Average Error: 5.6 → 0.1
Time: 26.5s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[y \cdot \left(y \cdot x\right) + x \cdot 1\]
x \cdot \left(1 + y \cdot y\right)
↓
y \cdot \left(y \cdot x\right) + x \cdot 1
double f(double x, double y) {
        double r22829868 = x;
        double r22829869 = 1.0;
        double r22829870 = y;
        double r22829871 = r22829870 * r22829870;
        double r22829872 = r22829869 + r22829871;
        double r22829873 = r22829868 * r22829872;
        return r22829873;
}
↓
double f(double x, double y) {
        double r22829874 = y;
        double r22829875 = x;
        double r22829876 = r22829874 * r22829875;
        double r22829877 = r22829874 * r22829876;
        double r22829878 = 1.0;
        double r22829879 = r22829875 * r22829878;
        double r22829880 = r22829877 + r22829879;
        return r22829880;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.6
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.6

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

  3. Applied distribute-lft-in5.6

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

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"

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

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