Average Error: 5.4 → 0.1
Time: 2.7s
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 r580878 = x;
        double r580879 = 1.0;
        double r580880 = y;
        double r580881 = r580880 * r580880;
        double r580882 = r580879 + r580881;
        double r580883 = r580878 * r580882;
        return r580883;
}
↓
double f(double x, double y) {
        double r580884 = x;
        double r580885 = 1.0;
        double r580886 = r580884 * r580885;
        double r580887 = y;
        double r580888 = r580884 * r580887;
        double r580889 = r580888 * r580887;
        double r580890 = r580886 + r580889;
        return r580890;
}

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

Original5.4
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  3. Applied distribute-lft-in5.4

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]
  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 2019354 +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))))