Average Error: 0.1 → 0.1
Time: 9.0s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\left(y \cdot x + z\right) \cdot y + t\]
\left(x \cdot y + z\right) \cdot y + t
↓
\left(y \cdot x + z\right) \cdot y + t
double f(double x, double y, double z, double t) {
        double r101933 = x;
        double r101934 = y;
        double r101935 = r101933 * r101934;
        double r101936 = z;
        double r101937 = r101935 + r101936;
        double r101938 = r101937 * r101934;
        double r101939 = t;
        double r101940 = r101938 + r101939;
        return r101940;
}
↓
double f(double x, double y, double z, double t) {
        double r101941 = y;
        double r101942 = x;
        double r101943 = r101941 * r101942;
        double r101944 = z;
        double r101945 = r101943 + r101944;
        double r101946 = r101945 * r101941;
        double r101947 = t;
        double r101948 = r101946 + r101947;
        return r101948;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y + z\right) \cdot y + t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{y \cdot \left(z + x \cdot y\right) + t}\]
  3. Using strategy rm

  4. Applied *-commutative0.1

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

  5. Final simplification0.1

    \[\leadsto \left(y \cdot x + z\right) \cdot y + t\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))