Expression 2, p15

Average Error: 0.0 → 0

Time: 352.0ms

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

\[0.0 \le x \le 2\]

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r110735 = x;
        double r110736 = r110735 * r110735;
        double r110737 = r110735 + r110736;
        return r110737;
}

↓

double f(double x) {
        double r110738 = x;
        double r110739 = fma(r110738, r110738, r110738);
        return r110739;
}

Error

Bits error versus x

Target

Original	0.0
Target	0.0
Herbie	0

\[\left(1 + x\right) \cdot x\]

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 2020042 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

  (+ x (* x x)))