Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[t + \left(y \cdot \left(x \cdot y\right) + z \cdot y\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
t + \left(y \cdot \left(x \cdot y\right) + z \cdot y\right)
double f(double x, double y, double z, double t) {
        double r7840570 = x;
        double r7840571 = y;
        double r7840572 = r7840570 * r7840571;
        double r7840573 = z;
        double r7840574 = r7840572 + r7840573;
        double r7840575 = r7840574 * r7840571;
        double r7840576 = t;
        double r7840577 = r7840575 + r7840576;
        return r7840577;
}
↓
double f(double x, double y, double z, double t) {
        double r7840578 = t;
        double r7840579 = y;
        double r7840580 = x;
        double r7840581 = r7840580 * r7840579;
        double r7840582 = r7840579 * r7840581;
        double r7840583 = z;
        double r7840584 = r7840583 * r7840579;
        double r7840585 = r7840582 + r7840584;
        double r7840586 = r7840578 + r7840585;
        return r7840586;
}

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. Taylor expanded around 0 4.2

    \[\leadsto \color{blue}{\left(x \cdot {y}^{2} + z \cdot y\right)} + t\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))