Average Error: 0.1 → 0.1
Time: 3.6s
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 f(double x, double y, double z) {
        double r14450 = x;
        double r14451 = y;
        double r14452 = log(r14451);
        double r14453 = r14450 * r14452;
        double r14454 = z;
        double r14455 = r14453 - r14454;
        double r14456 = r14455 - r14451;
        return r14456;
}
↓
double f(double x, double y, double z) {
        double r14457 = x;
        double r14458 = y;
        double r14459 = log(r14458);
        double r14460 = z;
        double r14461 = -r14460;
        double r14462 = fma(r14457, r14459, r14461);
        double r14463 = r14462 - r14458;
        return r14463;
}

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. 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))