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

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 15

Speedup: 1.0×

• 59.1% 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: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq 50:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 50.0) (* (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 <= 50.0) {
		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 <= 50.0d0) 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 <= 50.0) {
		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 <= 50.0:
		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 <= 50.0)
		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 <= 50.0)
		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, 50.0], 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)) < 50

   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 50 < (*.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 95.8%

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

Alternative 3: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0032:\\ \;\;\;\;e^{-z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0032)
   (exp (- z))
   (if (<= z 7.5e-7) (* (pow y y) (exp x)) (exp (- (* y (log y)) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0032) {
		tmp = exp(-z);
	} else if (z <= 7.5e-7) {
		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 <= (-0.0032d0)) then
        tmp = exp(-z)
    else if (z <= 7.5d-7) 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 <= -0.0032) {
		tmp = Math.exp(-z);
	} else if (z <= 7.5e-7) {
		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 <= -0.0032:
		tmp = math.exp(-z)
	elif z <= 7.5e-7:
		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 <= -0.0032)
		tmp = exp(Float64(-z));
	elseif (z <= 7.5e-7)
		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 <= -0.0032)
		tmp = exp(-z);
	elseif (z <= 7.5e-7)
		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, -0.0032], N[Exp[(-z)], $MachinePrecision], If[LessEqual[z, 7.5e-7], 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 < -0.00320000000000000015

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 92.1%

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

      1. neg-mul-1 92.1%

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

   5. Simplified 92.1%

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

   if -0.00320000000000000015 < z < 7.5000000000000002e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. exp-sum 93.0%

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

      3. *-commutative 93.0%

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

      4. exp-to-pow 93.0%

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

   5. Simplified 93.0%

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

   if 7.5000000000000002e-7 < 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 90.9%

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

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 3.15 \cdot 10^{+43}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0032) (not (<= z 3.15e+43)))
   (exp (- z))
   (* (pow y y) (exp x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0032) || !(z <= 3.15e+43)) {
		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 <= (-0.0032d0)) .or. (.not. (z <= 3.15d+43))) 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 <= -0.0032) || !(z <= 3.15e+43)) {
		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 <= -0.0032) or not (z <= 3.15e+43):
		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 <= -0.0032) || !(z <= 3.15e+43))
		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 <= -0.0032) || ~((z <= 3.15e+43)))
		tmp = exp(-z);
	else
		tmp = (y ^ y) * exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0032], N[Not[LessEqual[z, 3.15e+43]], $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 < -0.00320000000000000015 or 3.1499999999999999e43 < 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 84.5%

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

      1. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

   if -0.00320000000000000015 < z < 3.1499999999999999e43

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. exp-sum 91.3%

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

      3. *-commutative 91.3%

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

      4. exp-to-pow 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 3.15 \cdot 10^{+43}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 10^{+23}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0032) (not (<= z 1e+23))) (exp (- z)) (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0032) || !(z <= 1e+23)) {
		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 <= (-0.0032d0)) .or. (.not. (z <= 1d+23))) 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 <= -0.0032) || !(z <= 1e+23)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0032) or not (z <= 1e+23):
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0032) || !(z <= 1e+23))
		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 <= -0.0032) || ~((z <= 1e+23)))
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0032], N[Not[LessEqual[z, 1e+23]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00320000000000000015 or 9.9999999999999992e22 < 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 82.6%

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

      1. neg-mul-1 82.6%

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

   5. Simplified 82.6%

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

   if -0.00320000000000000015 < z < 9.9999999999999992e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 10^{+23}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.44:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 0.44) (exp x) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.44) {
		tmp = exp(x);
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.44d0) then
        tmp = exp(x)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.44) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.44:
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.44)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.44)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.44], N[Exp[x], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.440000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.8%

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

   if 0.440000000000000002 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.7%

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

   4. Taylor expanded in z around 0 85.2%

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

Alternative 7: 61.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e+102)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = exp(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.7d+102)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = exp(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+102) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e+102:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e+102)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = exp(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e+102)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e+102], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000023e102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. neg-mul-1 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in z around 0 88.6%

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

   7. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

   9. Simplified 88.6%

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

   if -3.70000000000000023e102 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+102}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.6% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.95e+39)
   (+ 1.0 (* z (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e+39) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.95d+39) then
        tmp = 1.0d0 + (z * ((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e+39) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.95e+39:
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.95e+39)
		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(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.95e+39)
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.95e+39], 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[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.95e39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 56.4%

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

      1. neg-mul-1 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around 0 31.7%

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

   if 1.95e39 < 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 92.1%

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

   4. Taylor expanded in x around 0 78.4%

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

   5. Taylor expanded in x around inf 78.4%

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

      1. *-commutative 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.1% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e+99)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+99) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.4d+99)) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+99) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.4e+99:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e+99)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(z * -0.16666666666666666)) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.4e+99)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.4e+99], N[(1.0 + N[(z * N[(N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e99

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.1%

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

      1. neg-mul-1 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in z around 0 85.2%

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

   7. Taylor expanded in z around inf 85.2%

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

      1. *-commutative 85.2%

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

   9. Simplified 85.2%

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

   if -2.4000000000000001e99 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.8%

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

   4. Taylor expanded in x around 0 34.1%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.6% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.95e+39)
   (+ 1.0 (* z (+ (* z (* z -0.16666666666666666)) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e+39) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.95d+39) then
        tmp = 1.0d0 + (z * ((z * (z * (-0.16666666666666666d0))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e+39) {
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.95e+39:
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.95e+39)
		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(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.95e+39)
		tmp = 1.0 + (z * ((z * (z * -0.16666666666666666)) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.95e+39], 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[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.95e39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 56.4%

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

      1. neg-mul-1 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around 0 31.7%

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

   7. Taylor expanded in z around inf 31.4%

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

      1. *-commutative 31.4%

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

   9. Simplified 31.4%

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

   if 1.95e39 < 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 92.1%

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

   4. Taylor expanded in x around 0 78.4%

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

   5. Taylor expanded in x around inf 78.4%

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

      1. *-commutative 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.4% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 40000000000000:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 40000000000000.0)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (+ 1.0 (* x (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 40000000000000.0) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 40000000000000.0d0) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 40000000000000.0) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 40000000000000.0:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 40000000000000.0)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 40000000000000.0)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 40000000000000.0], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4e13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. neg-mul-1 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around 0 30.3%

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

   if 4e13 < 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 89.9%

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

   4. Taylor expanded in x around 0 71.8%

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

   5. Taylor expanded in x around inf 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 40000000000000:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.0% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+153}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e+153) (+ 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 <= -2.8e+153) {
		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 <= (-2.8d+153)) 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 <= -2.8e+153) {
		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 <= -2.8e+153:
		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 <= -2.8e+153)
		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 <= -2.8e+153)
		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, -2.8e+153], 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 < -2.79999999999999985e153

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.1%

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

      1. neg-mul-1 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

   7. Taylor expanded in z around inf 88.1%

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

      1. *-commutative 88.1%

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

   9. Simplified 88.1%

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

   if -2.79999999999999985e153 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.1%

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

   4. Taylor expanded in x around 0 32.0%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+153}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.1% accurate, 29.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 51.0%

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

   1. neg-mul-1 51.0%

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

5. Simplified 51.0%

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

6. Taylor expanded in z around 0 26.2%

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

7. Taylor expanded in z around inf 25.9%

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

   1. *-commutative 25.9%

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

9. Simplified 25.9%

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

Alternative 14: 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 50.4%

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

4. Taylor expanded in x around 0 14.1%

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

5. Final simplification 14.1%

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

Alternative 15: 14.4% 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 50.4%

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

4. Taylor expanded in x around 0 13.6%

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

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024135 
(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)))