Average Error: 0.0 → 0
Time: 10.3s
Precision: 64
\[x \cdot \left(y + 1\right)\]
↓
\[\mathsf{fma}\left(x, y, 1 \cdot x\right)\]
x \cdot \left(y + 1\right)
↓
\mathsf{fma}\left(x, y, 1 \cdot x\right)
double f(double x, double y) {
        double r635644 = x;
        double r635645 = y;
        double r635646 = 1.0;
        double r635647 = r635645 + r635646;
        double r635648 = r635644 * r635647;
        return r635648;
}
↓
double f(double x, double y) {
        double r635649 = x;
        double r635650 = y;
        double r635651 = 1.0;
        double r635652 = r635651 * r635649;
        double r635653 = fma(r635649, r635650, r635652);
        return r635653;
}

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. Simplified0.0

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

  6. Applied fma-def0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019347 +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)))