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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+54} \lor \neg \left(x \leq 2.9 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+54) (not (<= x 2.9e+147)))
   (- (* x (log y)) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+54) || !(x <= 2.9e+147)) {
		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 <= (-5.5d+54)) .or. (.not. (x <= 2.9d+147))) 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 <= -5.5e+54) || !(x <= 2.9e+147)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+54) or not (x <= 2.9e+147):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+54) || !(x <= 2.9e+147))
		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 <= -5.5e+54) || ~((x <= 2.9e+147)))
		tmp = (x * log(y)) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+54], N[Not[LessEqual[x, 2.9e+147]], $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 < -5.50000000000000026e54 or 2.8999999999999998e147 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 87.7%

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

   if -5.50000000000000026e54 < x < 2.8999999999999998e147

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. distribute-neg-in 88.1%

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

      3. +-commutative 88.1%

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

      4. sub-neg 88.1%

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

   4. Simplified 88.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+54} \lor \neg \left(x \leq 2.9 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 3: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+38} \lor \neg \left(z \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;t_0 - z\\ \mathbf{else}:\\ \;\;\;\;t_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (or (<= z -4.2e+38) (not (<= z 5.2e-15))) (- t_0 z) (- t_0 y))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if ((z <= -4.2e+38) || !(z <= 5.2e-15)) {
		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 ((z <= (-4.2d+38)) .or. (.not. (z <= 5.2d-15))) 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 ((z <= -4.2e+38) || !(z <= 5.2e-15)) {
		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 (z <= -4.2e+38) or not (z <= 5.2e-15):
		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 ((z <= -4.2e+38) || !(z <= 5.2e-15))
		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 ((z <= -4.2e+38) || ~((z <= 5.2e-15)))
		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[z, -4.2e+38], N[Not[LessEqual[z, 5.2e-15]], $MachinePrecision]], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e38 or 5.20000000000000009e-15 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.1%

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

   if -4.2e38 < z < 5.20000000000000009e-15

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 91.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+38} \lor \neg \left(z \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 4: 52.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-16}:\\ \;\;\;\;z - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e+37) (- z) (if (<= z 4.3e-16) (- z y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e+37) {
		tmp = -z;
	} else if (z <= 4.3e-16) {
		tmp = z - 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 <= (-7.8d+37)) then
        tmp = -z
    else if (z <= 4.3d-16) then
        tmp = z - 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 <= -7.8e+37) {
		tmp = -z;
	} else if (z <= 4.3e-16) {
		tmp = z - y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e+37:
		tmp = -z
	elif z <= 4.3e-16:
		tmp = z - y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e+37)
		tmp = Float64(-z);
	elseif (z <= 4.3e-16)
		tmp = Float64(z - y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e+37)
		tmp = -z;
	elseif (z <= 4.3e-16)
		tmp = z - y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e+37], (-z), If[LessEqual[z, 4.3e-16], N[(z - y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -7.7999999999999997e37 or 4.2999999999999999e-16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 61.5%

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

      1. mul-1-neg 61.5%

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

   4. Simplified 61.5%

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

   if -7.7999999999999997e37 < z < 4.2999999999999999e-16

   1. Initial program 99.8%

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

      1. flip-- 74.5%

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

      2. div-inv 74.4%

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

      3. difference-of-squares 74.4%

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

      4. add-sqr-sqrt 29.9%

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

      5. sqrt-unprod 68.5%

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

      6. sqr-neg 68.5%

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

      7. sqrt-unprod 38.6%

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

      8. add-sqr-sqrt 67.5%

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

      9. sub-neg 67.5%

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

      10. pow2 67.5%

          \[\leadsto \color{blue}{{\left(x \cdot \log y - z\right)}^{2}} \cdot \frac{1}{x \cdot \log y + z} - y \]

      11. fma-neg 67.5%

          \[\leadsto {\color{blue}{\left(\mathsf{fma}\left(x, \log y, -z\right)\right)}}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      12. add-sqr-sqrt 38.6%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right)\right)}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      13. sqrt-unprod 67.5%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)\right)}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      14. sqr-neg 67.5%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, \sqrt{\color{blue}{z \cdot z}}\right)\right)}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      15. sqrt-unprod 28.9%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, \color{blue}{\sqrt{z} \cdot \sqrt{z}}\right)\right)}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      16. add-sqr-sqrt 67.5%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, \color{blue}{z}\right)\right)}^{2} \cdot \frac{1}{x \cdot \log y + z} - y \]

      17. fma-def 67.5%

          \[\leadsto {\left(\mathsf{fma}\left(x, \log y, z\right)\right)}^{2} \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(x, \log y, z\right)}} - y \]

   3. Applied egg-rr 67.5%

      \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(x, \log y, z\right)\right)}^{2} \cdot \frac{1}{\mathsf{fma}\left(x, \log y, z\right)}} - y \]

   4. Taylor expanded in x around 0 46.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-16}:\\ \;\;\;\;z - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 52.0% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-16}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8e+37) (- z) (if (<= z 4.3e-16) (- y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+37) {
		tmp = -z;
	} else if (z <= 4.3e-16) {
		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 <= (-6.8d+37)) then
        tmp = -z
    else if (z <= 4.3d-16) 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 <= -6.8e+37) {
		tmp = -z;
	} else if (z <= 4.3e-16) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8e+37:
		tmp = -z
	elif z <= 4.3e-16:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8e+37)
		tmp = Float64(-z);
	elseif (z <= 4.3e-16)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.8e+37)
		tmp = -z;
	elseif (z <= 4.3e-16)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8e+37], (-z), If[LessEqual[z, 4.3e-16], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000011e37 or 4.2999999999999999e-16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 61.5%

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

      1. mul-1-neg 61.5%

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

   4. Simplified 61.5%

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

   if -6.80000000000000011e37 < z < 4.2999999999999999e-16

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   4. Simplified 46.5%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-16}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 65.9% 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. Taylor expanded in x around 0 63.6%

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

   1. mul-1-neg 63.6%

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

   2. distribute-neg-in 63.6%

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

   3. +-commutative 63.6%

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

   4. sub-neg 63.6%

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

4. Simplified 63.6%

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

5. Final simplification 63.6%

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

Alternative 7: 34.4% 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. Taylor expanded in y around inf 30.8%

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

   1. neg-mul-1 30.8%

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

4. Simplified 30.8%

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

5. Final simplification 30.8%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))