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

Average Error: 0.13% → 0.15%

Time: 9.2s

Precision: binary64

Cost: 7040

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (- (- (* (log (/ 1.0 y)) (- x)) z) y))

C

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

↓

double code(double x, double y, double z) {
	return ((log((1.0 / y)) * -x) - 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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((log((1.0d0 / y)) * -x) - z) - y
end function

Java

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

↓

public static double code(double x, double y, double z) {
	return ((Math.log((1.0 / y)) * -x) - z) - y;
}

Python

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

↓

def code(x, y, z):
	return ((math.log((1.0 / y)) * -x) - z) - y

Julia

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

↓

function code(x, y, z)
	return Float64(Float64(Float64(log(Float64(1.0 / y)) * Float64(-x)) - z) - y)
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = ((log((1.0 / y)) * -x) - z) - y;
end

Wolfram

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

↓

code[x_, y_, z_] := N[(N[(N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 0.13

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

2. Taylor expanded in y around inf 0.15

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

3. Final simplification 0.15

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

Alternatives

Alternative 1
Error	16.01%
Cost	7250

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+135} \lor \neg \left(z \leq -2.15 \cdot 10^{+71} \lor \neg \left(z \leq -0.00045\right) \land z \leq 6 \cdot 10^{+17}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 2
Error	20.61%
Cost	7122

\[\begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+165} \lor \neg \left(x \leq 4.6 \cdot 10^{+97} \lor \neg \left(x \leq 1.7 \cdot 10^{+137}\right) \land x \leq 1.3 \cdot 10^{+190}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 3
Error	0.13%
Cost	6848

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

Alternative 4
Error	33.04%
Cost	256

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

Alternative 5
Error	65.4%
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))