Average Error: 0.0 → 0.0
Time: 2.9s
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 r13315 = x;
        double r13316 = y;
        double r13317 = z;
        double r13318 = r13317 - r13315;
        double r13319 = r13316 * r13318;
        double r13320 = r13315 + r13319;
        return r13320;
}
↓
double f(double x, double y, double z) {
        double r13321 = z;
        double r13322 = x;
        double r13323 = r13321 - r13322;
        double r13324 = y;
        double r13325 = fma(r13323, r13324, r13322);
        return r13325;
}

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 2019362 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))