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

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

Alternatives: 9

Speedup: 1.0×

• 59.4% 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. Final simplification 100.0%

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

Alternative 2: 87.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \log y\\ \mathbf{if}\;t_0 \leq 50:\\ \;\;\;\;e^{x - z}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+214} \lor \neg \left(t_0 \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (log y)))))
   (if (<= t_0 50.0)
     (exp (- x z))
     (if (or (<= t_0 5e+214) (not (<= t_0 5e+262)))
       (* (pow y y) (exp x))
       (pow y y)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * log(y));
	double tmp;
	if (t_0 <= 50.0) {
		tmp = exp((x - z));
	} else if ((t_0 <= 5e+214) || !(t_0 <= 5e+262)) {
		tmp = pow(y, y) * 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) :: t_0
    real(8) :: tmp
    t_0 = x + (y * log(y))
    if (t_0 <= 50.0d0) then
        tmp = exp((x - z))
    else if ((t_0 <= 5d+214) .or. (.not. (t_0 <= 5d+262))) then
        tmp = (y ** y) * exp(x)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * Math.log(y));
	double tmp;
	if (t_0 <= 50.0) {
		tmp = Math.exp((x - z));
	} else if ((t_0 <= 5e+214) || !(t_0 <= 5e+262)) {
		tmp = Math.pow(y, y) * Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * math.log(y))
	tmp = 0
	if t_0 <= 50.0:
		tmp = math.exp((x - z))
	elif (t_0 <= 5e+214) or not (t_0 <= 5e+262):
		tmp = math.pow(y, y) * math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * log(y)))
	tmp = 0.0
	if (t_0 <= 50.0)
		tmp = exp(Float64(x - z));
	elseif ((t_0 <= 5e+214) || !(t_0 <= 5e+262))
		tmp = Float64((y ^ y) * exp(x));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * log(y));
	tmp = 0.0;
	if (t_0 <= 50.0)
		tmp = exp((x - z));
	elseif ((t_0 <= 5e+214) || ~((t_0 <= 5e+262)))
		tmp = (y ^ y) * exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 50.0], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[t$95$0, 5e+214], N[Not[LessEqual[t$95$0, 5e+262]], $MachinePrecision]], N[(N[Power[y, y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision], N[Power[y, y], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 y (log.f64 y))) < 50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.2%

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

   if 50 < (+.f64 x (*.f64 y (log.f64 y))) < 4.99999999999999953e214 or 5.00000000000000008e262 < (+.f64 x (*.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 z around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. exp-sum 86.0%

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

      3. *-commutative 86.0%

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

      4. exp-to-pow 86.0%

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

   5. Simplified 86.0%

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

   if 4.99999999999999953e214 < (+.f64 x (*.f64 y (log.f64 y))) < 5.00000000000000008e262

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.2%

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

   4. Taylor expanded in x around 0 88.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \cdot \log y \leq 50:\\ \;\;\;\;e^{x - z}\\ \mathbf{elif}\;x + y \cdot \log y \leq 5 \cdot 10^{+214} \lor \neg \left(x + y \cdot \log y \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;{y}^{y} \cdot e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t_0 \leq 50 \lor \neg \left(t_0 \leq 4 \cdot 10^{+21}\right) \land t_0 \leq 10^{+103}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (or (<= t_0 50.0) (and (not (<= t_0 4e+21)) (<= t_0 1e+103)))
     (exp (- x z))
     (pow y y))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if ((t_0 <= 50.0) || (!(t_0 <= 4e+21) && (t_0 <= 1e+103))) {
		tmp = exp((x - z));
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * log(y)
    if ((t_0 <= 50.0d0) .or. (.not. (t_0 <= 4d+21)) .and. (t_0 <= 1d+103)) then
        tmp = exp((x - z))
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if ((t_0 <= 50.0) || (!(t_0 <= 4e+21) && (t_0 <= 1e+103))) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if (t_0 <= 50.0) or (not (t_0 <= 4e+21) and (t_0 <= 1e+103)):
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if ((t_0 <= 50.0) || (!(t_0 <= 4e+21) && (t_0 <= 1e+103)))
		tmp = exp(Float64(x - z));
	else
		tmp = y ^ y;
	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) || (~((t_0 <= 4e+21)) && (t_0 <= 1e+103)))
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 50.0], And[N[Not[LessEqual[t$95$0, 4e+21]], $MachinePrecision], LessEqual[t$95$0, 1e+103]]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < 50 or 4e21 < (*.f64 y (log.f64 y)) < 1e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 92.4%

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

   if 50 < (*.f64 y (log.f64 y)) < 4e21 or 1e103 < (*.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 z around 0 95.7%

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

   4. Taylor expanded in x around 0 89.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq 50 \lor \neg \left(y \cdot \log y \leq 4 \cdot 10^{+21}\right) \land y \cdot \log y \leq 10^{+103}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t_0 \leq 10000000000:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{x + t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 10000000000.0) (* (pow y y) (exp (- x z))) (exp (+ x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= 10000000000.0) {
		tmp = pow(y, y) * exp((x - z));
	} else {
		tmp = exp((x + t_0));
	}
	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 <= 10000000000.0d0) then
        tmp = (y ** y) * exp((x - z))
    else
        tmp = exp((x + t_0))
    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 <= 10000000000.0) {
		tmp = Math.pow(y, y) * Math.exp((x - z));
	} else {
		tmp = Math.exp((x + t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= 10000000000.0:
		tmp = math.pow(y, y) * math.exp((x - z))
	else:
		tmp = math.exp((x + t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= 10000000000.0)
		tmp = Float64((y ^ y) * exp(Float64(x - z)));
	else
		tmp = exp(Float64(x + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= 10000000000.0)
		tmp = (y ^ y) * exp((x - z));
	else
		tmp = exp((x + t_0));
	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, 10000000000.0], N[(N[Power[y, y], $MachinePrecision] * N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(x + t$95$0), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < 1e10

   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 1e10 < (*.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 z around 0 92.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq 10000000000:\\ \;\;\;\;{y}^{y} \cdot e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{x + y \cdot \log y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y)))) (if (<= t_0 50.0) (exp (- x z)) (exp (+ x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= 50.0) {
		tmp = exp((x - z));
	} else {
		tmp = exp((x + t_0));
	}
	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 = exp((x - z))
    else
        tmp = exp((x + t_0))
    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.exp((x - z));
	} else {
		tmp = Math.exp((x + t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= 50.0:
		tmp = math.exp((x - z))
	else:
		tmp = math.exp((x + t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= 50.0)
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(x + t_0));
	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 = exp((x - z));
	else
		tmp = exp((x + t_0));
	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[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(x + t$95$0), $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. Add Preprocessing

   3. Taylor expanded in x around inf 99.3%

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

   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 z around 0 92.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq 50:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{x + y \cdot \log y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -160 \lor \neg \left(z \leq 1.7 \cdot 10^{+14}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -160.0) (not (<= z 1.7e+14))) (exp (- z)) (exp x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -160.0) || !(z <= 1.7e+14)) {
		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 <= (-160.0d0)) .or. (.not. (z <= 1.7d+14))) 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 <= -160.0) || !(z <= 1.7e+14)) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.exp(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -160.0) or not (z <= 1.7e+14):
		tmp = math.exp(-z)
	else:
		tmp = math.exp(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -160.0) || !(z <= 1.7e+14))
		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 <= -160.0) || ~((z <= 1.7e+14)))
		tmp = exp(-z);
	else
		tmp = exp(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -160.0], N[Not[LessEqual[z, 1.7e+14]], $MachinePrecision]], N[Exp[(-z)], $MachinePrecision], N[Exp[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -160 or 1.7e14 < 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 82.5%

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

      1. neg-mul-1 82.5%

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

   5. Simplified 82.5%

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

   if -160 < z < 1.7e14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in y around 0 66.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -160 \lor \neg \left(z \leq 1.7 \cdot 10^{+14}\right):\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;e^{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.3e-178) (exp x) (if (<= y 14000.0) (exp (- z)) (pow y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.3e-178) {
		tmp = exp(x);
	} else if (y <= 14000.0) {
		tmp = exp(-z);
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 3.3d-178) then
        tmp = exp(x)
    else if (y <= 14000.0d0) then
        tmp = exp(-z)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.3e-178) {
		tmp = Math.exp(x);
	} else if (y <= 14000.0) {
		tmp = Math.exp(-z);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.3e-178:
		tmp = math.exp(x)
	elif y <= 14000.0:
		tmp = math.exp(-z)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.3e-178)
		tmp = exp(x);
	elseif (y <= 14000.0)
		tmp = exp(Float64(-z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.3e-178)
		tmp = exp(x);
	elseif (y <= 14000.0)
		tmp = exp(-z);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.3e-178], N[Exp[x], $MachinePrecision], If[LessEqual[y, 14000.0], N[Exp[(-z)], $MachinePrecision], N[Power[y, y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.3000000000000002e-178

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.2%

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

   4. Taylor expanded in y around 0 76.2%

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

   if 3.3000000000000002e-178 < y < 14000

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.4%

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

      1. neg-mul-1 76.4%

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

   5. Simplified 76.4%

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

   if 14000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.3%

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

   4. Taylor expanded in x around 0 78.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;e^{x}\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;e^{-z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{x} \end{array} \]

FPCore

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

C

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

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)
end function

Java

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

Python

def code(x, y, z):
	return math.exp(x)

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Exp[x], $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 0 80.1%

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

4. Taylor expanded in y around 0 52.9%

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

5. Final simplification 52.9%

   \[\leadsto e^{x} \]
6. Add Preprocessing

Alternative 9: 14.8% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0 80.1%

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

4. Taylor expanded in x around 0 36.6%

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

   1. distribute-lft1-in 46.5%

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

   2. *-commutative 46.5%

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

6. Simplified 46.5%

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

7. Taylor expanded in y around 0 14.5%

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

8. Final simplification 14.5%

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

Developer target: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

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