Average Error: 0.0 → 0.0
Time: 679.0ms
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2
double f(double x, double y) {
        double r579060 = 2.0;
        double r579061 = x;
        double r579062 = r579061 * r579061;
        double r579063 = y;
        double r579064 = r579061 * r579063;
        double r579065 = r579062 + r579064;
        double r579066 = r579060 * r579065;
        return r579066;
}
↓
double f(double x, double y) {
        double r579067 = x;
        double r579068 = y;
        double r579069 = r579067 * r579068;
        double r579070 = fma(r579067, r579067, r579069);
        double r579071 = 2.0;
        double r579072 = r579070 * r579071;
        return r579072;
}

Error

Bits error versus x

Bits error versus y

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

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