Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(y, z - x, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)
double f(double x, double y, double z) {
        double r326212 = x;
        double r326213 = y;
        double r326214 = z;
        double r326215 = r326214 - r326212;
        double r326216 = r326213 * r326215;
        double r326217 = r326212 + r326216;
        return r326217;
}
↓
double f(double x, double y, double z) {
        double r326218 = y;
        double r326219 = z;
        double r326220 = x;
        double r326221 = r326219 - r326220;
        double r326222 = fma(r326218, r326221, r326220);
        return r326222;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))