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

Percentage Accurate: 99.9% → 99.9%

Time: 8.7s

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, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(log(y), x, -z) - y;
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+39} \lor \neg \left(z \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e+39) (not (<= z 4e+85))) (- (- y) z) (- (* (log y) x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e+39) || !(z <= 4e+85)) {
		tmp = -y - z;
	} else {
		tmp = (log(y) * x) - 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 <= (-3.4d+39)) .or. (.not. (z <= 4d+85))) then
        tmp = -y - z
    else
        tmp = (log(y) * x) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e+39) || !(z <= 4e+85)) {
		tmp = -y - z;
	} else {
		tmp = (Math.log(y) * x) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e+39) or not (z <= 4e+85):
		tmp = -y - z
	else:
		tmp = (math.log(y) * x) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e+39) || !(z <= 4e+85))
		tmp = Float64(Float64(-y) - z);
	else
		tmp = Float64(Float64(log(y) * x) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e+39) || ~((z <= 4e+85)))
		tmp = -y - z;
	else
		tmp = (log(y) * x) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e+39], N[Not[LessEqual[z, 4e+85]], $MachinePrecision]], N[((-y) - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999999e39 or 4.0000000000000001e85 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.8%

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

      1. neg-mul-1 82.8%

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

   4. Simplified 82.8%

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

   if -3.3999999999999999e39 < z < 4.0000000000000001e85

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. fma-neg 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 95.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+39} \lor \neg \left(z \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 4: 67.0% 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. Taylor expanded in x around 0 62.6%

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

   1. neg-mul-1 62.6%

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

4. Simplified 62.6%

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

5. Final simplification 62.6%

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

Reproduce

herbie shell --seed 2023312 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))