Average Error: 0.0 → 0
Time: 934.0ms
Precision: 64
\[0 \le x \le 2\]
\[x + x \cdot x\]
↓
\[\mathsf{fma}\left(x, x, x\right)\]
x + x \cdot x
↓
\mathsf{fma}\left(x, x, x\right)
double f(double x) {
        double r1927765 = x;
        double r1927766 = r1927765 * r1927765;
        double r1927767 = r1927765 + r1927766;
        return r1927767;
}
↓
double f(double x) {
        double r1927768 = x;
        double r1927769 = fma(r1927768, r1927768, r1927768);
        return r1927769;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))