Average Error: 0.0 → 0.0
Time: 10.9s
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 r525858 = x;
        double r525859 = y;
        double r525860 = z;
        double r525861 = r525860 - r525858;
        double r525862 = r525859 * r525861;
        double r525863 = r525858 + r525862;
        return r525863;
}
↓
double f(double x, double y, double z) {
        double r525864 = y;
        double r525865 = z;
        double r525866 = x;
        double r525867 = r525865 - r525866;
        double r525868 = fma(r525864, r525867, r525866);
        return r525868;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))