Average Error: 5.1 → 0.1
Time: 6.1s
Precision: 64
\[x \cdot \left(1.0 + y \cdot y\right)\]
↓
\[y \cdot \left(y \cdot x\right) + x \cdot 1.0\]
x \cdot \left(1.0 + y \cdot y\right)
↓
y \cdot \left(y \cdot x\right) + x \cdot 1.0
double f(double x, double y) {
        double r9515487 = x;
        double r9515488 = 1.0;
        double r9515489 = y;
        double r9515490 = r9515489 * r9515489;
        double r9515491 = r9515488 + r9515490;
        double r9515492 = r9515487 * r9515491;
        return r9515492;
}
↓
double f(double x, double y) {
        double r9515493 = y;
        double r9515494 = x;
        double r9515495 = r9515493 * r9515494;
        double r9515496 = r9515493 * r9515495;
        double r9515497 = 1.0;
        double r9515498 = r9515494 * r9515497;
        double r9515499 = r9515496 + r9515498;
        return r9515499;
}

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

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

Derivation

  1. Initial program 5.1

    \[x \cdot \left(1.0 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.1

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(y \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

    \[\leadsto x \cdot 1.0 + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  6. Final simplification0.1

    \[\leadsto y \cdot \left(y \cdot x\right) + x \cdot 1.0\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))