Average Error: 0.0 → 0.0
Time: 6.4s
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 r69598 = x;
        double r69599 = y;
        double r69600 = z;
        double r69601 = r69600 + r69598;
        double r69602 = r69599 * r69601;
        double r69603 = r69598 + r69602;
        return r69603;
}
↓
double f(double x, double y, double z) {
        double r69604 = z;
        double r69605 = x;
        double r69606 = r69604 + r69605;
        double r69607 = y;
        double r69608 = fma(r69606, r69607, r69605);
        return r69608;
}

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 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))