Average Error: 5.5 → 5.5
Time: 3.4s
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 r473500 = x;
        double r473501 = 1.0;
        double r473502 = y;
        double r473503 = r473502 * r473502;
        double r473504 = r473501 + r473503;
        double r473505 = r473500 * r473504;
        return r473505;
}
↓
double f(double x, double y) {
        double r473506 = x;
        double r473507 = 1.0;
        double r473508 = y;
        double r473509 = r473508 * r473508;
        double r473510 = r473507 + r473509;
        double r473511 = r473506 * r473510;
        return r473511;
}

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 2020062 +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))))