Average Error: 0.1 → 0.1
Time: 10.2s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\left(\left(x \cdot y\right) \cdot y + t\right) + y \cdot z\]
\left(x \cdot y + z\right) \cdot y + t
↓
\left(\left(x \cdot y\right) \cdot y + t\right) + y \cdot z
double f(double x, double y, double z, double t) {
        double r101067 = x;
        double r101068 = y;
        double r101069 = r101067 * r101068;
        double r101070 = z;
        double r101071 = r101069 + r101070;
        double r101072 = r101071 * r101068;
        double r101073 = t;
        double r101074 = r101072 + r101073;
        return r101074;
}
↓
double f(double x, double y, double z, double t) {
        double r101075 = x;
        double r101076 = y;
        double r101077 = r101075 * r101076;
        double r101078 = r101077 * r101076;
        double r101079 = t;
        double r101080 = r101078 + r101079;
        double r101081 = z;
        double r101082 = r101076 * r101081;
        double r101083 = r101080 + r101082;
        return r101083;
}

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 distribute-lft-in0.1

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

  5. Applied associate-+l+0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))