Average Error: 0.0 → 0.0
Time: 6.3s
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 r8481 = x;
        double r8482 = y;
        double r8483 = z;
        double r8484 = r8483 - r8481;
        double r8485 = r8482 * r8484;
        double r8486 = r8481 + r8485;
        return r8486;
}
↓
double f(double x, double y, double z) {
        double r8487 = z;
        double r8488 = x;
        double r8489 = r8487 - r8488;
        double r8490 = y;
        double r8491 = fma(r8489, r8490, r8488);
        return r8491;
}

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))))