Expression 2, p15

Average Error: 0.0 → 0

Time: 379.0ms

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 r93650 = x;
        double r93651 = r93650 * r93650;
        double r93652 = r93650 + r93651;
        return r93652;
}

↓

double f(double x) {
        double r93653 = x;
        double r93654 = fma(r93653, r93653, r93653);
        return r93654;
}

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 2019350 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

  (+ x (* x x)))