Expression 2, p15

Average Error: 0.0 → 0

Time: 860.0ms

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 r2004856 = x;
        double r2004857 = r2004856 * r2004856;
        double r2004858 = r2004856 + r2004857;
        return r2004858;
}

↓

double f(double x) {
        double r2004859 = x;
        double r2004860 = fma(r2004859, r2004859, r2004859);
        return r2004860;
}

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 2019133 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))