Average Error: 5.0 → 0.1
Time: 42.9s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[1 \cdot x + \left(y \cdot x\right) \cdot y\]
x \cdot \left(1 + y \cdot y\right)
↓
1 \cdot x + \left(y \cdot x\right) \cdot y
double f(double x, double y) {
        double r20497925 = x;
        double r20497926 = 1.0;
        double r20497927 = y;
        double r20497928 = r20497927 * r20497927;
        double r20497929 = r20497926 + r20497928;
        double r20497930 = r20497925 * r20497929;
        return r20497930;
}
↓
double f(double x, double y) {
        double r20497931 = 1.0;
        double r20497932 = x;
        double r20497933 = r20497931 * r20497932;
        double r20497934 = y;
        double r20497935 = r20497934 * r20497932;
        double r20497936 = r20497935 * r20497934;
        double r20497937 = r20497933 + r20497936;
        return r20497937;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))