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

Average Error: 0.1 → 0.1

Time: 7.1s

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 r159318 = x;
        double r159319 = y;
        double r159320 = r159318 * r159319;
        double r159321 = z;
        double r159322 = r159320 + r159321;
        double r159323 = r159322 * r159319;
        double r159324 = t;
        double r159325 = r159323 + r159324;
        return r159325;
}

↓

double f(double x, double y, double z, double t) {
        double r159326 = x;
        double r159327 = y;
        double r159328 = z;
        double r159329 = fma(r159326, r159327, r159328);
        double r159330 = t;
        double r159331 = fma(r159329, r159327, r159330);
        return r159331;
}

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 2020045 +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))