Expression 2, p15

Average Error: 0.0 → 0

Time: 1.6m

Precision: 64

\[0 \le x \le 2\]

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r3158285 = x;
        double r3158286 = r3158285 * r3158285;
        double r3158287 = r3158285 + r3158286;
        return r3158287;
}

↓

double f(double x) {
        double r3158288 = x;
        double r3158289 = fma(r3158288, r3158288, r3158288);
        return r3158289;
}

Error

Bits error versus x

Target

Original	0.0
Target	0.0
Herbie	0

\[\left(1.0 + x\right) \cdot x\]

Derivation

1. Initial program 0.0

   \[x + x \cdot x\]

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))