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

Percentage Accurate: 99.9% → 99.9%

Time: 6.2s

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 99.8%

   \[\left(x \cdot \log y - z\right) - y \]

2. Final simplification 99.8%

   \[\leadsto \left(x \cdot \log y - z\right) - y \]

Alternative 2: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+157} \lor \neg \left(z \leq 4.8 \cdot 10^{+55}\right):\\ \;\;\;\;-\left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.8e+157) (not (<= z 4.8e+55)))
   (- (+ y z))
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.8e+157) || !(z <= 4.8e+55)) {
		tmp = -(y + z);
	} else {
		tmp = (x * log(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 ((z <= (-9.8d+157)) .or. (.not. (z <= 4.8d+55))) then
        tmp = -(y + z)
    else
        tmp = (x * log(y)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.8e+157) || !(z <= 4.8e+55)) {
		tmp = -(y + z);
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.8e+157) or not (z <= 4.8e+55):
		tmp = -(y + z)
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.8e+157) || !(z <= 4.8e+55))
		tmp = Float64(-Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.8e+157) || ~((z <= 4.8e+55)))
		tmp = -(y + z);
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.8e+157], N[Not[LessEqual[z, 4.8e+55]], $MachinePrecision]], (-N[(y + z), $MachinePrecision]), N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000003e157 or 4.7999999999999998e55 < z

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]

   2. Taylor expanded in x around 0 86.2%

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

      1. mul-1-neg 86.2%

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

   4. Simplified 86.2%

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

   if -9.8000000000000003e157 < z < 4.7999999999999998e55

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate--l+ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 87.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+157} \lor \neg \left(z \leq 4.8 \cdot 10^{+55}\right):\\ \;\;\;\;-\left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 3: 67.0% accurate, 26.8× speedup

Math

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

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. Taylor expanded in x around 0 58.5%

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

   1. mul-1-neg 58.5%

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

4. Simplified 58.5%

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

5. Final simplification 58.5%

   \[\leadsto -\left(y + z\right) \]

Alternative 4: 34.5% 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. Step-by-step derivation

   1. sub-neg 99.8%

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

   2. associate--l+ 99.8%

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

   3. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around inf 30.1%

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

   1. neg-mul-1 30.1%

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

6. Simplified 30.1%

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

7. Final simplification 30.1%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))