Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Average Error: 0.1 → 0.1

Time: 10.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(x \cdot y + z\right) \cdot y + t\]

↓

\[\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]

C

double f(double x, double y, double z, double t) {
        double r187017 = x;
        double r187018 = y;
        double r187019 = r187017 * r187018;
        double r187020 = z;
        double r187021 = r187019 + r187020;
        double r187022 = r187021 * r187018;
        double r187023 = t;
        double r187024 = r187022 + r187023;
        return r187024;
}

↓

double f(double x, double y, double z, double t) {
        double r187025 = x;
        double r187026 = y;
        double r187027 = z;
        double r187028 = fma(r187025, r187026, r187027);
        double r187029 = t;
        double r187030 = fma(r187028, r187026, r187029);
        return r187030;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Initial program 0.1

   \[\left(x \cdot y + z\right) \cdot y + t\]

2. Simplified 0.1

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

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))