Average Error: 0.1 → 0.1
Time: 14.4s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)
double f(double x, double y, double z, double t) {
        double r12672529 = x;
        double r12672530 = y;
        double r12672531 = r12672529 * r12672530;
        double r12672532 = z;
        double r12672533 = r12672531 + r12672532;
        double r12672534 = r12672533 * r12672530;
        double r12672535 = t;
        double r12672536 = r12672534 + r12672535;
        return r12672536;
}
↓
double f(double x, double y, double z, double t) {
        double r12672537 = x;
        double r12672538 = y;
        double r12672539 = z;
        double r12672540 = fma(r12672537, r12672538, r12672539);
        double r12672541 = t;
        double r12672542 = fma(r12672540, r12672538, r12672541);
        return r12672542;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))