \[\leadsto 1 + x \cdot \color{blue}{\left(x \cdot 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+152}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.5% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.1e+150) (+ 1.0 (* z (* z 0.5))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.1e+150) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	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 <= 1.1d+150) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    else
        tmp = 1.0d0 + (x * (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.1e+150) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.1e+150:
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.1e+150)
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.1e+150)
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.1e+150], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1e150

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 57.1%

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

      1. neg-mul-1 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in z around 0 27.9%

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

   7. Taylor expanded in z around inf 27.8%

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

      1. *-commutative 27.8%

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

   9. Simplified 27.8%

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

   if 1.1e150 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.5%

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

   6. Taylor expanded in x around inf 88.5%

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

      1. *-commutative 88.5%

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

   8. Simplified 88.5%

      \[\leadsto 1 + x \cdot \color{blue}{\left(x \cdot 0.5\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 28.7% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ 1 + x \cdot \left(x \cdot 0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (* x (* x 0.5))))

C

double code(double x, double y, double z) {
	return 1.0 + (x * (x * 0.5));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (x * (x * 0.5d0))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (x * (x * 0.5));
}

Python

def code(x, y, z):
	return 1.0 + (x * (x * 0.5))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(x * Float64(x * 0.5)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (x * (x * 0.5));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 81.8%

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

4. Taylor expanded in z around 0 56.2%

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

5. Taylor expanded in x around 0 27.9%

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

6. Taylor expanded in x around inf 27.7%

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

   1. *-commutative 27.7%

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

8. Simplified 27.7%

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

Alternative 14: 14.8% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 81.8%

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

4. Taylor expanded in z around 0 56.2%

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

5. Taylor expanded in x around 0 15.8%

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

6. Final simplification 15.8%

   \[\leadsto x + 1 \]
7. Add Preprocessing

Alternative 15: 14.6% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 53.5%

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

   1. neg-mul-1 53.5%

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

5. Simplified 53.5%

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

6. Taylor expanded in z around 0 15.5%

   \[\leadsto \color{blue}{1} \]
7. 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 2024110 
(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)))