Average Error: 0.1 → 0.1
Time: 9.6s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y \]
↓
\[\mathsf{fma}\left(x, \log y, -z\right) - y \]
\left(x \cdot \log y - z\right) - y
↓
\mathsf{fma}\left(x, \log y, -z\right) - y

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z) :precision binary64 (- (fma x (log y) (- z)) y))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	return fma(x, log(y), -z) - y;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Applied fma-neg_binary640.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2022077 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))