Average Error: 0.0 → 0.0
Time: 636.0ms
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 r535202 = 2.0;
        double r535203 = x;
        double r535204 = r535203 * r535203;
        double r535205 = y;
        double r535206 = r535203 * r535205;
        double r535207 = r535204 + r535206;
        double r535208 = r535202 * r535207;
        return r535208;
}
↓
double f(double x, double y) {
        double r535209 = x;
        double r535210 = y;
        double r535211 = r535209 * r535210;
        double r535212 = fma(r535209, r535209, r535211);
        double r535213 = 2.0;
        double r535214 = r535212 * r535213;
        return r535214;
}

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 2020060 +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))))