Average Error: 0.0 → 0
Time: 1.5s
Precision: 64
\[x + x \cdot x\]
↓
\[(x \cdot x + x)_*\]
double f(double x) {
        double r12993384 = x;
        double r12993385 = r12993384 * r12993384;
        double r12993386 = r12993384 + r12993385;
        return r12993386;
}
↓
double f(double x) {
        double r12993387 = x;
        double r12993388 = fma(r12993387, r12993387, r12993387);
        return r12993388;
}


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 2019101 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))