Average Error: 0.1 → 0.1
Time: 55.3s
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 r7761948 = x;
        double r7761949 = y;
        double r7761950 = r7761948 * r7761949;
        double r7761951 = z;
        double r7761952 = r7761950 + r7761951;
        double r7761953 = r7761952 * r7761949;
        double r7761954 = t;
        double r7761955 = r7761953 + r7761954;
        return r7761955;
}
↓
double f(double x, double y, double z, double t) {
        double r7761956 = y;
        double r7761957 = x;
        double r7761958 = z;
        double r7761959 = fma(r7761956, r7761957, r7761958);
        double r7761960 = t;
        double r7761961 = fma(r7761956, r7761959, r7761960);
        return r7761961;
}

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 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))