Average Error: 0.0 → 0.0
Time: 4.3s
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 r8411 = x;
        double r8412 = y;
        double r8413 = z;
        double r8414 = r8413 - r8411;
        double r8415 = r8412 * r8414;
        double r8416 = r8411 + r8415;
        return r8416;
}
↓
double f(double x, double y, double z) {
        double r8417 = z;
        double r8418 = x;
        double r8419 = r8417 - r8418;
        double r8420 = y;
        double r8421 = fma(r8419, r8420, r8418);
        return r8421;
}

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 2019347 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))