Average Error: 5.0 → 5.0
Time: 4.4s
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 r508177 = x;
        double r508178 = 1.0;
        double r508179 = y;
        double r508180 = r508179 * r508179;
        double r508181 = r508178 + r508180;
        double r508182 = r508177 * r508181;
        return r508182;
}
↓
double f(double x, double y) {
        double r508183 = x;
        double r508184 = 1.0;
        double r508185 = y;
        double r508186 = r508185 * r508185;
        double r508187 = r508184 + r508186;
        double r508188 = r508183 * r508187;
        return r508188;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.0
Target0.1
Herbie5.0
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.0

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

  2. Final simplification5.0

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

Reproduce

herbie shell --seed 2020018 +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))))