Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(z - x, y, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(z - x, y, x\right)
double f(double x, double y, double z) {
        double r12227 = x;
        double r12228 = y;
        double r12229 = z;
        double r12230 = r12229 - r12227;
        double r12231 = r12228 * r12230;
        double r12232 = r12227 + r12231;
        return r12232;
}
↓
double f(double x, double y, double z) {
        double r12233 = z;
        double r12234 = x;
        double r12235 = r12233 - r12234;
        double r12236 = y;
        double r12237 = fma(r12235, r12236, r12234);
        return r12237;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))