Expression 2, p15

Average Error: 0.0 → 0

Time: 1.1s

Precision: 64

\[0 \le x \le 2\]

Math

\[x + x \cdot x\]

↓

\[(x \cdot x + x)_*\]

C

double f(double x) {
        double r7784701 = x;
        double r7784702 = r7784701 * r7784701;
        double r7784703 = r7784701 + r7784702;
        return r7784703;
}

↓

double f(double x) {
        double r7784704 = x;
        double r7784705 = fma(r7784704, r7784704, r7784704);
        return r7784705;
}

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

   \[\leadsto \color{blue}{(x \cdot x + x)_*}\]

3. Final simplification 0

   \[\leadsto (x \cdot x + x)_*\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))