Expression 2, p15

Average Error: 0.0 → 0

Time: 351.0ms

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 r104829 = x;
        double r104830 = r104829 * r104829;
        double r104831 = r104829 + r104830;
        return r104831;
}

↓

double f(double x) {
        double r104832 = x;
        double r104833 = fma(r104832, r104832, r104832);
        return r104833;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

  (+ x (* x x)))