Average Error: 5.7 → 5.7
Time: 8.2s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[\left(1 + y \cdot y\right) \cdot x\]
x \cdot \left(1 + y \cdot y\right)
↓
\left(1 + y \cdot y\right) \cdot x
double f(double x, double y) {
        double r307464 = x;
        double r307465 = 1.0;
        double r307466 = y;
        double r307467 = r307466 * r307466;
        double r307468 = r307465 + r307467;
        double r307469 = r307464 * r307468;
        return r307469;
}
↓
double f(double x, double y) {
        double r307470 = 1.0;
        double r307471 = y;
        double r307472 = r307471 * r307471;
        double r307473 = r307470 + r307472;
        double r307474 = x;
        double r307475 = r307473 * r307474;
        return r307475;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target0.1
Herbie5.7
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.7

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

  3. Applied add-sqr-sqrt5.7

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

  4. Applied associate-*r*5.7

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

  5. Final simplification5.7

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

Reproduce

herbie shell --seed 2019298 
(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))))