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

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 18

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = -8.677254101075743e+252
  2. y = 6.1374035390252006e-207
  3. z = -1.4170444478132154e+162

• 57.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

public static double code(double x, double y, double z) {
	return Math.exp(((x + (y * Math.log(y))) - z));
}

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

public static double code(double x, double y, double z) {
	return Math.exp(((x + (y * Math.log(y))) - z));
}

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))

C

double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function

Java

public static double code(double x, double y, double z) {
	return Math.exp(((x + (y * Math.log(y))) - z));
}

Python

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))

Julia

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 94.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 -2e-300) (* (pow y y) (exp (- x z))) (exp (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= -2e-300) {
		tmp = pow(y, y) * exp((x - z));
	} else {
		tmp = exp((t_0 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * log(y)
    if (t_0 <= (-2d-300)) then
        tmp = (y ** y) * exp((x - z))
    else
        tmp = exp((t_0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (t_0 <= -2e-300) {
		tmp = Math.pow(y, y) * Math.exp((x - z));
	} else {
		tmp = Math.exp((t_0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= -2e-300:
		tmp = math.pow(y, y) * math.exp((x - z))
	else:
		tmp = math.exp((t_0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= -2e-300)
		tmp = Float64((y ^ y) * exp(Float64(x - z)));
	else
		tmp = exp(Float64(t_0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= -2e-300)
		tmp = (y ^ y) * exp((x - z));
	else
		tmp = exp((t_0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-300], N[(N[Power[y, y], $MachinePrecision] * N[Exp[N[(x - z), $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)) < -2.00000000000000005e-300

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 100.0%

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

      4. *-commutative 100.0%

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

      5. exp-to-pow 100.0%

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

   3. Simplified 100.0%

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

   if -2.00000000000000005e-300 < (*.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 94.1%

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

Alternative 3: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -660:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-77}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -660.0)
   (exp (- z))
   (if (<= z 2.3e-77) (* (pow y y) (exp x)) (exp (- (* y (log y)) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -660.0) {
		tmp = exp(-z);
	} else if (z <= 2.3e-77) {
		tmp = pow(y, y) * exp(x);
	} 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 (z <= (-660.0d0)) then
        tmp = exp(-z)
    else if (z <= 2.3d-77) then
        tmp = (y ** y) * exp(x)
    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 (z <= -660.0) {
		tmp = Math.exp(-z);
	} else if (z <= 2.3e-77) {
		tmp = Math.pow(y, y) * Math.exp(x);
	} else {
		tmp = Math.exp(((y * Math.log(y)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -660.0:
		tmp = math.exp(-z)
	elif z <= 2.3e-77:
		tmp = math.pow(y, y) * math.exp(x)
	else:
		tmp = math.exp(((y * math.log(y)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -660.0)
		tmp = exp(Float64(-z));
	elseif (z <= 2.3e-77)
		tmp = Float64((y ^ y) * exp(x));
	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 (z <= -660.0)
		tmp = exp(-z);
	elseif (z <= 2.3e-77)
		tmp = (y ^ y) * exp(x);
	else
		tmp = exp(((y * log(y)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -660.0], N[Exp[(-z)], $MachinePrecision], If[LessEqual[z, 2.3e-77], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision], N[Exp[N[(N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -660

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.8%

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

      1. neg-mul-1 93.8%

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

   5. Simplified 93.8%

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

   if -660 < z < 2.29999999999999999e-77

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 94.1%

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

      4. *-commutative 94.1%

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

      5. exp-to-pow 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 93.9%

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

   if 2.29999999999999999e-77 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.8%

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

Alternative 4: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -720 \lor \neg \left(z \leq 6 \cdot 10^{+95}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -720.0) (not (<= z 6e+95))) (exp (- z)) (* (pow y y) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -720.0) || !(z <= 6e+95)) {
		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 <= (-720.0d0)) .or. (.not. (z <= 6d+95))) 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 <= -720.0) || !(z <= 6e+95)) {
		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 <= -720.0) or not (z <= 6e+95):
		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 <= -720.0) || !(z <= 6e+95))
		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 <= -720.0) || ~((z <= 6e+95)))
		tmp = exp(-z);
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -720.0], N[Not[LessEqual[z, 6e+95]], $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 < -720 or 5.99999999999999982e95 < 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 91.3%

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

      1. neg-mul-1 91.3%

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

   5. Simplified 91.3%

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

   if -720 < z < 5.99999999999999982e95

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 89.6%

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

      4. *-commutative 89.6%

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

      5. exp-to-pow 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in z around 0 89.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -720 \lor \neg \left(z \leq 6 \cdot 10^{+95}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -620 \lor \neg \left(z \leq 1.32 \cdot 10^{-11}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -620.0) (not (<= z 1.32e-11))) (exp (- z)) (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -620.0) || !(z <= 1.32e-11)) {
		tmp = exp(-z);
	} else {
		tmp = exp(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-620.0d0)) .or. (.not. (z <= 1.32d-11))) then
        tmp = exp(-z)
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -620.0) || !(z <= 1.32e-11)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -620.0) or not (z <= 1.32e-11):
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -620.0) || !(z <= 1.32e-11))
		tmp = exp(Float64(-z));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -620.0) || ~((z <= 1.32e-11)))
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -620.0], N[Not[LessEqual[z, 1.32e-11]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -620 or 1.32e-11 < 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 85.4%

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

      1. neg-mul-1 85.4%

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

   5. Simplified 85.4%

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

   if -620 < z < 1.32e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620 \lor \neg \left(z \leq 1.32 \cdot 10^{-11}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-246}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+29}:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.5e-246) (exp x) (if (<= y 1.4e+29) (exp (- z)) (pow y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-246) {
		tmp = exp(x);
	} else if (y <= 1.4e+29) {
		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 <= 8.5d-246) then
        tmp = exp(x)
    else if (y <= 1.4d+29) 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 <= 8.5e-246) {
		tmp = Math.exp(x);
	} else if (y <= 1.4e+29) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.5e-246:
		tmp = math.exp(x)
	elif y <= 1.4e+29:
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.5e-246)
		tmp = exp(x);
	elseif (y <= 1.4e+29)
		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 <= 8.5e-246)
		tmp = exp(x);
	elseif (y <= 1.4e+29)
		tmp = exp(-z);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.5e-246], N[Exp[x], $MachinePrecision], If[LessEqual[y, 1.4e+29], N[Exp[(-z)], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.4999999999999998e-246

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.6%

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

   if 8.4999999999999998e-246 < y < 1.4e29

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. neg-mul-1 74.9%

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

   5. Simplified 74.9%

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

   if 1.4e29 < 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 94.5%

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

   4. Taylor expanded in z around 0 84.4%

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

Alternative 7: 62.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+95}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e+95)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e+95) {
		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 <= (-8d+95)) 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 <= -8e+95) {
		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 <= -8e+95:
		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 <= -8e+95)
		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 <= -8e+95)
		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, -8e+95], 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 < -8.00000000000000016e95

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.4%

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

      1. neg-mul-1 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 91.4%

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

   7. Taylor expanded in z around inf 91.4%

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

      1. *-commutative 91.4%

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

   9. Simplified 91.4%

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

   if -8.00000000000000016e95 < 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 60.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+95}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.7% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.55e+82)
   (+ 1.0 (* z (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.55d+82) then
        tmp = 1.0d0 + (z * ((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.55e+82:
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.55e+82)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(0.5 + Float64(z * -0.16666666666666666))) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.55e+82)
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.55e+82], N[(1.0 + N[(z * N[(N[(z * N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55000000000000016e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.8%

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

      1. neg-mul-1 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 35.9%

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

   if 1.55000000000000016e82 < 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 88.2%

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

   4. Taylor expanded in x around 0 86.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.7% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.55e+82)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.55d+82) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.55e+82:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.55e+82)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.55e+82)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.55e+82], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55000000000000016e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.8%

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

      1. neg-mul-1 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 35.9%

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

   7. Taylor expanded in z around inf 35.8%

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

      1. *-commutative 35.8%

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

   9. Simplified 35.8%

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

   if 1.55000000000000016e82 < 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 88.2%

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

   4. Taylor expanded in x around 0 86.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.6% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+77)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+77) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.4d+77)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+77) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e+77:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+77)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.4e+77)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+77], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e77

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.8%

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

      1. neg-mul-1 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in z around 0 86.1%

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

   7. Taylor expanded in z around inf 86.1%

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

      1. *-commutative 86.1%

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

   9. Simplified 86.1%

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

   if -1.4e77 < 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 60.3%

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

   4. Taylor expanded in x around 0 35.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.5% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.46 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.46e+82) (+ 1.0 (* z (+ (* z 0.5) -1.0))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.46e+82) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.46d+82) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.46e+82) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.46e+82:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.46e+82)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.46e+82)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.46e+82], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4599999999999999e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.8%

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

      1. neg-mul-1 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 34.2%

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

   if 1.4599999999999999e82 < 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 88.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   5. Taylor expanded in x around inf 75.1%

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

      1. *-commutative 75.1%

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

   7. Simplified 75.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.46 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.6% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+177}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e+177) (+ 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 (z <= -2.3e+177) {
		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 (z <= (-2.3d+177)) 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 (z <= -2.3e+177) {
		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 z <= -2.3e+177:
		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 (z <= -2.3e+177)
		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 (z <= -2.3e+177)
		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[z, -2.3e+177], 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 z < -2.2999999999999999e177

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -2.2999999999999999e177 < 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 59.7%

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

   4. Taylor expanded in x around 0 35.3%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+177}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.3% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.55e+82) (+ 1.0 (* z (* z 0.5))) (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.55d+82) then
        tmp = 1.0d0 + (z * (z * 0.5d0))
    else
        tmp = 1.0d0 + (x * (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.55e+82) {
		tmp = 1.0 + (z * (z * 0.5));
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.55e+82:
		tmp = 1.0 + (z * (z * 0.5))
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.55e+82)
		tmp = Float64(1.0 + Float64(z * Float64(z * 0.5)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.55e+82)
		tmp = 1.0 + (z * (z * 0.5));
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.55e+82], N[(1.0 + N[(z * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55000000000000016e82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.8%

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

      1. neg-mul-1 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 34.2%

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

   7. Taylor expanded in z around inf 34.1%

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

      1. *-commutative 34.1%

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

   9. Simplified 34.1%

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

   if 1.55000000000000016e82 < 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 88.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   5. Taylor expanded in x around inf 75.1%

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

      1. *-commutative 75.1%

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

   7. Simplified 75.1%

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

Alternative 14: 29.1% 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 57.5%

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

4. Taylor expanded in x around 0 35.3%

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

5. Taylor expanded in x around inf 35.2%

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

   1. *-commutative 35.2%

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

7. Simplified 35.2%

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

Alternative 15: 15.5% accurate, 29.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z * N[(N[(1.0 / z), $MachinePrecision] + -1.0), $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 57.9%

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

   1. neg-mul-1 57.9%

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

5. Simplified 57.9%

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

6. Taylor expanded in z around 0 19.3%

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

   1. neg-mul-1 19.3%

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

   2. unsub-neg 19.3%

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

8. Simplified 19.3%

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

9. Taylor expanded in z around inf 19.6%

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

10. Final simplification 19.6%

    \[\leadsto z \cdot \left(\frac{1}{z} + -1\right) \]
11. Add Preprocessing

Alternative 16: 15.5% 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 57.9%

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

   1. neg-mul-1 57.9%

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

5. Simplified 57.9%

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

6. Taylor expanded in z around 0 19.3%

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

   1. neg-mul-1 19.3%

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

   2. unsub-neg 19.3%

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

8. Simplified 19.3%

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

Alternative 17: 15.6% 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 57.5%

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

4. Taylor expanded in x around 0 19.2%

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

5. Final simplification 19.2%

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

Alternative 18: 15.3% 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 57.5%

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

4. Taylor expanded in x around 0 19.0%

   \[\leadsto \color{blue}{1} \]
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 2024172 
(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)))