Average Error: 5.3 → 0.1
Time: 13.0s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot 1 + \left(x \cdot y\right) \cdot y\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot 1 + \left(x \cdot y\right) \cdot y
double f(double x, double y) {
        double r469326 = x;
        double r469327 = 1.0;
        double r469328 = y;
        double r469329 = r469328 * r469328;
        double r469330 = r469327 + r469329;
        double r469331 = r469326 * r469330;
        return r469331;
}
↓
double f(double x, double y) {
        double r469332 = x;
        double r469333 = 1.0;
        double r469334 = r469332 * r469333;
        double r469335 = y;
        double r469336 = r469332 * r469335;
        double r469337 = r469336 * r469335;
        double r469338 = r469334 + r469337;
        return r469338;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.3
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.3

    \[x \cdot \left(1 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.3

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]

  4. Simplified5.3

    \[\leadsto x \cdot 1 + \color{blue}{x \cdot {y}^{2}}\]
  5. Using strategy rm

  6. Applied unpow25.3

    \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left(y \cdot y\right)}\]

  7. Applied associate-*r*0.1

    \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  8. Final simplification0.1

    \[\leadsto x \cdot 1 + \left(x \cdot y\right) \cdot y\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1 (* y y))))