Average Error: 5.4 → 0.1
Time: 2.4s
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 r541610 = x;
        double r541611 = 1.0;
        double r541612 = y;
        double r541613 = r541612 * r541612;
        double r541614 = r541611 + r541613;
        double r541615 = r541610 * r541614;
        return r541615;
}
↓
double f(double x, double y) {
        double r541616 = x;
        double r541617 = 1.0;
        double r541618 = r541616 * r541617;
        double r541619 = y;
        double r541620 = r541616 * r541619;
        double r541621 = r541620 * r541619;
        double r541622 = r541618 + r541621;
        return r541622;
}

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

Original5.4
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  3. Applied distribute-lft-in5.4

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]
  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 2020065 
(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))))