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

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 17

Speedup: 1.0×

• 59.0% 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: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+58} \lor \neg \left(x \leq 7.2 \cdot 10^{+56}\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.35e+58) (not (<= x 7.2e+56)))
   (exp (- x z))
   (exp (- (* y (log y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.35e+58) || !(x <= 7.2e+56)) {
		tmp = exp((x - z));
	} else {
		tmp = exp(((y * log(y)) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.35d+58)) .or. (.not. (x <= 7.2d+56))) then
        tmp = exp((x - z))
    else
        tmp = exp(((y * log(y)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.35e+58) || !(x <= 7.2e+56)) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp(((y * Math.log(y)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.35e+58) or not (x <= 7.2e+56):
		tmp = math.exp((x - z))
	else:
		tmp = math.exp(((y * math.log(y)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.35e+58) || !(x <= 7.2e+56))
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(Float64(y * log(y)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.35e+58) || ~((x <= 7.2e+56)))
		tmp = exp((x - z));
	else
		tmp = exp(((y * log(y)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.35e+58], N[Not[LessEqual[x, 7.2e+56]], $MachinePrecision]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999986e58 or 7.19999999999999996e56 < 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 94.5%

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

   if -2.34999999999999986e58 < x < 7.19999999999999996e56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+58} \lor \neg \left(x \leq 7.2 \cdot 10^{+56}\right):\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29000000000 \lor \neg \left(x \leq 500\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -29000000000.0) (not (<= x 500.0))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -29000000000.0) || !(x <= 500.0)) {
		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 <= (-29000000000.0d0)) .or. (.not. (x <= 500.0d0))) 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 <= -29000000000.0) || !(x <= 500.0)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -29000000000.0) or not (x <= 500.0):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -29000000000.0) || !(x <= 500.0))
		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 <= -29000000000.0) || ~((x <= 500.0)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -29000000000.0], N[Not[LessEqual[x, 500.0]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e10 or 500 < 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 92.2%

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

   4. Taylor expanded in z around 0 87.9%

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

   if -2.9e10 < x < 500

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.6%

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

      1. neg-mul-1 66.6%

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

   5. Simplified 66.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000000000 \lor \neg \left(x \leq 500\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 850:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 850.0) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 850.0) {
		tmp = exp((x - z));
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 850.0d0) then
        tmp = exp((x - z))
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 850.0) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 850.0:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 850.0)
		tmp = exp(Float64(x - z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 850.0)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 850.0], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 850

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.3%

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

   if 850 < 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 89.1%

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

   4. Taylor expanded in z around 0 82.2%

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

Alternative 5: 73.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.4) (exp (- z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.4) {
		tmp = exp(-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 <= 3.4d0) then
        tmp = exp(-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 <= 3.4) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.4:
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.4)
		tmp = exp(Float64(-z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.4)
		tmp = exp(-z);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.4], N[Exp[(-z)], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.39999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. neg-mul-1 74.8%

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

   5. Simplified 74.8%

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

   if 3.39999999999999991 < 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 88.5%

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

   4. Taylor expanded in z around 0 81.7%

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

Alternative 6: 63.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+100}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(1 - z\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+100) (+ 1.0 (* z (+ (* z (- 1.0 z)) -1.0))) (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+100) {
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -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 <= (-1.8d+100)) then
        tmp = 1.0d0 + (z * ((z * (1.0d0 - z)) + (-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 <= -1.8e+100) {
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0));
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+100:
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0))
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+100)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(1.0 - z)) + -1.0)));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+100)
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0));
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+100], N[(1.0 + N[(z * N[(N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e100

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.4%

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

      1. exp-diff 94.4%

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

      2. *-commutative 94.4%

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

      3. exp-to-pow 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in z around 0 0.8%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 0.8%

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

   8. Simplified 0.8%

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

   9. Taylor expanded in y around 0 1.4%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 1.4%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 1.4%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around 0 92.8%

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

   if -1.8e100 < 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 72.3%

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

   4. Taylor expanded in z around 0 56.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+100}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(1 - z\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.1% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(1 - z\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-306} \lor \neg \left(z \leq 9.5 \cdot 10^{-144}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.16e+50)
   (+ 1.0 (* z (+ (* z (- 1.0 z)) -1.0)))
   (if (or (<= z 8.2e-306) (not (<= z 9.5e-144)))
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (/ (+ 1.0 (/ (+ (/ 1.0 z) -1.0) z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0));
	} else if ((z <= 8.2e-306) || !(z <= 9.5e-144)) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / 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 <= (-2.16d+50)) then
        tmp = 1.0d0 + (z * ((z * (1.0d0 - z)) + (-1.0d0)))
    else if ((z <= 8.2d-306) .or. (.not. (z <= 9.5d-144))) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = (1.0d0 + (((1.0d0 / z) + (-1.0d0)) / z)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0));
	} else if ((z <= 8.2e-306) || !(z <= 9.5e-144)) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.16e+50:
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0))
	elif (z <= 8.2e-306) or not (z <= 9.5e-144):
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.16e+50)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(1.0 - z)) + -1.0)));
	elseif ((z <= 8.2e-306) || !(z <= 9.5e-144))
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(Float64(1.0 / z) + -1.0) / z)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.16e+50)
		tmp = 1.0 + (z * ((z * (1.0 - z)) + -1.0));
	elseif ((z <= 8.2e-306) || ~((z <= 9.5e-144)))
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.16e+50], N[(1.0 + N[(z * N[(N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8.2e-306], N[Not[LessEqual[z, 9.5e-144]], $MachinePrecision]], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.16000000000000008e50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.5%

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

      1. exp-diff 91.5%

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

      2. *-commutative 91.5%

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

      3. exp-to-pow 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 0.8%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 0.8%

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

   8. Simplified 0.8%

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

   9. Taylor expanded in y around 0 1.5%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 1.5%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 1.5%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around 0 85.1%

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

   if -2.16000000000000008e50 < z < 8.19999999999999969e-306 or 9.49999999999999953e-144 < 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 72.3%

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

   4. Taylor expanded in z around 0 54.8%

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

   5. Taylor expanded in x around 0 32.2%

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

   if 8.19999999999999969e-306 < z < 9.49999999999999953e-144

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.7%

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

      1. exp-diff 70.7%

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

      2. *-commutative 70.7%

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

      3. exp-to-pow 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around 0 70.7%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around 0 12.7%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 12.7%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 12.7%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around inf 73.9%

       \[\leadsto \color{blue}{\frac{\left(1 + \frac{1}{{z}^{2}}\right) - \frac{1}{z}}{z}} \]
   13. Step-by-step derivation

       1. associate--l+ 73.9%

          \[\leadsto \frac{\color{blue}{1 + \left(\frac{1}{{z}^{2}} - \frac{1}{z}\right)}}{z} \]

       2. unpow2 73.9%

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

       3. associate-/r* 73.9%

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

       4. div-sub 73.9%

          \[\leadsto \frac{1 + \color{blue}{\frac{\frac{1}{z} - 1}{z}}}{z} \]

       5. sub-neg 73.9%

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

       6. metadata-eval 73.9%

          \[\leadsto \frac{1 + \frac{\frac{1}{z} + \color{blue}{-1}}{z}}{z} \]

   14. Simplified 73.9%

       \[\leadsto \color{blue}{\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(1 - z\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-306} \lor \neg \left(z \leq 9.5 \cdot 10^{-144}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.0% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-305} \lor \neg \left(z \leq 6 \cdot 10^{-150}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.16e+50)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (or (<= z 8.4e-305) (not (<= z 6e-150)))
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (/ (+ 1.0 (/ (+ (/ 1.0 z) -1.0) z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 8.4e-305) || !(z <= 6e-150)) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / 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 <= (-2.16d+50)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if ((z <= 8.4d-305) .or. (.not. (z <= 6d-150))) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = (1.0d0 + (((1.0d0 / z) + (-1.0d0)) / z)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 8.4e-305) || !(z <= 6e-150)) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.16e+50:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif (z <= 8.4e-305) or not (z <= 6e-150):
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.16e+50)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif ((z <= 8.4e-305) || !(z <= 6e-150))
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(Float64(1.0 / z) + -1.0) / z)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.16e+50)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif ((z <= 8.4e-305) || ~((z <= 6e-150)))
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.16e+50], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8.4e-305], N[Not[LessEqual[z, 6e-150]], $MachinePrecision]], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.16000000000000008e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.5%

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

      1. neg-mul-1 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 85.1%

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

   7. Taylor expanded in z around inf 85.1%

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

      1. *-commutative 85.1%

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

   9. Simplified 85.1%

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

   if -2.16000000000000008e50 < z < 8.3999999999999999e-305 or 6.0000000000000003e-150 < 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 72.3%

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

   4. Taylor expanded in z around 0 54.8%

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

   5. Taylor expanded in x around 0 32.2%

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

   if 8.3999999999999999e-305 < z < 6.0000000000000003e-150

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.7%

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

      1. exp-diff 70.7%

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

      2. *-commutative 70.7%

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

      3. exp-to-pow 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around 0 70.7%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around 0 12.7%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 12.7%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 12.7%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around inf 73.9%

       \[\leadsto \color{blue}{\frac{\left(1 + \frac{1}{{z}^{2}}\right) - \frac{1}{z}}{z}} \]
   13. Step-by-step derivation

       1. associate--l+ 73.9%

          \[\leadsto \frac{\color{blue}{1 + \left(\frac{1}{{z}^{2}} - \frac{1}{z}\right)}}{z} \]

       2. unpow2 73.9%

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

       3. associate-/r* 73.9%

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

       4. div-sub 73.9%

          \[\leadsto \frac{1 + \color{blue}{\frac{\frac{1}{z} - 1}{z}}}{z} \]

       5. sub-neg 73.9%

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

       6. metadata-eval 73.9%

          \[\leadsto \frac{1 + \frac{\frac{1}{z} + \color{blue}{-1}}{z}}{z} \]

   14. Simplified 73.9%

       \[\leadsto \color{blue}{\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-305} \lor \neg \left(z \leq 6 \cdot 10^{-150}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.3% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-305} \lor \neg \left(z \leq 1.2 \cdot 10^{-147}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.16e+50)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (if (or (<= z 8.2e-305) (not (<= z 1.2e-147)))
     (+ 1.0 (* x (+ 1.0 (* x 0.5))))
     (/ (+ 1.0 (/ (+ (/ 1.0 z) -1.0) z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 8.2e-305) || !(z <= 1.2e-147)) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / 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 <= (-2.16d+50)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else if ((z <= 8.2d-305) .or. (.not. (z <= 1.2d-147))) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = (1.0d0 + (((1.0d0 / z) + (-1.0d0)) / z)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.16e+50) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else if ((z <= 8.2e-305) || !(z <= 1.2e-147)) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.16e+50:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	elif (z <= 8.2e-305) or not (z <= 1.2e-147):
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.16e+50)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	elseif ((z <= 8.2e-305) || !(z <= 1.2e-147))
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(Float64(1.0 / z) + -1.0) / z)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.16e+50)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	elseif ((z <= 8.2e-305) || ~((z <= 1.2e-147)))
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = (1.0 + (((1.0 / z) + -1.0) / z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.16e+50], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8.2e-305], N[Not[LessEqual[z, 1.2e-147]], $MachinePrecision]], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.16000000000000008e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.5%

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

      1. neg-mul-1 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 85.1%

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

   7. Taylor expanded in z around inf 85.1%

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

      1. *-commutative 85.1%

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

   9. Simplified 85.1%

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

   if -2.16000000000000008e50 < z < 8.2000000000000005e-305 or 1.19999999999999999e-147 < 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 72.3%

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

   4. Taylor expanded in z around 0 54.8%

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

   5. Taylor expanded in x around 0 29.6%

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

   if 8.2000000000000005e-305 < z < 1.19999999999999999e-147

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.7%

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

      1. exp-diff 70.7%

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

      2. *-commutative 70.7%

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

      3. exp-to-pow 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around 0 70.7%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around 0 12.7%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 12.7%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 12.7%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around inf 73.9%

       \[\leadsto \color{blue}{\frac{\left(1 + \frac{1}{{z}^{2}}\right) - \frac{1}{z}}{z}} \]
   13. Step-by-step derivation

       1. associate--l+ 73.9%

          \[\leadsto \frac{\color{blue}{1 + \left(\frac{1}{{z}^{2}} - \frac{1}{z}\right)}}{z} \]

       2. unpow2 73.9%

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

       3. associate-/r* 73.9%

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

       4. div-sub 73.9%

          \[\leadsto \frac{1 + \color{blue}{\frac{\frac{1}{z} - 1}{z}}}{z} \]

       5. sub-neg 73.9%

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

       6. metadata-eval 73.9%

          \[\leadsto \frac{1 + \frac{\frac{1}{z} + \color{blue}{-1}}{z}}{z} \]

   14. Simplified 73.9%

       \[\leadsto \color{blue}{\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-305} \lor \neg \left(z \leq 1.2 \cdot 10^{-147}\right):\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \frac{\frac{1}{z} + -1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.8% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.16e+50)
   (+ 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 <= -2.16e+50) {
		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 <= (-2.16d+50)) 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 <= -2.16e+50) {
		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 <= -2.16e+50:
		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 <= -2.16e+50)
		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 <= -2.16e+50)
		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, -2.16e+50], 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 < -2.16000000000000008e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.5%

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

      1. neg-mul-1 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 85.1%

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

   7. Taylor expanded in z around inf 85.1%

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

      1. *-commutative 85.1%

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

   9. Simplified 85.1%

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

   if -2.16000000000000008e50 < 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 71.6%

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

   4. Taylor expanded in z around 0 56.8%

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

   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 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.16 \cdot 10^{+50}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.9% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e+128)
   (+ 1.0 (* z (+ z -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+128) {
		tmp = 1.0 + (z * (z + -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 <= (-3.2d+128)) then
        tmp = 1.0d0 + (z * (z + (-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 <= -3.2e+128) {
		tmp = 1.0 + (z * (z + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e+128:
		tmp = 1.0 + (z * (z + -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 <= -3.2e+128)
		tmp = Float64(1.0 + Float64(z * Float64(z + -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 <= -3.2e+128)
		tmp = 1.0 + (z * (z + -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, -3.2e+128], N[(1.0 + N[(z * N[(z + -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 < -3.19999999999999986e128

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.7%

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

      1. exp-diff 93.7%

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

      2. *-commutative 93.7%

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

      3. exp-to-pow 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in z around 0 0.8%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 0.8%

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

   8. Simplified 0.8%

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

   9. Taylor expanded in y around 0 1.5%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 1.5%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 1.5%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around 0 86.3%

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

   if -3.19999999999999986e128 < 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 73.1%

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

   4. Taylor expanded in z around 0 55.3%

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

   5. Taylor expanded in x around 0 28.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+128) (+ 1.0 (* z (+ z -1.0))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+128) {
		tmp = 1.0 + (z * (z + -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 (z <= (-1.1d+128)) then
        tmp = 1.0d0 + (z * (z + (-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 (z <= -1.1e+128) {
		tmp = 1.0 + (z * (z + -1.0));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+128:
		tmp = 1.0 + (z * (z + -1.0))
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+128)
		tmp = Float64(1.0 + Float64(z * Float64(z + -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 (z <= -1.1e+128)
		tmp = 1.0 + (z * (z + -1.0));
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+128], N[(1.0 + N[(z * N[(z + -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 z < -1.10000000000000008e128

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.7%

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

      1. exp-diff 93.7%

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

      2. *-commutative 93.7%

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

      3. exp-to-pow 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in z around 0 0.8%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{1 + z}} \]
   7. Step-by-step derivation

      1. +-commutative 0.8%

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

   8. Simplified 0.8%

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

   9. Taylor expanded in y around 0 1.5%

      \[\leadsto \color{blue}{\frac{1}{1 + z}} \]
   10. Step-by-step derivation

       1. +-commutative 1.5%

          \[\leadsto \frac{1}{\color{blue}{z + 1}} \]

   11. Simplified 1.5%

       \[\leadsto \color{blue}{\frac{1}{z + 1}} \]

   12. Taylor expanded in z around 0 86.3%

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

   if -1.10000000000000008e128 < 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 73.1%

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

   4. Taylor expanded in z around 0 55.3%

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

   5. Taylor expanded in x around 0 28.1%

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

   6. Taylor expanded in x around inf 28.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.8% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e+128) (+ 1.0 (* z (* z 0.5))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+128) {
		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 (z <= (-2.8d+128)) 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 (z <= -2.8e+128) {
		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 z <= -2.8e+128:
		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 (z <= -2.8e+128)
		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 (z <= -2.8e+128)
		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[z, -2.8e+128], 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 z < -2.79999999999999983e128

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.7%

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

      1. neg-mul-1 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in z around 0 86.2%

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

   7. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

   9. Simplified 86.2%

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

   if -2.79999999999999983e128 < 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 73.1%

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

   4. Taylor expanded in z around 0 55.3%

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

   5. Taylor expanded in x around 0 28.1%

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

   6. Taylor expanded in x around inf 28.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.6% 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 x around inf 78.0%

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

4. Taylor expanded in z around 0 51.8%

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

5. Taylor expanded in x around 0 25.1%

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

6. Taylor expanded in x around inf 25.1%

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

7. Final simplification 25.1%

   \[\leadsto 1 + x \cdot \left(x \cdot 0.5\right) \]
8. Add Preprocessing

Alternative 15: 14.7% accurate, 69.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 - 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 = 1.0d0 - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 - z), $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 52.6%

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

   1. neg-mul-1 52.6%

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

5. Simplified 52.6%

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

6. Taylor expanded in z around 0 14.5%

   \[\leadsto \color{blue}{1 + -1 \cdot z} \]
7. Step-by-step derivation

   1. neg-mul-1 14.5%

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

   2. unsub-neg 14.5%

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

8. Simplified 14.5%

   \[\leadsto \color{blue}{1 - z} \]
9. Add Preprocessing

Alternative 16: 14.7% 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 78.0%

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

4. Taylor expanded in z around 0 51.8%

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

5. Taylor expanded in x around 0 14.3%

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

6. Final simplification 14.3%

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

Alternative 17: 14.5% 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 52.6%

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

   1. neg-mul-1 52.6%

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

5. Simplified 52.6%

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

6. Taylor expanded in z around 0 14.0%

   \[\leadsto \color{blue}{1} \]
7. 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 2024116 
(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)))