Average Error: 0.0 → 0
Time: 3.8s
Precision: 64
\[0.0 \le x \le 2\]
\[x + x \cdot x\]
↓
\[\mathsf{fma}\left(x, x, x\right)\]
x + x \cdot x
↓
\mathsf{fma}\left(x, x, x\right)
double f(double x) {
        double r2898990 = x;
        double r2898991 = r2898990 * r2898990;
        double r2898992 = r2898990 + r2898991;
        return r2898992;
}
↓
double f(double x) {
        double r2898993 = x;
        double r2898994 = fma(r2898993, r2898993, r2898993);
        return r2898994;
}

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0
\[\left(1 + x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

  :herbie-target
  (* (+ 1.0 x) x)

  (+ x (* x x)))