Average Error: 0.1 → 0.1
Time: 19.8s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)
double f(double x, double y, double z, double t) {
        double r20683010 = x;
        double r20683011 = y;
        double r20683012 = r20683010 * r20683011;
        double r20683013 = z;
        double r20683014 = r20683012 + r20683013;
        double r20683015 = r20683014 * r20683011;
        double r20683016 = t;
        double r20683017 = r20683015 + r20683016;
        return r20683017;
}
↓
double f(double x, double y, double z, double t) {
        double r20683018 = x;
        double r20683019 = y;
        double r20683020 = z;
        double r20683021 = fma(r20683018, r20683019, r20683020);
        double r20683022 = t;
        double r20683023 = fma(r20683021, r20683019, r20683022);
        return r20683023;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))