Average Error: 0.0 → 0.0
Time: 20.6s
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 r914531 = x;
        double r914532 = y;
        double r914533 = z;
        double r914534 = r914533 - r914531;
        double r914535 = r914532 * r914534;
        double r914536 = r914531 + r914535;
        return r914536;
}
↓
double f(double x, double y, double z) {
        double r914537 = y;
        double r914538 = z;
        double r914539 = x;
        double r914540 = r914538 - r914539;
        double r914541 = fma(r914537, r914540, r914539);
        return r914541;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))