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

Average Error: 0.1 → 0.1

Time: 8.9s

Precision: binary64

Cost: 13184

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma (log 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 fma(log(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 fma(log(y), x, Float64(Float64(-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[Log[y], $MachinePrecision] * x + N[((-z) - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	9.6
Cost	7248

\[\begin{array}{l} t_0 := \log y \cdot x\\ t_1 := t_0 - z\\ \mathbf{if}\;x \leq -4.897597566761816 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.9320526182820556 \cdot 10^{+55}:\\ \;\;\;\;t_0 - y\\ \mathbf{elif}\;x \leq -4.576675431855361 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2409318134142352 \cdot 10^{-11}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.6
Cost	6984

\[\begin{array}{l} t_0 := \log y \cdot x - z\\ \mathbf{if}\;x \leq -4.576675431855361 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.2409318134142352 \cdot 10^{-11}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	13.4
Cost	6856

\[\begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -8.003814958431991 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.119936313382802 \cdot 10^{+155}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.1
Cost	6848

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

Alternative 5
Error	30.6
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -3.597000426817767 \cdot 10^{+37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.183362055643945 \cdot 10^{-61}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6
Error	21.1
Cost	256

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

Alternative 7
Error	41.8
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))