Average Error: 0.0 → 0.0
Time: 1.1s
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 r523 = x;
        double r524 = y;
        double r525 = z;
        double r526 = r525 - r523;
        double r527 = r524 * r526;
        double r528 = r523 + r527;
        return r528;
}
↓
double f(double x, double y, double z) {
        double r529 = z;
        double r530 = x;
        double r531 = r529 - r530;
        double r532 = y;
        double r533 = fma(r531, r532, r530);
        return r533;
}

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 2020036 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))