Average Error: 5.5 → 5.5
Time: 3.0s
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 r467704 = x;
        double r467705 = 1.0;
        double r467706 = y;
        double r467707 = r467706 * r467706;
        double r467708 = r467705 + r467707;
        double r467709 = r467704 * r467708;
        return r467709;
}
↓
double f(double x, double y) {
        double r467710 = x;
        double r467711 = 1.0;
        double r467712 = y;
        double r467713 = r467712 * r467712;
        double r467714 = r467711 + r467713;
        double r467715 = r467710 * r467714;
        return r467715;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.5
Target0.1
Herbie5.5
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.5

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

  2. Final simplification5.5

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

Reproduce

herbie shell --seed 2020001 +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))))