Average Error: 5.0 → 0.1
Time: 1.8s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot 1 + \left(x \cdot y\right) \cdot y\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot 1 + \left(x \cdot y\right) \cdot y
double f(double x, double y) {
        double r432231 = x;
        double r432232 = 1.0;
        double r432233 = y;
        double r432234 = r432233 * r432233;
        double r432235 = r432232 + r432234;
        double r432236 = r432231 * r432235;
        return r432236;
}
↓
double f(double x, double y) {
        double r432237 = x;
        double r432238 = 1.0;
        double r432239 = r432237 * r432238;
        double r432240 = y;
        double r432241 = r432237 * r432240;
        double r432242 = r432241 * r432240;
        double r432243 = r432239 + r432242;
        return r432243;
}

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
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.0

    \[x \cdot \left(1 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.0

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

    \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(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))))