Average Error: 0.0 → 0.0
Time: 7.3s
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 r17057263 = x;
        double r17057264 = 2.0;
        double r17057265 = r17057263 * r17057264;
        double r17057266 = r17057263 * r17057263;
        double r17057267 = r17057265 + r17057266;
        double r17057268 = y;
        double r17057269 = r17057268 * r17057268;
        double r17057270 = r17057267 + r17057269;
        return r17057270;
}
↓
double f(double x, double y) {
        double r17057271 = y;
        double r17057272 = x;
        double r17057273 = 2.0;
        double r17057274 = r17057273 + r17057272;
        double r17057275 = r17057272 * r17057274;
        double r17057276 = fma(r17057271, r17057271, r17057275);
        return r17057276;
}

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 2019171 +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)))