Average Error: 0.0 → 0.0
Time: 870.0ms
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 r534 = x;
        double r535 = y;
        double r536 = z;
        double r537 = r536 - r534;
        double r538 = r535 * r537;
        double r539 = r534 + r538;
        return r539;
}
↓
double f(double x, double y, double z) {
        double r540 = z;
        double r541 = x;
        double r542 = r540 - r541;
        double r543 = y;
        double r544 = fma(r542, r543, r541);
        return r544;
}

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 2020001 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))