Average Error: 5.4 → 5.4
Time: 5.5s
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 r2583 = x;
        double r2584 = 1.0;
        double r2585 = y;
        double r2586 = r2585 * r2585;
        double r2587 = r2584 + r2586;
        double r2588 = r2583 * r2587;
        return r2588;
}
↓
double f(double x, double y) {
        double r2589 = x;
        double r2590 = 1.0;
        double r2591 = y;
        double r2592 = r2591 * r2591;
        double r2593 = r2590 + r2592;
        double r2594 = r2589 * r2593;
        return r2594;
}

Error

Bits error versus x

Bits error versus y

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Results

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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))))