Average Error: 0.1 → 0.1
Time: 18.1s
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 r4470508 = x;
        double r4470509 = y;
        double r4470510 = r4470508 * r4470509;
        double r4470511 = z;
        double r4470512 = r4470510 + r4470511;
        double r4470513 = r4470512 * r4470509;
        double r4470514 = t;
        double r4470515 = r4470513 + r4470514;
        return r4470515;
}
↓
double f(double x, double y, double z, double t) {
        double r4470516 = y;
        double r4470517 = x;
        double r4470518 = z;
        double r4470519 = fma(r4470516, r4470517, r4470518);
        double r4470520 = t;
        double r4470521 = fma(r4470516, r4470519, r4470520);
        return r4470521;
}

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 2019192 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))