Expression 2, p15

Average Error: 0.0 → 0

Time: 916.0ms

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 r2009454 = x;
        double r2009455 = r2009454 * r2009454;
        double r2009456 = r2009454 + r2009455;
        return r2009456;
}

↓

double f(double x) {
        double r2009457 = x;
        double r2009458 = fma(r2009457, r2009457, r2009457);
        return r2009458;
}

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 2019152 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))