Average Error: 0.1 → 0.1
Time: 46.4s
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 r9474209 = x;
        double r9474210 = y;
        double r9474211 = r9474209 * r9474210;
        double r9474212 = z;
        double r9474213 = r9474211 + r9474212;
        double r9474214 = r9474213 * r9474210;
        double r9474215 = t;
        double r9474216 = r9474214 + r9474215;
        return r9474216;
}
↓
double f(double x, double y, double z, double t) {
        double r9474217 = y;
        double r9474218 = x;
        double r9474219 = z;
        double r9474220 = fma(r9474217, r9474218, r9474219);
        double r9474221 = t;
        double r9474222 = fma(r9474217, r9474220, r9474221);
        return r9474222;
}

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 2019165 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))