Average Error: 0.0 → 0.0
Time: 16.3s
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 r986972 = x;
        double r986973 = y;
        double r986974 = z;
        double r986975 = r986974 - r986972;
        double r986976 = r986973 * r986975;
        double r986977 = r986972 + r986976;
        return r986977;
}
↓
double f(double x, double y, double z) {
        double r986978 = y;
        double r986979 = z;
        double r986980 = x;
        double r986981 = r986979 - r986980;
        double r986982 = fma(r986978, r986981, r986980);
        return r986982;
}

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 2019171 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))