Average Error: 5.1 → 5.1
Time: 6.9s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(y \cdot y + 1\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(y \cdot y + 1\right)
double f(double x, double y) {
        double r362562 = x;
        double r362563 = 1.0;
        double r362564 = y;
        double r362565 = r362564 * r362564;
        double r362566 = r362563 + r362565;
        double r362567 = r362562 * r362566;
        return r362567;
}
↓
double f(double x, double y) {
        double r362568 = x;
        double r362569 = y;
        double r362570 = r362569 * r362569;
        double r362571 = 1.0;
        double r362572 = r362570 + r362571;
        double r362573 = r362568 * r362572;
        return r362573;
}

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

Original5.1
Target0.1
Herbie5.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.1

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

  3. Applied distribute-lft-in5.1

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]
  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 simplification5.1

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

Reproduce

herbie shell --seed 2019291 
(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))))