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

Percentage Accurate: 100.0% → 100.0%

Time: 10.0s

Alternatives: 17

Speedup: 1.0×

• 57.8% 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: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z - x}}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 -5e-303) (/ (pow y y) (exp (- z x))) (exp (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= -5e-303) {
		tmp = pow(y, y) / exp((z - x));
	} else {
		tmp = exp((t_0 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * log(y)
    if (t_0 <= (-5d-303)) then
        tmp = (y ** y) / exp((z - x))
    else
        tmp = exp((t_0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (t_0 <= -5e-303) {
		tmp = Math.pow(y, y) / Math.exp((z - x));
	} else {
		tmp = Math.exp((t_0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= -5e-303:
		tmp = math.pow(y, y) / math.exp((z - x))
	else:
		tmp = math.exp((t_0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= -5e-303)
		tmp = Float64((y ^ y) / exp(Float64(z - x)));
	else
		tmp = exp(Float64(t_0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= -5e-303)
		tmp = (y ^ y) / exp((z - x));
	else
		tmp = exp((t_0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-303], N[(N[Power[y, y], $MachinePrecision] / N[Exp[N[(z - x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(t$95$0 - z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < -4.9999999999999998e-303

   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 83.3%

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

      4. exp-diff 83.3%

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

      5. associate-/r/ 83.3%

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

      6. *-commutative 83.3%

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

      7. exp-to-pow 83.3%

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

      8. div-exp 100.0%

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

   3. Simplified 100.0%

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

   if -4.9999999999999998e-303 < (*.f64 y (log.f64 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 90.5%

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

Alternative 3: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+157}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+119}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+157)
   (exp x)
   (if (<= x 4e+119)
     (exp (- (* y (log y)) z))
     (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+157) {
		tmp = exp(x);
	} else if (x <= 4e+119) {
		tmp = exp(((y * log(y)) - z));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (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 (x <= (-2.5d+157)) then
        tmp = exp(x)
    else if (x <= 4d+119) then
        tmp = exp(((y * log(y)) - z))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+157) {
		tmp = Math.exp(x);
	} else if (x <= 4e+119) {
		tmp = Math.exp(((y * Math.log(y)) - z));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e+157:
		tmp = math.exp(x)
	elif x <= 4e+119:
		tmp = math.exp(((y * math.log(y)) - z))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+157)
		tmp = exp(x);
	elseif (x <= 4e+119)
		tmp = exp(Float64(Float64(y * log(y)) - z));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e+157)
		tmp = exp(x);
	elseif (x <= 4e+119)
		tmp = exp(((y * log(y)) - z));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+157], N[Exp[x], $MachinePrecision], If[LessEqual[x, 4e+119], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999988e157

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.6%

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

   if -2.49999999999999988e157 < x < 3.99999999999999978e119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.0%

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

   if 3.99999999999999978e119 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.3%

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

   4. Taylor expanded in x around 0 91.3%

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

   5. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

   7. Simplified 91.3%

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

Alternative 4: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+130} \lor \neg \left(x \leq 1.7 \cdot 10^{+99}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+130) (not (<= x 1.7e+99))) (exp x) (/ (pow y y) (exp z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+130) || !(x <= 1.7e+99)) {
		tmp = exp(x);
	} else {
		tmp = pow(y, y) / 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 <= (-9.5d+130)) .or. (.not. (x <= 1.7d+99))) then
        tmp = exp(x)
    else
        tmp = (y ** y) / exp(z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+130) || !(x <= 1.7e+99)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y) / Math.exp(z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+130) or not (x <= 1.7e+99):
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y) / math.exp(z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+130) || !(x <= 1.7e+99))
		tmp = exp(x);
	else
		tmp = Float64((y ^ y) / exp(z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e+130) || ~((x <= 1.7e+99)))
		tmp = exp(x);
	else
		tmp = (y ^ y) / exp(z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+130], N[Not[LessEqual[x, 1.7e+99]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] / N[Exp[z], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000009e130 or 1.69999999999999992e99 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.1%

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

   if -9.5000000000000009e130 < x < 1.69999999999999992e99

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. exp-diff 84.9%

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

      2. *-commutative 84.9%

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

      3. exp-to-pow 84.9%

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

   5. Simplified 84.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+130} \lor \neg \left(x \leq 1.7 \cdot 10^{+99}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-7} \lor \neg \left(z \leq 6 \cdot 10^{+111}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e-7) (not (<= z 6e+111)))
   (exp (- z))
   (* (pow y y) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-7) || !(z <= 6e+111)) {
		tmp = exp(-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 <= (-5.8d-7)) .or. (.not. (z <= 6d+111))) then
        tmp = exp(-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 <= -5.8e-7) || !(z <= 6e+111)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y) * Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e-7) or not (z <= 6e+111):
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y) * math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e-7) || !(z <= 6e+111))
		tmp = exp(Float64(-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 <= -5.8e-7) || ~((z <= 6e+111)))
		tmp = exp(-z);
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e-7], N[Not[LessEqual[z, 6e+111]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999995e-7 or 6e111 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. neg-mul-1 83.2%

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

   5. Simplified 83.2%

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

   if -5.7999999999999995e-7 < z < 6e111

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. exp-sum 80.8%

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

      3. *-commutative 80.8%

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

      4. exp-to-pow 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-7} \lor \neg \left(z \leq 6 \cdot 10^{+111}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+83} \lor \neg \left(x \leq 90\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e+83) (not (<= x 90.0))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e+83) || !(x <= 90.0)) {
		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 <= (-1.3d+83)) .or. (.not. (x <= 90.0d0))) 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 <= -1.3e+83) || !(x <= 90.0)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e+83) or not (x <= 90.0):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e+83) || !(x <= 90.0))
		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 <= -1.3e+83) || ~((x <= 90.0)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e+83], N[Not[LessEqual[x, 90.0]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e83 or 90 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.6%

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

   if -1.3000000000000001e83 < x < 90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. neg-mul-1 66.7%

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

   5. Simplified 66.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+83} \lor \neg \left(x \leq 90\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-139}:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.25e-139) (exp (- z)) (if (<= y 3.5e-13) (exp x) (pow y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-139) {
		tmp = exp(-z);
	} else if (y <= 3.5e-13) {
		tmp = exp(x);
	} 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 <= 1.25d-139) then
        tmp = exp(-z)
    else if (y <= 3.5d-13) then
        tmp = exp(x)
    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 <= 1.25e-139) {
		tmp = Math.exp(-z);
	} else if (y <= 3.5e-13) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.25e-139:
		tmp = math.exp(-z)
	elif y <= 3.5e-13:
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e-139)
		tmp = exp(Float64(-z));
	elseif (y <= 3.5e-13)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.25e-139)
		tmp = exp(-z);
	elseif (y <= 3.5e-13)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.25e-139], N[Exp[(-z)], $MachinePrecision], If[LessEqual[y, 3.5e-13], N[Exp[x], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.25000000000000008e-139

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

   if 1.25000000000000008e-139 < y < 3.5000000000000002e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.5%

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

   if 3.5000000000000002e-13 < 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 90.6%

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

   4. Taylor expanded in z around 0 78.8%

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

Alternative 8: 62.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+105}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.55e+105)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+105) {
		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 <= (-2.55d+105)) 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 <= -2.55e+105) {
		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 <= -2.55e+105:
		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 <= -2.55e+105)
		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 <= -2.55e+105)
		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, -2.55e+105], 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 < -2.54999999999999996e105

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. neg-mul-1 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in z around 0 87.2%

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

   7. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

   9. Simplified 87.2%

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

   if -2.54999999999999996e105 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+105}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+85}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8e+80)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 3.3e+85)
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (+ 1.0 (* z (+ 1.0 (* z (+ 0.5 (* z 0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 3.3e+85) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 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 <= (-6.8d+80)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 3.3d+85) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = 1.0d0 + (z * (1.0d0 + (z * (0.5d0 + (z * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 3.3e+85) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8e+80:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 3.3e+85:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8e+80)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 3.3e+85)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(1.0 + Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.8e+80)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 3.3e+85)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = 1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8e+80], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+85], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999984e80

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. neg-mul-1 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around 0 80.7%

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

   7. Taylor expanded in z around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -6.79999999999999984e80 < z < 3.2999999999999999e85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.7%

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

   4. Taylor expanded in x around 0 39.0%

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

   if 3.2999999999999999e85 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 25.3%

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

      3. sqr-neg 25.3%

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

      4. sqrt-unprod 25.3%

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

      5. add-sqr-sqrt 25.3%

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

      6. expm1-log1p-u 25.3%

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

      7. expm1-undefine 25.3%

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

   7. Applied egg-rr 25.3%

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

      1. log1p-undefine 25.3%

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

      2. rem-exp-log 25.3%

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

      3. associate-+r- 25.3%

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

      4. expm1-undefine 25.3%

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

      5. rem-exp-log 25.3%

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

      6. log1p-define 25.3%

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

      7. log1p-expm1 25.3%

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

   9. Simplified 25.3%

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

   10. Taylor expanded in z around 0 22.1%

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

       1. *-commutative 22.1%

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

   12. Simplified 22.1%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+85}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6e+80)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 8.5e+163)
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (+ 1.0 (* z (* z 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 8.5e+163) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (z * 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 <= (-6.6d+80)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 8.5d+163) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = 1.0d0 + (z * (z * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 8.5e+163) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = 1.0 + (z * (z * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6e+80:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 8.5e+163:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = 1.0 + (z * (z * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6e+80)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 8.5e+163)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.6e+80)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 8.5e+163)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = 1.0 + (z * (z * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6e+80], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+163], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999982e80

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. neg-mul-1 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around 0 80.7%

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

   7. Taylor expanded in z around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -6.59999999999999982e80 < z < 8.5000000000000003e163

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.1%

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

   4. Taylor expanded in x around 0 36.9%

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

   if 8.5000000000000003e163 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. neg-mul-1 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around 0 18.4%

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

   7. Taylor expanded in z around inf 18.4%

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

      1. *-commutative 18.4%

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

   9. Simplified 18.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.3e+80)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (<= z 7.5e+163)
     (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))
     (+ 1.0 (* z (* z 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 7.5e+163) {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	} else {
		tmp = 1.0 + (z * (z * 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 <= (-4.3d+80)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if (z <= 7.5d+163) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    else
        tmp = 1.0d0 + (z * (z * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+80) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if (z <= 7.5e+163) {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	} else {
		tmp = 1.0 + (z * (z * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.3e+80:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif z <= 7.5e+163:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	else:
		tmp = 1.0 + (z * (z * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.3e+80)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif (z <= 7.5e+163)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	else
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.3e+80)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif (z <= 7.5e+163)
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	else
		tmp = 1.0 + (z * (z * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.3e+80], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+163], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000004e80

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. neg-mul-1 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around 0 80.7%

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

   7. Taylor expanded in z around inf 80.7%

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

      1. *-commutative 80.7%

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

   9. Simplified 80.7%

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

   if -4.30000000000000004e80 < z < 7.50000000000000001e163

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.1%

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

   4. Taylor expanded in x around 0 36.9%

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

   5. Taylor expanded in x around inf 36.8%

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

      1. *-commutative 36.8%

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

   7. Simplified 36.8%

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

   if 7.50000000000000001e163 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. neg-mul-1 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around 0 18.4%

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

   7. Taylor expanded in z around inf 18.4%

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

      1. *-commutative 18.4%

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

   9. Simplified 18.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+80}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.2% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.45e+52)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e+52) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (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 (x <= 1.45d+52) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e+52) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.45e+52:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.45e+52)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.45e+52)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.45e+52], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.45e52

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 57.8%

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

      1. neg-mul-1 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in z around 0 30.8%

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

   if 1.45e52 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

   4. Taylor expanded in x around 0 71.2%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. *-commutative 71.2%

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

   7. Simplified 71.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.6e+134)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.6e+134) {
		tmp = 1.0 + (z * ((z * 0.5) + -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 (x <= 1.6d+134) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-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 (x <= 1.6e+134) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.6e+134:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.6e+134)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -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 (x <= 1.6e+134)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.6e+134], N[(1.0 + N[(z * N[(N[(z * 0.5), $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 x < 1.6e134

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.1%

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

      1. neg-mul-1 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 28.7%

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

   if 1.6e134 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.2%

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

   4. Taylor expanded in x around 0 85.6%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.6% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.6e+134) (+ 1.0 (* z (* z 0.5))) (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.6e+134) {
		tmp = 1.0 + (z * (z * 0.5));
	} 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 (x <= 1.6d+134) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    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 (x <= 1.6e+134) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.6e+134:
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.6e+134)
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	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 (x <= 1.6e+134)
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.6e+134], N[(1.0 + N[(z * N[(z * 0.5), $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 x < 1.6e134

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.1%

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

      1. neg-mul-1 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0 28.7%

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

   7. Taylor expanded in z around inf 28.7%

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

      1. *-commutative 28.7%

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

   9. Simplified 28.7%

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

   if 1.6e134 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.2%

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

   4. Taylor expanded in x around 0 85.6%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.2% accurate, 29.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + (z * (z * 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 + (z * (z * 0.5d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(z * N[(z * 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 z around inf 54.4%

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

   1. neg-mul-1 54.4%

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

5. Simplified 54.4%

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

6. Taylor expanded in z around 0 27.7%

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

7. Taylor expanded in z around inf 27.7%

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

   1. *-commutative 27.7%

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

9. Simplified 27.7%

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

Alternative 16: 14.1% 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 x around inf 49.9%

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

4. Taylor expanded in x around 0 13.0%

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

5. Final simplification 13.0%

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

Alternative 17: 14.0% 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 x around inf 49.9%

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

4. Taylor expanded in x around 0 12.6%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Developer Target 1: 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 2024132 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (exp (+ (- x z) (* (log y) y))))

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