Average Error: 0.0 → 0
Time: 2.8m
Precision: 64
\[0.0 \le x \le 2.0\]
\[x + x \cdot x\]
↓
\[\mathsf{fma}\left(x, x, x\right)\]
x + x \cdot x
↓
\mathsf{fma}\left(x, x, x\right)
double f(double x) {
        double r3861506 = x;
        double r3861507 = r3861506 * r3861506;
        double r3861508 = r3861506 + r3861507;
        return r3861508;
}
↓
double f(double x) {
        double r3861509 = x;
        double r3861510 = fma(r3861509, r3861509, r3861509);
        return r3861510;
}

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 2019165 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

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

  (+ x (* x x)))