Average Error: 5.5 → 5.5
Time: 6.6s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[\left(x \cdot \sqrt{1 + y \cdot y}\right) \cdot \sqrt{1 + y \cdot y}\]
x \cdot \left(1 + y \cdot y\right)
↓
\left(x \cdot \sqrt{1 + y \cdot y}\right) \cdot \sqrt{1 + y \cdot y}
double f(double x, double y) {
        double r356077 = x;
        double r356078 = 1.0;
        double r356079 = y;
        double r356080 = r356079 * r356079;
        double r356081 = r356078 + r356080;
        double r356082 = r356077 * r356081;
        return r356082;
}
↓
double f(double x, double y) {
        double r356083 = x;
        double r356084 = 1.0;
        double r356085 = y;
        double r356086 = r356085 * r356085;
        double r356087 = r356084 + r356086;
        double r356088 = sqrt(r356087);
        double r356089 = r356083 * r356088;
        double r356090 = r356089 * r356088;
        return r356090;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.5
Target0.1
Herbie5.5
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.5

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

  3. Applied add-sqr-sqrt5.5

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

  4. Applied associate-*r*5.5

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

  5. Final simplification5.5

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

Reproduce

herbie shell --seed 2019212 
(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))))