Average Error: 0.0 → 0
Time: 765.0ms
Precision: 64
\[x + x \cdot x\]
↓
\[(x \cdot x + x)_*\]
double f(double x) {
        double r6906480 = x;
        double r6906481 = r6906480 * r6906480;
        double r6906482 = r6906480 + r6906481;
        return r6906482;
}
↓
double f(double x) {
        double r6906483 = x;
        double r6906484 = fma(r6906483, r6906483, r6906483);
        return r6906484;
}


x + x \cdot x
↓
(x \cdot x + x)_*

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0
\[\left(1.0 + x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))