Average Error: 5.3 → 0.1
Time: 15.5s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[1 \cdot x + \left(x \cdot y\right) \cdot y\]
x \cdot \left(1 + y \cdot y\right)
↓
1 \cdot x + \left(x \cdot y\right) \cdot y
double f(double x, double y) {
        double r753625 = x;
        double r753626 = 1.0;
        double r753627 = y;
        double r753628 = r753627 * r753627;
        double r753629 = r753626 + r753628;
        double r753630 = r753625 * r753629;
        return r753630;
}
↓
double f(double x, double y) {
        double r753631 = 1.0;
        double r753632 = x;
        double r753633 = r753631 * r753632;
        double r753634 = y;
        double r753635 = r753632 * r753634;
        double r753636 = r753635 * r753634;
        double r753637 = r753633 + r753636;
        return r753637;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original5.3
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.3

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

  3. Applied distribute-lft-in5.3

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

  4. Simplified5.3

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(y \cdot y\right)\]
  5. Using strategy rm

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))))