Average Error: 0.0 → 0.0
Time: 9.8s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\mathsf{fma}\left(x + y, x, \left(x + y\right) \cdot y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\mathsf{fma}\left(x + y, x, \left(x + y\right) \cdot y\right)
double f(double x, double y) {
        double r444714 = x;
        double r444715 = y;
        double r444716 = r444714 + r444715;
        double r444717 = r444716 * r444716;
        return r444717;
}
↓
double f(double x, double y) {
        double r444718 = x;
        double r444719 = y;
        double r444720 = r444718 + r444719;
        double r444721 = r444720 * r444719;
        double r444722 = fma(r444720, r444718, r444721);
        return r444722;
}

Error

Bits error versus x

Bits error versus y

Target

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

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(x + y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot x + \left(x + y\right) \cdot y}\]
  4. Using strategy rm

  5. Applied fma-def0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2 (* y x))))

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