Average Error: 0.0 → 0
Time: 779.0ms
Precision: 64
\[x \cdot \left(y + 1\right)\]
↓
\[\mathsf{fma}\left(x, y, x \cdot 1\right)\]
x \cdot \left(y + 1\right)
↓
\mathsf{fma}\left(x, y, x \cdot 1\right)
double f(double x, double y) {
        double r786354 = x;
        double r786355 = y;
        double r786356 = 1.0;
        double r786357 = r786355 + r786356;
        double r786358 = r786354 * r786357;
        return r786358;
}
↓
double f(double x, double y) {
        double r786359 = x;
        double r786360 = y;
        double r786361 = 1.0;
        double r786362 = r786359 * r786361;
        double r786363 = fma(r786359, r786360, r786362);
        return r786363;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0
\[x + x \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(y + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot y + x \cdot 1}\]
  4. Using strategy rm

  5. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, x \cdot 1\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, y, x \cdot 1\right)\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

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

  (* x (+ y 1)))