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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 7

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. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 2: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+32} \lor \neg \left(x \leq 9.5 \cdot 10^{+44}\right) \land \left(x \leq 2.3 \cdot 10^{+122} \lor \neg \left(x \leq 2.8 \cdot 10^{+154}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e+32)
         (and (not (<= x 9.5e+44)) (or (<= x 2.3e+122) (not (<= x 2.8e+154)))))
   (* x (log y))
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e+32) || (!(x <= 9.5e+44) && ((x <= 2.3e+122) || !(x <= 2.8e+154)))) {
		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 <= (-4.2d+32)) .or. (.not. (x <= 9.5d+44)) .and. (x <= 2.3d+122) .or. (.not. (x <= 2.8d+154))) 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 <= -4.2e+32) || (!(x <= 9.5e+44) && ((x <= 2.3e+122) || !(x <= 2.8e+154)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.2e+32) or (not (x <= 9.5e+44) and ((x <= 2.3e+122) or not (x <= 2.8e+154))):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e+32) || (!(x <= 9.5e+44) && ((x <= 2.3e+122) || !(x <= 2.8e+154))))
		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 <= -4.2e+32) || (~((x <= 9.5e+44)) && ((x <= 2.3e+122) || ~((x <= 2.8e+154)))))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e+32], And[N[Not[LessEqual[x, 9.5e+44]], $MachinePrecision], Or[LessEqual[x, 2.3e+122], N[Not[LessEqual[x, 2.8e+154]], $MachinePrecision]]]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000001e32 or 9.5000000000000004e44 < x < 2.3000000000000001e122 or 2.7999999999999999e154 < x

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate--l+ 99.6%

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

      3. add-cube-cbrt 98.7%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \log y + \left(\left(-z\right) - y\right) \]

      4. associate-*l* 98.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \log y\right)} + \left(\left(-z\right) - y\right) \]

      5. fma-define 98.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \log y, \left(-z\right) - y\right)} \]

      6. pow2 98.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x} \cdot \log y, \left(-z\right) - y\right) \]

   4. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x} \cdot \log y, \left(-z\right) - y\right)} \]

   5. Taylor expanded in x around inf 70.2%

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

   if -4.2000000000000001e32 < x < 9.5000000000000004e44 or 2.3000000000000001e122 < x < 2.7999999999999999e154

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.1%

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

      1. neg-mul-1 88.1%

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

      2. +-commutative 88.1%

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

      3. distribute-neg-in 88.1%

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

      4. sub-neg 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+32} \lor \neg \left(x \leq 9.5 \cdot 10^{+44}\right) \land \left(x \leq 2.3 \cdot 10^{+122} \lor \neg \left(x \leq 2.8 \cdot 10^{+154}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 4 \cdot 10^{-65} \lor \neg \left(y \leq 0.018\right) \land y \leq 1300000:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (or (<= y 4e-65) (and (not (<= y 0.018)) (<= y 1300000.0)))
     (- t_0 z)
     (- t_0 y))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if ((y <= 4e-65) || (!(y <= 0.018) && (y <= 1300000.0))) {
		tmp = t_0 - z;
	} 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 ((y <= 4d-65) .or. (.not. (y <= 0.018d0)) .and. (y <= 1300000.0d0)) then
        tmp = t_0 - z
    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 ((y <= 4e-65) || (!(y <= 0.018) && (y <= 1300000.0))) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if (y <= 4e-65) or (not (y <= 0.018) and (y <= 1300000.0)):
		tmp = t_0 - z
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if ((y <= 4e-65) || (!(y <= 0.018) && (y <= 1300000.0)))
		tmp = Float64(t_0 - z);
	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 ((y <= 4e-65) || (~((y <= 0.018)) && (y <= 1300000.0)))
		tmp = t_0 - z;
	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[Or[LessEqual[y, 4e-65], And[N[Not[LessEqual[y, 0.018]], $MachinePrecision], LessEqual[y, 1300000.0]]], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.99999999999999969e-65 or 0.0179999999999999986 < y < 1.3e6

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 95.4%

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

   if 3.99999999999999969e-65 < y < 0.0179999999999999986 or 1.3e6 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 84.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-65} \lor \neg \left(y \leq 0.018\right) \land y \leq 1300000:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+106} \lor \neg \left(z \leq 3.6 \cdot 10^{+149}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e+106) (not (<= z 3.6e+149)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+106) || !(z <= 3.6e+149)) {
		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 <= (-1.1d+106)) .or. (.not. (z <= 3.6d+149))) 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 <= -1.1e+106) || !(z <= 3.6e+149)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e+106) or not (z <= 3.6e+149):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e+106) || !(z <= 3.6e+149))
		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 <= -1.1e+106) || ~((z <= 3.6e+149)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e+106], N[Not[LessEqual[z, 3.6e+149]], $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 < -1.09999999999999996e106 or 3.59999999999999995e149 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. +-commutative 83.8%

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

      3. distribute-neg-in 83.8%

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

      4. sub-neg 83.8%

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

   5. Simplified 83.8%

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

   if -1.09999999999999996e106 < z < 3.59999999999999995e149

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 88.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+106} \lor \neg \left(z \leq 3.6 \cdot 10^{+149}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.1 \cdot 10^{-65}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 6.1e-65) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.1e-65) {
		tmp = -z;
	} else {
		tmp = -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 (y <= 6.1d-65) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.1e-65) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.1e-65:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.1e-65)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.1e-65)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.1e-65], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 6.10000000000000014e-65

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. neg-mul-1 44.5%

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

   5. Simplified 44.5%

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

   if 6.10000000000000014e-65 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 52.9%

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

      1. neg-mul-1 52.9%

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

   5. Simplified 52.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.1 \cdot 10^{-65}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.3% 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 99.8%

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

3. Taylor expanded in x around 0 61.6%

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

   1. neg-mul-1 61.6%

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

   2. +-commutative 61.6%

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

   3. distribute-neg-in 61.6%

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

   4. sub-neg 61.6%

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

5. Simplified 61.6%

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

6. Final simplification 61.6%

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

Alternative 7: 34.0% 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 34.8%

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

   1. neg-mul-1 34.8%

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

5. Simplified 34.8%

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

6. Final simplification 34.8%

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

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))