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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 6

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate--l- 99.9%

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

   2. fma-neg 99.9%

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

   3. +-commutative 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+103} \lor \neg \left(x \leq 1.1 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.4e+103) (not (<= x 1.1e+33)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.4e+103) || !(x <= 1.1e+33)) {
		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 <= (-6.4d+103)) .or. (.not. (x <= 1.1d+33))) 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 <= -6.4e+103) || !(x <= 1.1e+33)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.4e+103) or not (x <= 1.1e+33):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.4e+103) || !(x <= 1.1e+33))
		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 <= -6.4e+103) || ~((x <= 1.1e+33)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.4e+103], N[Not[LessEqual[x, 1.1e+33]], $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 < -6.39999999999999985e103 or 1.09999999999999997e33 < x

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

      2. fma-neg 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 86.5%

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

   if -6.39999999999999985e103 < x < 1.09999999999999997e33

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. fma-neg 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.0%

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

      1. mul-1-neg 92.0%

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

      2. +-commutative 92.0%

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

      3. distribute-neg-in 92.0%

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

      4. sub-neg 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+103} \lor \neg \left(x \leq 1.1 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 49.9% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+149}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+45}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-52}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6e+149)
   (- z)
   (if (<= z -3.1e+45)
     (- y)
     (if (<= z -1.35e-32) (- z) (if (<= z 1.25e-52) (- y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+149) {
		tmp = -z;
	} else if (z <= -3.1e+45) {
		tmp = -y;
	} else if (z <= -1.35e-32) {
		tmp = -z;
	} else if (z <= 1.25e-52) {
		tmp = -y;
	} else {
		tmp = -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 (z <= (-6.6d+149)) then
        tmp = -z
    else if (z <= (-3.1d+45)) then
        tmp = -y
    else if (z <= (-1.35d-32)) then
        tmp = -z
    else if (z <= 1.25d-52) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+149) {
		tmp = -z;
	} else if (z <= -3.1e+45) {
		tmp = -y;
	} else if (z <= -1.35e-32) {
		tmp = -z;
	} else if (z <= 1.25e-52) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6e+149:
		tmp = -z
	elif z <= -3.1e+45:
		tmp = -y
	elif z <= -1.35e-32:
		tmp = -z
	elif z <= 1.25e-52:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6e+149)
		tmp = Float64(-z);
	elseif (z <= -3.1e+45)
		tmp = Float64(-y);
	elseif (z <= -1.35e-32)
		tmp = Float64(-z);
	elseif (z <= 1.25e-52)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.6e+149)
		tmp = -z;
	elseif (z <= -3.1e+45)
		tmp = -y;
	elseif (z <= -1.35e-32)
		tmp = -z;
	elseif (z <= 1.25e-52)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6e+149], (-z), If[LessEqual[z, -3.1e+45], (-y), If[LessEqual[z, -1.35e-32], (-z), If[LessEqual[z, 1.25e-52], (-y), (-z)]]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e149 or -3.09999999999999988e45 < z < -1.3499999999999999e-32 or 1.25e-52 < z

   1. Initial program 99.9%

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

      1. associate--l- 99.9%

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

      2. fma-neg 99.9%

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

      3. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 61.2%

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

      1. neg-mul-1 61.2%

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

   6. Simplified 61.2%

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

   if -6.6e149 < z < -3.09999999999999988e45 or -1.3499999999999999e-32 < z < 1.25e-52

   1. Initial program 99.9%

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

      1. associate--l- 99.9%

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

      2. fma-neg 99.9%

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

      3. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 59.6%

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

      1. neg-mul-1 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+149}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+45}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-52}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 66.2% 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. Step-by-step derivation

   1. associate--l- 99.9%

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

   2. fma-neg 99.9%

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

   3. +-commutative 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 71.7%

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

   1. mul-1-neg 71.7%

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

   2. +-commutative 71.7%

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

   3. distribute-neg-in 71.7%

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

   4. sub-neg 71.7%

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

6. Simplified 71.7%

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

7. Final simplification 71.7%

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

Alternative 6: 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 99.9%

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

   1. associate--l- 99.9%

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

   2. fma-neg 99.9%

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

   3. +-commutative 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 38.5%

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

   1. neg-mul-1 38.5%

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

6. Simplified 38.5%

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

7. Final simplification 38.5%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))