Average Error: 0.0 → 0.0
Time: 6.5s
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 r17641832 = x;
        double r17641833 = 2.0;
        double r17641834 = r17641832 * r17641833;
        double r17641835 = r17641832 * r17641832;
        double r17641836 = r17641834 + r17641835;
        double r17641837 = y;
        double r17641838 = r17641837 * r17641837;
        double r17641839 = r17641836 + r17641838;
        return r17641839;
}
↓
double f(double x, double y) {
        double r17641840 = y;
        double r17641841 = x;
        double r17641842 = 2.0;
        double r17641843 = r17641842 + r17641841;
        double r17641844 = r17641841 * r17641843;
        double r17641845 = fma(r17641840, r17641840, r17641844);
        return r17641845;
}

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 2019179 +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)))