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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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. sub-neg N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-neg.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+23}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;t\_0 - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= z -9.4e+23) (- t_0 z) (if (<= z 1.3e+33) (- t_0 y) (- (- z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (z <= -9.4e+23) {
		tmp = t_0 - z;
	} else if (z <= 1.3e+33) {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (z <= (-9.4d+23)) then
        tmp = t_0 - z
    else if (z <= 1.3d+33) then
        tmp = t_0 - y
    else
        tmp = -z - 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 <= -9.4e+23) {
		tmp = t_0 - z;
	} else if (z <= 1.3e+33) {
		tmp = t_0 - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if z <= -9.4e+23:
		tmp = t_0 - z
	elif z <= 1.3e+33:
		tmp = t_0 - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -9.4e+23)
		tmp = Float64(t_0 - z);
	elseif (z <= 1.3e+33)
		tmp = Float64(t_0 - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (z <= -9.4e+23)
		tmp = t_0 - z;
	elseif (z <= 1.3e+33)
		tmp = t_0 - y;
	else
		tmp = -z - 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, -9.4e+23], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[z, 1.3e+33], N[(t$95$0 - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.3999999999999994e23

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. log-pow-rev N/A

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

      4. lower-log.f64 N/A

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

      5. lower-pow.f64 53.2

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

   4. Applied rewrites 53.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\log \left({y}^{x}\right) - z} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. exp-to-pow N/A

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

      3. remove-double-neg N/A

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

      4. log-rec N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. lower-log.f64 N/A

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

      9. mul-1-neg N/A

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

      10. *-commutative N/A

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

      11. distribute-lft-neg-in N/A

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

      12. log-rec N/A

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

      13. remove-double-neg N/A

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

      14. exp-to-pow N/A

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

      15. lower-pow.f64 43.5

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

   7. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\log \left({y}^{x}\right) - z} \]
   8. Step-by-step derivation

   9. Applied rewrites 86.4%

      \[\leadsto \log y \cdot x - z \]

   if -9.3999999999999994e23 < z < 1.2999999999999999e33

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   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. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 95.4

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

   7. Applied rewrites 95.4%

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

   if 1.2999999999999999e33 < z

   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 82.6

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

   5. Applied rewrites 82.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) - y\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+115}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- z) y)))
   (if (<= z -1.85e+115) t_0 (if (<= z 1.3e+33) (- (* x (log y)) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z - y;
	double tmp;
	if (z <= -1.85e+115) {
		tmp = t_0;
	} else if (z <= 1.3e+33) {
		tmp = (x * log(y)) - 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 = -z - y
    if (z <= (-1.85d+115)) then
        tmp = t_0
    else if (z <= 1.3d+33) then
        tmp = (x * log(y)) - 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 = -z - y;
	double tmp;
	if (z <= -1.85e+115) {
		tmp = t_0;
	} else if (z <= 1.3e+33) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z - y
	tmp = 0
	if z <= -1.85e+115:
		tmp = t_0
	elif z <= 1.3e+33:
		tmp = (x * math.log(y)) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) - y)
	tmp = 0.0
	if (z <= -1.85e+115)
		tmp = t_0;
	elseif (z <= 1.3e+33)
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z - y;
	tmp = 0.0;
	if (z <= -1.85e+115)
		tmp = t_0;
	elseif (z <= 1.3e+33)
		tmp = (x * log(y)) - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) - y), $MachinePrecision]}, If[LessEqual[z, -1.85e+115], t$95$0, If[LessEqual[z, 1.3e+33], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000003e115 or 1.2999999999999999e33 < z

   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 83.5

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

   5. Applied rewrites 83.5%

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

   if -1.85000000000000003e115 < z < 1.2999999999999999e33

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   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. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 92.8

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

   7. Applied rewrites 92.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+115}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 5: 66.2% 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 60.1

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

5. Applied rewrites 60.1%

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

Alternative 6: 34.0% 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 32.8

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

5. Applied rewrites 32.8%

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

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))