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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

Alternatives: 9

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: 99.8% 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: 99.8% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+68} \lor \neg \left(x \leq 3 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e+68) (not (<= x 3e+110))) (- (* x (log y)) y) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+68) || !(x <= 3e+110)) {
		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 <= (-1.4d+68)) .or. (.not. (x <= 3d+110))) 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 <= -1.4e+68) || !(x <= 3e+110)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e+68) or not (x <= 3e+110):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e+68) || !(x <= 3e+110))
		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 <= -1.4e+68) || ~((x <= 3e+110)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e+68], N[Not[LessEqual[x, 3e+110]], $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 < -1.4e68 or 3.00000000000000007e110 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 85.0%

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

   if -1.4e68 < x < 3.00000000000000007e110

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.3%

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

      1. neg-mul-1 88.3%

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

      2. +-commutative 88.3%

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

      3. distribute-neg-in 88.3%

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

      4. sub-neg 88.3%

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

   5. Simplified 88.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+68} \lor \neg \left(x \leq 3 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+144} \lor \neg \left(x \leq 4.4 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e+144) (not (<= x 4.4e+110))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e+144) || !(x <= 4.4e+110)) {
		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 <= (-3.4d+144)) .or. (.not. (x <= 4.4d+110))) 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 <= -3.4e+144) || !(x <= 4.4e+110)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e+144) or not (x <= 4.4e+110):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e+144) || !(x <= 4.4e+110))
		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 <= -3.4e+144) || ~((x <= 4.4e+110)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e+144], N[Not[LessEqual[x, 4.4e+110]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999999e144 or 4.39999999999999984e110 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.2%

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

   if -3.3999999999999999e144 < x < 4.39999999999999984e110

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. +-commutative 86.9%

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

      3. distribute-neg-in 86.9%

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

      4. sub-neg 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+144} \lor \neg \left(x \leq 4.4 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.6e-7) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e-7) {
		tmp = (x * log(y)) - z;
	} 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 (y <= 3.6d-7) then
        tmp = (x * log(y)) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e-7) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.6e-7:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.6e-7)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.6e-7)
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.6e-7], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.59999999999999994e-7

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.9%

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

   if 3.59999999999999994e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. +-commutative 82.1%

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

      3. distribute-neg-in 82.1%

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

      4. sub-neg 82.1%

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

   5. Simplified 82.1%

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

Alternative 5: 52.1% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+66}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.2e+66) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.2e+66) {
		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 <= 5.2d+66) 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 <= 5.2e+66) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.2e+66:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.2e+66)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.2e+66)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.2e+66], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.20000000000000024e66

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 49.2%

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

      1. neg-mul-1 49.2%

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

   5. Simplified 49.2%

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

   if 5.20000000000000024e66 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. neg-mul-1 68.4%

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

   5. Simplified 68.4%

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

Alternative 6: 65.7% 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. Add Preprocessing

3. Taylor expanded in x around 0 69.8%

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

   1. neg-mul-1 69.8%

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

   2. +-commutative 69.8%

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

   3. distribute-neg-in 69.8%

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

   4. sub-neg 69.8%

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

5. Simplified 69.8%

   \[\leadsto \color{blue}{\left(-z\right) - y} \]
6. Add Preprocessing

Alternative 7: 34.9% 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. Add Preprocessing

3. Taylor expanded in y around inf 35.7%

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

   1. neg-mul-1 35.7%

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

5. Simplified 35.7%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Alternative 8: 2.3% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf 35.9%

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

   1. neg-mul-1 35.9%

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

5. Simplified 35.9%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

   1. neg-sub0 35.9%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 35.9%

      \[\leadsto \color{blue}{0 + \left(-z\right)} \]

   3. add-sqr-sqrt 20.5%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 8.8%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \]

   5. sqr-neg 8.8%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 0.8%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.2%

      \[\leadsto 0 + \color{blue}{z} \]

7. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{0 + z} \]
8. Step-by-step derivation

   1. +-lft-identity 2.2%

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

9. Simplified 2.2%

   \[\leadsto \color{blue}{z} \]
10. Add Preprocessing

Alternative 9: 2.2% accurate, 107.0× 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 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. Add Preprocessing

3. Taylor expanded in x around inf 78.6%

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

   1. mul-1-neg 78.6%

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

   2. unsub-neg 78.6%

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

5. Simplified 78.6%

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

6. Taylor expanded in y around inf 25.0%

   \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} \]
7. Step-by-step derivation

   1. associate-*r/ 25.0%

      \[\leadsto x \cdot \color{blue}{\frac{-1 \cdot y}{x}} \]

   2. mul-1-neg 25.0%

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

8. Simplified 25.0%

   \[\leadsto x \cdot \color{blue}{\frac{-y}{x}} \]
9. Step-by-step derivation

   1. associate-*r/ 29.7%

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

   2. add-sqr-sqrt 0.0%

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

   3. sqrt-unprod 2.1%

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

   4. sqr-neg 2.1%

      \[\leadsto \frac{x \cdot \sqrt{\color{blue}{y \cdot y}}}{x} \]

   5. sqrt-unprod 2.1%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}}{x} \]

   6. add-sqr-sqrt 2.1%

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

10. Applied egg-rr 2.1%

    \[\leadsto \color{blue}{\frac{x \cdot y}{x}} \]
11. Step-by-step derivation

    1. *-commutative 2.1%

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

    2. associate-/l* 2.1%

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

    3. *-inverses 2.1%

       \[\leadsto y \cdot \color{blue}{1} \]

    4. *-rgt-identity 2.1%

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

12. Simplified 2.1%

    \[\leadsto \color{blue}{y} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))