Average Error: 5.8 → 0.1
Time: 8.9s
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 r566437 = x;
        double r566438 = 1.0;
        double r566439 = y;
        double r566440 = r566439 * r566439;
        double r566441 = r566438 + r566440;
        double r566442 = r566437 * r566441;
        return r566442;
}
↓
double f(double x, double y) {
        double r566443 = 1.0;
        double r566444 = x;
        double r566445 = r566443 * r566444;
        double r566446 = y;
        double r566447 = r566444 * r566446;
        double r566448 = r566447 * r566446;
        double r566449 = r566445 + r566448;
        return r566449;
}

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

Original5.8
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.8

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

  3. Applied distribute-lft-in5.8

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

  4. Simplified5.8

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(y \cdot y\right)\]
  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 2020046 
(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))))