Average Error: 0.1 → 0.1
Time: 14.7s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)
double f(double x, double y, double z, double t) {
        double r150310 = x;
        double r150311 = y;
        double r150312 = r150310 * r150311;
        double r150313 = z;
        double r150314 = r150312 + r150313;
        double r150315 = r150314 * r150311;
        double r150316 = t;
        double r150317 = r150315 + r150316;
        return r150317;
}
↓
double f(double x, double y, double z, double t) {
        double r150318 = y;
        double r150319 = x;
        double r150320 = z;
        double r150321 = fma(r150318, r150319, r150320);
        double r150322 = t;
        double r150323 = fma(r150318, r150321, r150322);
        return r150323;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))