Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - 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 = ((x * log(y)) - z) - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - 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 = ((x * log(y)) - z) - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - 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 = ((x * log(y)) - z) - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+126} \lor \neg \left(x \leq 5.5 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+126) (not (<= x 5.5e+69)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+126) || !(x <= 5.5e+69)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = -z - 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 ((x <= (-2.8d+126)) .or. (.not. (x <= 5.5d+69))) then
        tmp = (x * log(y)) - y
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+126) || !(x <= 5.5e+69)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+126) or not (x <= 5.5e+69):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+126) || !(x <= 5.5e+69))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e+126) || ~((x <= 5.5e+69)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+126], N[Not[LessEqual[x, 5.5e+69]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000009e126 or 5.50000000000000002e69 < x

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. add-cube-cbrt 98.5%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - z\right) - y \]

      3. associate-*r* 98.5%

         \[\leadsto \left(\color{blue}{\left(\log y \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}} - z\right) - y \]

      4. fma-neg 98.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right), \sqrt[3]{x}, -z\right)} - y \]

      5. pow2 98.5%

         \[\leadsto \mathsf{fma}\left(\log y \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, -z\right) - y \]

   4. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot {\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, -z\right)} - y \]

   5. Taylor expanded in x around inf 85.9%

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

   if -2.80000000000000009e126 < x < 5.50000000000000002e69

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.2%

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

      1. neg-mul-1 91.2%

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

   5. Simplified 91.2%

      \[\leadsto \color{blue}{\left(-z\right)} - y \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+126} \lor \neg \left(x \leq 5.5 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.3% accurate, 26.8× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) - y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in x around 0 72.2%

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

   1. neg-mul-1 72.2%

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

5. Simplified 72.2%

   \[\leadsto \color{blue}{\left(-z\right)} - y \]
6. Add Preprocessing

Alternative 4: 34.8% accurate, 35.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-cube-cbrt 98.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \log y - z} \cdot \sqrt[3]{x \cdot \log y - z}\right) \cdot \sqrt[3]{x \cdot \log y - z}} - y \]

   2. pow3 98.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \log y - z}\right)}^{3}} - y \]

4. Applied egg-rr 98.4%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \log y - z}\right)}^{3}} - y \]
5. Step-by-step derivation

   1. rem-cube-cbrt 99.9%

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

   2. sub-neg 99.9%

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

   3. *-commutative 99.9%

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

   4. add-sqr-sqrt 51.8%

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

   5. associate-*r* 51.8%

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

   6. fma-undefine 51.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, -z\right)} - y \]

   7. add-sqr-sqrt 22.9%

      \[\leadsto \mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right) - y \]

   8. sqrt-unprod 31.9%

      \[\leadsto \mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right) - y \]

   9. sqr-neg 31.9%

      \[\leadsto \mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, \sqrt{\color{blue}{z \cdot z}}\right) - y \]

   10. sqrt-unprod 16.4%

       \[\leadsto \mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{\sqrt{z} \cdot \sqrt{z}}\right) - y \]

   11. add-sqr-sqrt 30.2%

       \[\leadsto \mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, \color{blue}{z}\right) - y \]

6. Applied egg-rr 30.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot \sqrt{x}, \sqrt{x}, z\right)} - y \]

7. Taylor expanded in x around 0 28.9%

   \[\leadsto \color{blue}{z} - y \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))