Average Error: 5.5 → 5.5
Time: 3.6s
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 r461199 = x;
        double r461200 = 1.0;
        double r461201 = y;
        double r461202 = r461201 * r461201;
        double r461203 = r461200 + r461202;
        double r461204 = r461199 * r461203;
        return r461204;
}
↓
double f(double x, double y) {
        double r461205 = x;
        double r461206 = 1.0;
        double r461207 = y;
        double r461208 = r461207 * r461207;
        double r461209 = r461206 + r461208;
        double r461210 = r461205 * r461209;
        return r461210;
}

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))))