Average Error: 5.8 → 0.1
Time: 2.3s
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 r655700 = x;
        double r655701 = 1.0;
        double r655702 = y;
        double r655703 = r655702 * r655702;
        double r655704 = r655701 + r655703;
        double r655705 = r655700 * r655704;
        return r655705;
}
↓
double f(double x, double y) {
        double r655706 = x;
        double r655707 = 1.0;
        double r655708 = r655706 * r655707;
        double r655709 = y;
        double r655710 = r655706 * r655709;
        double r655711 = r655710 * r655709;
        double r655712 = r655708 + r655711;
        return r655712;
}

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. 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 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))))