Average Error: 0.1 → 0.1
Time: 15.9s
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 r6091207 = x;
        double r6091208 = y;
        double r6091209 = r6091207 * r6091208;
        double r6091210 = z;
        double r6091211 = r6091209 + r6091210;
        double r6091212 = r6091211 * r6091208;
        double r6091213 = t;
        double r6091214 = r6091212 + r6091213;
        return r6091214;
}
↓
double f(double x, double y, double z, double t) {
        double r6091215 = y;
        double r6091216 = x;
        double r6091217 = z;
        double r6091218 = fma(r6091215, r6091216, r6091217);
        double r6091219 = t;
        double r6091220 = fma(r6091215, r6091218, r6091219);
        return r6091220;
}

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))