Average Error: 0.1 → 0.1
Time: 37.2s
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 r9285160 = x;
        double r9285161 = y;
        double r9285162 = r9285160 * r9285161;
        double r9285163 = z;
        double r9285164 = r9285162 + r9285163;
        double r9285165 = r9285164 * r9285161;
        double r9285166 = t;
        double r9285167 = r9285165 + r9285166;
        return r9285167;
}
↓
double f(double x, double y, double z, double t) {
        double r9285168 = y;
        double r9285169 = x;
        double r9285170 = z;
        double r9285171 = fma(r9285168, r9285169, r9285170);
        double r9285172 = t;
        double r9285173 = fma(r9285168, r9285171, r9285172);
        return r9285173;
}

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 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))