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

Percentage Accurate: 99.8% → 99.9%

Time: 8.1s

Alternatives: 7

Speedup: 0.5×

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: 99.9% 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 99.8%

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

   1. sub-neg 99.8%

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

   2. associate--l+ 99.8%

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

   3. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-73} \lor \neg \left(x \leq 3.3 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.1e-73) (not (<= x 3.3e+125)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.1e-73) || !(x <= 3.3e+125)) {
		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 <= (-1.1d-73)) .or. (.not. (x <= 3.3d+125))) 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 <= -1.1e-73) || !(x <= 3.3e+125)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.1e-73) or not (x <= 3.3e+125):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.1e-73) || !(x <= 3.3e+125))
		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 <= -1.1e-73) || ~((x <= 3.3e+125)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.1e-73], N[Not[LessEqual[x, 3.3e+125]], $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 < -1.1e-73 or 3.30000000000000005e125 < x

   1. Initial program 99.7%

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

      1. associate--l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--r+ 99.7%

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

   3. Simplified 99.7%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around 0 82.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(\log y \cdot x\right) - y} \]
   7. Step-by-step derivation

      1. pow-base-1 82.5%

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

      2. associate-*r* 82.5%

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

      3. *-lft-identity 82.5%

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

   8. Simplified 82.5%

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

   if -1.1e-73 < x < 3.30000000000000005e125

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 90.7%

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

      1. neg-mul-1 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-73} \lor \neg \left(x \leq 3.3 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 3: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000112 \lor \neg \left(x \leq 2.7 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.000112) (not (<= x 2.7e+85)))
   (- (* x (log y)) z)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000112) || !(x <= 2.7e+85)) {
		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 ((x <= (-0.000112d0)) .or. (.not. (x <= 2.7d+85))) 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 ((x <= -0.000112) || !(x <= 2.7e+85)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.000112) or not (x <= 2.7e+85):
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.000112) || !(x <= 2.7e+85))
		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 ((x <= -0.000112) || ~((x <= 2.7e+85)))
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.000112], N[Not[LessEqual[x, 2.7e+85]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999998e-4 or 2.69999999999999983e85 < x

   1. Initial program 99.7%

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

      1. associate--l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--r+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 89.1%

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

   if -1.11999999999999998e-4 < x < 2.69999999999999983e85

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 91.0%

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

      1. neg-mul-1 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000112 \lor \neg \left(x \leq 2.7 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - y) - z;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - y) - z

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate--l- 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--r+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 5: 50.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+162}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-50}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+162) (- z) (if (<= z 2.2e-50) (- y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+162) {
		tmp = -z;
	} else if (z <= 2.2e-50) {
		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 <= (-1.9d+162)) then
        tmp = -z
    else if (z <= 2.2d-50) 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 <= -1.9e+162) {
		tmp = -z;
	} else if (z <= 2.2e-50) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+162:
		tmp = -z
	elif z <= 2.2e-50:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+162)
		tmp = Float64(-z);
	elseif (z <= 2.2e-50)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+162)
		tmp = -z;
	elseif (z <= 2.2e-50)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+162], (-z), If[LessEqual[z, 2.2e-50], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000012e162 or 2.1999999999999999e-50 < z

   1. Initial program 99.9%

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

      1. associate--l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. mul-1-neg 64.0%

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

   6. Simplified 64.0%

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

   if -1.90000000000000012e162 < z < 2.1999999999999999e-50

   1. Initial program 99.8%

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

      1. associate--l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 98.8%

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

      2. pow3 98.9%

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

   5. Applied egg-rr 98.9%

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

   6. Taylor expanded in y around inf 39.1%

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

      1. neg-mul-1 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+162}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-50}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 66.5% 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. Step-by-step derivation

   1. associate--l- 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--r+ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 61.9%

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

   1. neg-mul-1 61.9%

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

6. Simplified 61.9%

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

7. Final simplification 61.9%

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

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 99.8%

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

   1. associate--l- 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--r+ 99.8%

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

3. Simplified 99.8%

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

   1. add-cube-cbrt 99.1%

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

   2. pow3 99.1%

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

5. Applied egg-rr 99.1%

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

6. Taylor expanded in y around inf 29.6%

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

   1. neg-mul-1 29.6%

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

8. Simplified 29.6%

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

9. Final simplification 29.6%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))