Average Error: 0.1 → 0.1
Time: 3.3s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(x, y, z\right) \cdot y + t\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(x, y, z\right) \cdot y + t
double f(double x, double y, double z, double t) {
        double r125525 = x;
        double r125526 = y;
        double r125527 = r125525 * r125526;
        double r125528 = z;
        double r125529 = r125527 + r125528;
        double r125530 = r125529 * r125526;
        double r125531 = t;
        double r125532 = r125530 + r125531;
        return r125532;
}
↓
double f(double x, double y, double z, double t) {
        double r125533 = x;
        double r125534 = y;
        double r125535 = z;
        double r125536 = fma(r125533, r125534, r125535);
        double r125537 = r125536 * r125534;
        double r125538 = t;
        double r125539 = r125537 + r125538;
        return r125539;
}

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. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))