Average Error: 5.8 → 5.8
Time: 6.7s
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 r352640 = x;
        double r352641 = 1.0;
        double r352642 = y;
        double r352643 = r352642 * r352642;
        double r352644 = r352641 + r352643;
        double r352645 = r352640 * r352644;
        return r352645;
}
↓
double f(double x, double y) {
        double r352646 = x;
        double r352647 = 1.0;
        double r352648 = y;
        double r352649 = r352648 * r352648;
        double r352650 = r352647 + r352649;
        double r352651 = r352646 * r352650;
        return r352651;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie5.8
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.8

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

  2. Final simplification5.8

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

Reproduce

herbie shell --seed 2019208 
(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))))