Average Error: 5.3 → 0.1
Time: 7.7s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot 1 + y \cdot \left(y \cdot x\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot 1 + y \cdot \left(y \cdot x\right)
double f(double x, double y) {
        double r582387 = x;
        double r582388 = 1.0;
        double r582389 = y;
        double r582390 = r582389 * r582389;
        double r582391 = r582388 + r582390;
        double r582392 = r582387 * r582391;
        return r582392;
}
↓
double f(double x, double y) {
        double r582393 = x;
        double r582394 = 1.0;
        double r582395 = r582393 * r582394;
        double r582396 = y;
        double r582397 = r582396 * r582393;
        double r582398 = r582396 * r582397;
        double r582399 = r582395 + r582398;
        return r582399;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  6. Applied associate-*l*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +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))))