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

Percentage Accurate: 99.9% → 99.9%

Time: 11.5s

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, 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. Add Preprocessing

Alternative 2: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -4 \cdot 10^{+164}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+133}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -4e+164) t_0 (if (<= x 1.75e+133) (- (- z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -4e+164) {
		tmp = t_0;
	} else if (x <= 1.75e+133) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	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 (x <= (-4d+164)) then
        tmp = t_0
    else if (x <= 1.75d+133) then
        tmp = -z - y
    else
        tmp = t_0
    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 (x <= -4e+164) {
		tmp = t_0;
	} else if (x <= 1.75e+133) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -4e+164:
		tmp = t_0
	elif x <= 1.75e+133:
		tmp = -z - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -4e+164)
		tmp = t_0;
	elseif (x <= 1.75e+133)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (x <= -4e+164)
		tmp = t_0;
	elseif (x <= 1.75e+133)
		tmp = -z - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+164], t$95$0, If[LessEqual[x, 1.75e+133], N[((-z) - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4e164 or 1.7499999999999999e133 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -4e164 < x < 1.7499999999999999e133

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 82.2

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

   5. Applied rewrites 82.2%

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

Alternative 3: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 3.2 \cdot 10^{+76}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y)))) (if (<= y 3.2e+76) (- 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 <= 3.2e+76) {
		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 <= 3.2d+76) 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 <= 3.2e+76) {
		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 <= 3.2e+76:
		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 <= 3.2e+76)
		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 <= 3.2e+76)
		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[LessEqual[y, 3.2e+76], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.19999999999999976e76

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 89.7

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

   5. Applied rewrites 89.7%

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

   if 3.19999999999999976e76 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 85.9

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

   5. Applied rewrites 85.9%

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

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.7e+98) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.7e+98) {
		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 <= 3.7d+98) 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 <= 3.7e+98) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.7e+98:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.7e+98)
		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 <= 3.7e+98)
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.7e+98], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.6999999999999999e98

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 88.2

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

   5. Applied rewrites 88.2%

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

   if 3.6999999999999999e98 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 87.7

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

   5. Applied rewrites 87.7%

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

Alternative 5: 52.4% accurate, 12.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+76}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.2e+76) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.2e+76) {
		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 <= 3.2d+76) 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 <= 3.2e+76) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.2e+76:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.2e+76)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.2e+76)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.2e+76], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.19999999999999976e76

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 49.0

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

   5. Applied rewrites 49.0%

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

   if 3.19999999999999976e76 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. lower-neg.f64 68.7

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

   5. Applied rewrites 68.7%

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

Alternative 6: 66.8% accurate, 18.7× 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

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 66.4

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

5. Applied rewrites 66.4%

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

Alternative 7: 34.5% accurate, 37.3× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 31.3

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

5. Applied rewrites 31.3%

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

Alternative 8: 2.2% accurate, 112.0× 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 99.8%

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

   1. lift--.f64 N/A

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

   2. flip-- N/A

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

   3. clear-num N/A

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot \log y - z\right) + y}{\left(x \cdot \log y - z\right) \cdot \left(x \cdot \log y - z\right) - y \cdot y}}} \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot \log y - z\right) + y}{\left(x \cdot \log y - z\right) \cdot \left(x \cdot \log y - z\right) - y \cdot y}}} \]

   5. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\left(x \cdot \log y - z\right) \cdot \left(x \cdot \log y - z\right) - y \cdot y}{\left(x \cdot \log y - z\right) + y}}}} \]

   6. flip-- N/A

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{\left(x \cdot \log y - z\right) - y}}} \]

   7. lift--.f64 N/A

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{\left(x \cdot \log y - z\right) - y}}} \]

   8. lower-/.f64 99.6

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\left(x \cdot \log y - z\right) - y}}} \]

   9. lift--.f64 N/A

      \[\leadsto \frac{1}{\frac{1}{\color{blue}{\left(x \cdot \log y - z\right) - y}}} \]

   10. lift--.f64 N/A

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{\left(x \cdot \log y - z\right)} - y}} \]

   11. associate--l- N/A

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot \log y - \left(z + y\right)}}} \]

   12. lower--.f64 N/A

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot \log y - \left(z + y\right)}}} \]

   13. +-commutative N/A

       \[\leadsto \frac{1}{\frac{1}{x \cdot \log y - \color{blue}{\left(y + z\right)}}} \]

   14. lower-+.f64 99.6

       \[\leadsto \frac{1}{\frac{1}{x \cdot \log y - \color{blue}{\left(y + z\right)}}} \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}} \]

5. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 36.9

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

7. Applied rewrites 36.9%

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

9. Applied rewrites 2.2%

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

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))