Average Error: 0.0 → 0.0
Time: 10.1s
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 r220083 = x;
        double r220084 = y;
        double r220085 = z;
        double r220086 = r220085 - r220083;
        double r220087 = r220084 * r220086;
        double r220088 = r220083 + r220087;
        return r220088;
}
↓
double f(double x, double y, double z) {
        double r220089 = y;
        double r220090 = z;
        double r220091 = x;
        double r220092 = r220090 - r220091;
        double r220093 = fma(r220089, r220092, r220091);
        return r220093;
}

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 2019158 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))