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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 8

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. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+107}:\\ \;\;\;\;t_0 - z\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-9} \lor \neg \left(z \leq 3.75 \cdot 10^{+81}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= z -6.6e+107)
     (- t_0 z)
     (if (or (<= z -1.05e-9) (not (<= z 3.75e+81))) (- (- z) y) (- t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (z <= -6.6e+107) {
		tmp = t_0 - z;
	} else if ((z <= -1.05e-9) || !(z <= 3.75e+81)) {
		tmp = -z - y;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (z <= (-6.6d+107)) then
        tmp = t_0 - z
    else if ((z <= (-1.05d-9)) .or. (.not. (z <= 3.75d+81))) then
        tmp = -z - y
    else
        tmp = t_0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double tmp;
	if (z <= -6.6e+107) {
		tmp = t_0 - z;
	} else if ((z <= -1.05e-9) || !(z <= 3.75e+81)) {
		tmp = -z - y;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if z <= -6.6e+107:
		tmp = t_0 - z
	elif (z <= -1.05e-9) or not (z <= 3.75e+81):
		tmp = -z - y
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -6.6e+107)
		tmp = Float64(t_0 - z);
	elseif ((z <= -1.05e-9) || !(z <= 3.75e+81))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (z <= -6.6e+107)
		tmp = t_0 - z;
	elseif ((z <= -1.05e-9) || ~((z <= 3.75e+81)))
		tmp = -z - y;
	else
		tmp = t_0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+107], N[(t$95$0 - z), $MachinePrecision], If[Or[LessEqual[z, -1.05e-9], N[Not[LessEqual[z, 3.75e+81]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000064e107

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.9%

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

   if -6.60000000000000064e107 < z < -1.0500000000000001e-9 or 3.74999999999999986e81 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. distribute-neg-in 89.5%

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

      3. +-commutative 89.5%

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

      4. sub-neg 89.5%

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

   4. Simplified 89.5%

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

   if -1.0500000000000001e-9 < z < 3.74999999999999986e81

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 94.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-9} \lor \neg \left(z \leq 3.75 \cdot 10^{+81}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-8} \lor \neg \left(z \leq 3.7 \cdot 10^{+79}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e-8) (not (<= z 3.7e+79)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e-8) || !(z <= 3.7e+79)) {
		tmp = -z - y;
	} 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 <= (-1.05d-8)) .or. (.not. (z <= 3.7d+79))) then
        tmp = -z - y
    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 <= -1.05e-8) || !(z <= 3.7e+79)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e-8) or not (z <= 3.7e+79):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e-8) || !(z <= 3.7e+79))
		tmp = Float64(Float64(-z) - y);
	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 <= -1.05e-8) || ~((z <= 3.7e+79)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e-8], N[Not[LessEqual[z, 3.7e+79]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999997e-8 or 3.70000000000000009e79 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. distribute-neg-in 85.3%

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

      3. +-commutative 85.3%

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

      4. sub-neg 85.3%

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

   4. Simplified 85.3%

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

   if -1.04999999999999997e-8 < z < 3.70000000000000009e79

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 94.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-8} \lor \neg \left(z \leq 3.7 \cdot 10^{+79}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 4: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+49} \lor \neg \left(x \leq 3.2 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e+49) (not (<= x 3.2e+188))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e+49) || !(x <= 3.2e+188)) {
		tmp = x * log(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 <= (-3.1d+49)) .or. (.not. (x <= 3.2d+188))) then
        tmp = x * log(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 <= -3.1e+49) || !(x <= 3.2e+188)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.1e+49) or not (x <= 3.2e+188):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.1e+49) || !(x <= 3.2e+188))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.1e+49) || ~((x <= 3.2e+188)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.1e+49], N[Not[LessEqual[x, 3.2e+188]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999992e49 or 3.1999999999999997e188 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 85.0%

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

   3. Taylor expanded in x around inf 70.8%

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

   if -3.09999999999999992e49 < x < 3.1999999999999997e188

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.8%

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

      1. mul-1-neg 86.8%

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

      2. distribute-neg-in 86.8%

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

      3. +-commutative 86.8%

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

      4. sub-neg 86.8%

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

   4. Simplified 86.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+49} \lor \neg \left(x \leq 3.2 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 5: 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 6: 50.9% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.2e+96) (- z) (if (<= z 1.9e+128) (- y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e+96) {
		tmp = -z;
	} else if (z <= 1.9e+128) {
		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 <= (-7.2d+96)) then
        tmp = -z
    else if (z <= 1.9d+128) 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 <= -7.2e+96) {
		tmp = -z;
	} else if (z <= 1.9e+128) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.2e+96:
		tmp = -z
	elif z <= 1.9e+128:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.2e+96)
		tmp = Float64(-z);
	elseif (z <= 1.9e+128)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.2e+96)
		tmp = -z;
	elseif (z <= 1.9e+128)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.2e+96], (-z), If[LessEqual[z, 1.9e+128], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000026e96 or 1.89999999999999995e128 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.4%

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

      1. mul-1-neg 72.4%

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

   4. Simplified 72.4%

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

   if -7.20000000000000026e96 < z < 1.89999999999999995e128

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 50.7%

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

      1. neg-mul-1 50.7%

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

   4. Simplified 50.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 65.8% 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. Taylor expanded in x around 0 70.4%

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

   1. mul-1-neg 70.4%

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

   2. distribute-neg-in 70.4%

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

   3. +-commutative 70.4%

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

   4. sub-neg 70.4%

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

4. Simplified 70.4%

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

5. Final simplification 70.4%

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

Alternative 8: 33.7% 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. Taylor expanded in y around inf 37.9%

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

   1. neg-mul-1 37.9%

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

4. Simplified 37.9%

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

5. Final simplification 37.9%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))