Average Error: 0.0 → 0.0
Time: 15.5s
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 r15514 = x;
        double r15515 = y;
        double r15516 = z;
        double r15517 = r15516 - r15514;
        double r15518 = r15515 * r15517;
        double r15519 = r15514 + r15518;
        return r15519;
}
↓
double f(double x, double y, double z) {
        double r15520 = z;
        double r15521 = x;
        double r15522 = r15520 - r15521;
        double r15523 = y;
        double r15524 = fma(r15522, r15523, r15521);
        return r15524;
}

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 2019305 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))