Average Error: 0.0 → 0.0
Time: 6.6s
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 r4215549 = x;
        double r4215550 = y;
        double r4215551 = z;
        double r4215552 = r4215551 + r4215549;
        double r4215553 = r4215550 * r4215552;
        double r4215554 = r4215549 + r4215553;
        return r4215554;
}
↓
double f(double x, double y, double z) {
        double r4215555 = y;
        double r4215556 = x;
        double r4215557 = z;
        double r4215558 = r4215556 + r4215557;
        double r4215559 = fma(r4215555, r4215558, r4215556);
        return r4215559;
}

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 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))