Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\mathsf{fma}\left(x, \log y, -z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\mathsf{fma}\left(x, \log y, -z\right) - y
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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y\]
  2. Using strategy rm

  3. Applied fma-neg0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))