Average Error: 0.0 → 0.0
Time: 852.0ms
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 r130307 = x;
        double r130308 = y;
        double r130309 = z;
        double r130310 = r130309 + r130307;
        double r130311 = r130308 * r130310;
        double r130312 = r130307 + r130311;
        return r130312;
}
↓
double f(double x, double y, double z) {
        double r130313 = y;
        double r130314 = z;
        double r130315 = x;
        double r130316 = r130314 + r130315;
        double r130317 = fma(r130313, r130316, r130315);
        return r130317;
}

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 2020034 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))