Average Error: 5.4 → 5.4
Time: 11.2s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(1 + y \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(1 + y \cdot y\right)
double f(double x, double y) {
        double r364846 = x;
        double r364847 = 1.0;
        double r364848 = y;
        double r364849 = r364848 * r364848;
        double r364850 = r364847 + r364849;
        double r364851 = r364846 * r364850;
        return r364851;
}
↓
double f(double x, double y) {
        double r364852 = x;
        double r364853 = 1.0;
        double r364854 = y;
        double r364855 = r364854 * r364854;
        double r364856 = r364853 + r364855;
        double r364857 = r364852 * r364856;
        return r364857;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie5.4
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  2. Final simplification5.4

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

Reproduce

herbie shell --seed 2019323 
(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))))