Average Error: 5.0 → 0.1
Time: 1.9s
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 r456631 = x;
        double r456632 = 1.0;
        double r456633 = y;
        double r456634 = r456633 * r456633;
        double r456635 = r456632 + r456634;
        double r456636 = r456631 * r456635;
        return r456636;
}
↓
double f(double x, double y) {
        double r456637 = x;
        double r456638 = 1.0;
        double r456639 = r456637 * r456638;
        double r456640 = y;
        double r456641 = r456637 * r456640;
        double r456642 = r456641 * r456640;
        double r456643 = r456639 + r456642;
        return r456643;
}

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 +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))))