Average Error: 0.0 → 0.0
Time: 8.9s
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 r8294 = x;
        double r8295 = y;
        double r8296 = z;
        double r8297 = r8296 - r8294;
        double r8298 = r8295 * r8297;
        double r8299 = r8294 + r8298;
        return r8299;
}
↓
double f(double x, double y, double z) {
        double r8300 = y;
        double r8301 = z;
        double r8302 = x;
        double r8303 = r8301 - r8302;
        double r8304 = fma(r8300, r8303, r8302);
        return r8304;
}

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 2019179 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))