Average Error: 5.4 → 5.4
Time: 3.4s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(1 + y \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(1 + y \cdot y\right)
double f(double x, double y) {
        double r625557 = x;
        double r625558 = 1.0;
        double r625559 = y;
        double r625560 = r625559 * r625559;
        double r625561 = r625558 + r625560;
        double r625562 = r625557 * r625561;
        return r625562;
}
↓
double f(double x, double y) {
        double r625563 = x;
        double r625564 = 1.0;
        double r625565 = y;
        double r625566 = r625565 * r625565;
        double r625567 = r625564 + r625566;
        double r625568 = r625563 * r625567;
        return r625568;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original5.4
Target0.1
Herbie5.4
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  2. Final simplification5.4

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

Reproduce

herbie shell --seed 2020025 
(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))))