Average Error: 0.1 → 0.1
Time: 16.4s
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 r5737203 = x;
        double r5737204 = y;
        double r5737205 = r5737203 * r5737204;
        double r5737206 = z;
        double r5737207 = r5737205 + r5737206;
        double r5737208 = r5737207 * r5737204;
        double r5737209 = t;
        double r5737210 = r5737208 + r5737209;
        return r5737210;
}
↓
double f(double x, double y, double z, double t) {
        double r5737211 = y;
        double r5737212 = x;
        double r5737213 = z;
        double r5737214 = fma(r5737211, r5737212, r5737213);
        double r5737215 = t;
        double r5737216 = fma(r5737211, r5737214, r5737215);
        return r5737216;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))