Expression 2, p15

Average Error: 0.0 → 0

Time: 1.6m

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 r2469127 = x;
        double r2469128 = r2469127 * r2469127;
        double r2469129 = r2469127 + r2469128;
        return r2469129;
}

↓

double f(double x) {
        double r2469130 = x;
        double r2469131 = fma(r2469130, r2469130, r2469130);
        return r2469131;
}

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 2019168 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))