Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[\mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
\mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)
double f(double x, double y) {
        double r19243484 = x;
        double r19243485 = 2.0;
        double r19243486 = r19243484 * r19243485;
        double r19243487 = r19243484 * r19243484;
        double r19243488 = r19243486 + r19243487;
        double r19243489 = y;
        double r19243490 = r19243489 * r19243489;
        double r19243491 = r19243488 + r19243490;
        return r19243491;
}
↓
double f(double x, double y) {
        double r19243492 = y;
        double r19243493 = x;
        double r19243494 = 2.0;
        double r19243495 = r19243494 + r19243493;
        double r19243496 = r19243493 * r19243495;
        double r19243497 = fma(r19243492, r19243492, r19243496);
        return r19243497;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, \left(2 + x\right) \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, y, x \cdot \left(2 + x\right)\right)\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))