Average Error: 5.5 → 5.5
Time: 2.7s
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 r534452 = x;
        double r534453 = 1.0;
        double r534454 = y;
        double r534455 = r534454 * r534454;
        double r534456 = r534453 + r534455;
        double r534457 = r534452 * r534456;
        return r534457;
}
↓
double f(double x, double y) {
        double r534458 = x;
        double r534459 = 1.0;
        double r534460 = y;
        double r534461 = r534460 * r534460;
        double r534462 = r534459 + r534461;
        double r534463 = r534458 * r534462;
        return r534463;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.5
Target0.1
Herbie5.5
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.5

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

  2. Final simplification5.5

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

Reproduce

herbie shell --seed 2020060 
(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))))