Average Error: 0.0 → 0
Time: 1.0s
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 r2451844 = x;
        double r2451845 = r2451844 * r2451844;
        double r2451846 = r2451844 + r2451845;
        return r2451846;
}
↓
double f(double x) {
        double r2451847 = x;
        double r2451848 = fma(r2451847, r2451847, r2451847);
        return r2451848;
}

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 2019144 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

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

  (+ x (* x x)))