Average Error: 5.4 → 5.4
Time: 14.4s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(1 + y \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(1 + y \cdot y\right)
double f(double x, double y) {
        double r328617 = x;
        double r328618 = 1.0;
        double r328619 = y;
        double r328620 = r328619 * r328619;
        double r328621 = r328618 + r328620;
        double r328622 = r328617 * r328621;
        return r328622;
}
↓
double f(double x, double y) {
        double r328623 = x;
        double r328624 = 1.0;
        double r328625 = y;
        double r328626 = r328625 * r328625;
        double r328627 = r328624 + r328626;
        double r328628 = r328623 * r328627;
        return r328628;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.4
Target0.1
Herbie5.4
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  2. Final simplification5.4

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

Reproduce

herbie shell --seed 2019323 +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))))