Average Error: 0.0 → 0.0
Time: 6.0s
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 r8474 = x;
        double r8475 = y;
        double r8476 = z;
        double r8477 = r8476 - r8474;
        double r8478 = r8475 * r8477;
        double r8479 = r8474 + r8478;
        return r8479;
}
↓
double f(double x, double y, double z) {
        double r8480 = z;
        double r8481 = x;
        double r8482 = r8480 - r8481;
        double r8483 = y;
        double r8484 = fma(r8482, r8483, r8481);
        return r8484;
}

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 2019326 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))