Average Error: 0.1 → 0.1
Time: 18.2s
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 r6588945 = x;
        double r6588946 = y;
        double r6588947 = r6588945 * r6588946;
        double r6588948 = z;
        double r6588949 = r6588947 + r6588948;
        double r6588950 = r6588949 * r6588946;
        double r6588951 = t;
        double r6588952 = r6588950 + r6588951;
        return r6588952;
}
↓
double f(double x, double y, double z, double t) {
        double r6588953 = y;
        double r6588954 = x;
        double r6588955 = z;
        double r6588956 = fma(r6588953, r6588954, r6588955);
        double r6588957 = t;
        double r6588958 = fma(r6588953, r6588956, r6588957);
        return r6588958;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))