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

Average Error: 0.1 → 0.1

Time: 8.2s

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 r139970 = x;
        double r139971 = y;
        double r139972 = r139970 * r139971;
        double r139973 = z;
        double r139974 = r139972 + r139973;
        double r139975 = r139974 * r139971;
        double r139976 = t;
        double r139977 = r139975 + r139976;
        return r139977;
}

↓

double f(double x, double y, double z, double t) {
        double r139978 = x;
        double r139979 = y;
        double r139980 = z;
        double r139981 = fma(r139978, r139979, r139980);
        double r139982 = t;
        double r139983 = fma(r139981, r139979, r139982);
        return r139983;
}

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 2020046 +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))