Average Error: 5.3 → 5.3
Time: 8.8s
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 r379122 = x;
        double r379123 = 1.0;
        double r379124 = y;
        double r379125 = r379124 * r379124;
        double r379126 = r379123 + r379125;
        double r379127 = r379122 * r379126;
        return r379127;
}
↓
double f(double x, double y) {
        double r379128 = x;
        double r379129 = 1.0;
        double r379130 = y;
        double r379131 = r379130 * r379130;
        double r379132 = r379129 + r379131;
        double r379133 = r379128 * r379132;
        return r379133;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.3
Target0.1
Herbie5.3
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.3

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

  2. Final simplification5.3

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))