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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 3

Speedup: 1.0×

• 52.2% 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. Final simplification 100.0%

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

Alternative 2: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{x - z}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{-10} \lor \neg \left(x \leq -4.3 \cdot 10^{-175}\right) \land x \leq 4.35 \cdot 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- x z))))
   (if (or (<= x -8.2e-10) (and (not (<= x -4.3e-175)) (<= x 4.35e-299)))
     t_0
     (* t_0 (pow y y)))))

C

double code(double x, double y, double z) {
	double t_0 = exp((x - z));
	double tmp;
	if ((x <= -8.2e-10) || (!(x <= -4.3e-175) && (x <= 4.35e-299))) {
		tmp = t_0;
	} else {
		tmp = t_0 * 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 = exp((x - z))
    if ((x <= (-8.2d-10)) .or. (.not. (x <= (-4.3d-175))) .and. (x <= 4.35d-299)) then
        tmp = t_0
    else
        tmp = t_0 * (y ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.exp((x - z));
	double tmp;
	if ((x <= -8.2e-10) || (!(x <= -4.3e-175) && (x <= 4.35e-299))) {
		tmp = t_0;
	} else {
		tmp = t_0 * Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp((x - z))
	tmp = 0
	if (x <= -8.2e-10) or (not (x <= -4.3e-175) and (x <= 4.35e-299)):
		tmp = t_0
	else:
		tmp = t_0 * math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(x - z))
	tmp = 0.0
	if ((x <= -8.2e-10) || (!(x <= -4.3e-175) && (x <= 4.35e-299)))
		tmp = t_0;
	else
		tmp = Float64(t_0 * (y ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp((x - z));
	tmp = 0.0;
	if ((x <= -8.2e-10) || (~((x <= -4.3e-175)) && (x <= 4.35e-299)))
		tmp = t_0;
	else
		tmp = t_0 * (y ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[x, -8.2e-10], And[N[Not[LessEqual[x, -4.3e-175]], $MachinePrecision], LessEqual[x, 4.35e-299]]], t$95$0, N[(t$95$0 * N[Power[y, y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999996e-10 or -4.29999999999999998e-175 < x < 4.35000000000000012e-299

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 88.2%

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

   if -8.1999999999999996e-10 < x < -4.29999999999999998e-175 or 4.35000000000000012e-299 < x

   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 92.3%

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

      4. *-commutative 92.3%

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

      5. exp-to-pow 92.3%

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

   3. Simplified 92.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-10} \lor \neg \left(x \leq -4.3 \cdot 10^{-175}\right) \land x \leq 4.35 \cdot 10^{-299}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{x - z} \cdot {y}^{y}\\ \end{array} \]

Alternative 3: 78.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return exp((x - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf 83.8%

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

3. Final simplification 83.8%

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

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 2023196 
(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)))