Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, x + z, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, x + z, x\right)
double f(double x, double y, double z) {
        double r4416565 = x;
        double r4416566 = y;
        double r4416567 = z;
        double r4416568 = r4416567 + r4416565;
        double r4416569 = r4416566 * r4416568;
        double r4416570 = r4416565 + r4416569;
        return r4416570;
}
↓
double f(double x, double y, double z) {
        double r4416571 = y;
        double r4416572 = x;
        double r4416573 = z;
        double r4416574 = r4416572 + r4416573;
        double r4416575 = fma(r4416571, r4416574, r4416572);
        return r4416575;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x + z, x\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))