Average Error: 0.0 → 0
Time: 473.0ms
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 r98496 = x;
        double r98497 = r98496 * r98496;
        double r98498 = r98496 + r98497;
        return r98498;
}
↓
double f(double x) {
        double r98499 = x;
        double r98500 = fma(r98499, r98499, r98499);
        return r98500;
}

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 2019362 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (+ 1 x) x)

  (+ x (* x x)))