Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot (x \cdot x + x)_*\]
double f(double x) {
        double r6906193 = x;
        double r6906194 = r6906193 * r6906193;
        double r6906195 = r6906193 * r6906194;
        double r6906196 = r6906195 + r6906194;
        return r6906196;
}
↓
double f(double x) {
        double r6906197 = x;
        double r6906198 = fma(r6906197, r6906197, r6906197);
        double r6906199 = r6906197 * r6906198;
        return r6906199;
}


x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot (x \cdot x + x)_*

Error

Bits error versus x

Target

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

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

  (+ (* x (* x x)) (* x x)))