Average Error: 0.1 → 0.1
Time: 16.3s
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 r7578457 = x;
        double r7578458 = y;
        double r7578459 = r7578457 * r7578458;
        double r7578460 = z;
        double r7578461 = r7578459 + r7578460;
        double r7578462 = r7578461 * r7578458;
        double r7578463 = t;
        double r7578464 = r7578462 + r7578463;
        return r7578464;
}
↓
double f(double x, double y, double z, double t) {
        double r7578465 = y;
        double r7578466 = x;
        double r7578467 = z;
        double r7578468 = fma(r7578465, r7578466, r7578467);
        double r7578469 = t;
        double r7578470 = fma(r7578465, r7578468, r7578469);
        return r7578470;
}

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 2019170 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))