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

Percentage Accurate: 99.9% → 99.8%

Time: 9.0s

Alternatives: 5

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	return ((math.log((1.0 / y)) * -x) - z) - y

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around inf 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \left(\log \left(\frac{1}{y}\right) \cdot \left(-x\right) - z\right) - y \]
5. Add Preprocessing

Alternative 2: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+70} \lor \neg \left(x \leq 1.5 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.6e+70) (not (<= x 1.5e+79)))
   (- (* x (log y)) y)
   (- (- y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e+70) || !(x <= 1.5e+79)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = -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 ((x <= (-7.6d+70)) .or. (.not. (x <= 1.5d+79))) then
        tmp = (x * log(y)) - y
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e+70) || !(x <= 1.5e+79)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.6e+70) or not (x <= 1.5e+79):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.6e+70) || !(x <= 1.5e+79))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.6e+70) || ~((x <= 1.5e+79)))
		tmp = (x * log(y)) - y;
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.6e+70], N[Not[LessEqual[x, 1.5e+79]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999996e70 or 1.49999999999999987e79 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

   4. Taylor expanded in x around inf 82.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{y}\right)\right)} - y \]
   5. Step-by-step derivation

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-in 82.7%

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

      3. log-rec 82.7%

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

      4. remove-double-neg 82.7%

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

   6. Simplified 82.7%

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

   if -7.5999999999999996e70 < x < 1.49999999999999987e79

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.0%

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

      1. neg-mul-1 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+70} \lor \neg \left(x \leq 1.5 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 4: 66.7% accurate, 26.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 66.7%

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

   1. neg-mul-1 66.7%

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

5. Simplified 66.7%

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

6. Final simplification 66.7%

   \[\leadsto \left(-y\right) - z \]
7. Add Preprocessing

Alternative 5: 34.1% accurate, 53.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-y)

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around inf 99.8%

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

4. Taylor expanded in x around inf 68.2%

   \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{y}\right)\right)} - y \]
5. Step-by-step derivation

   1. mul-1-neg 68.2%

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

   2. distribute-rgt-neg-in 68.2%

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

   3. log-rec 68.2%

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

   4. remove-double-neg 68.2%

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

6. Simplified 68.2%

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

7. Taylor expanded in x around 0 35.4%

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

   1. neg-mul-1 35.4%

      \[\leadsto \color{blue}{-y} \]

9. Simplified 35.4%

   \[\leadsto \color{blue}{-y} \]

10. Final simplification 35.4%

    \[\leadsto -y \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))