Average Error: 0.0 → 0.0
Time: 8.7s
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 r326214 = x;
        double r326215 = y;
        double r326216 = z;
        double r326217 = r326216 - r326214;
        double r326218 = r326215 * r326217;
        double r326219 = r326214 + r326218;
        return r326219;
}
↓
double f(double x, double y, double z) {
        double r326220 = y;
        double r326221 = z;
        double r326222 = x;
        double r326223 = r326221 - r326222;
        double r326224 = fma(r326220, r326223, r326222);
        return r326224;
}

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 2019192 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))