Average Error: 0.0 → 0.0
Time: 26.4s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \mathsf{fma}\left(x, x, x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \mathsf{fma}\left(x, x, x\right)
double f(double x) {
        double r124360 = x;
        double r124361 = r124360 * r124360;
        double r124362 = r124360 * r124361;
        double r124363 = r124362 + r124361;
        return r124363;
}
↓
double f(double x) {
        double r124364 = x;
        double r124365 = fma(r124364, r124364, r124364);
        double r124366 = r124364 * r124365;
        return r124366;
}

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x, x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto x \cdot \mathsf{fma}\left(x, x, x\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

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