Average Error: 5.1 → 5.1
Time: 3.3s
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 r532132 = x;
        double r532133 = 1.0;
        double r532134 = y;
        double r532135 = r532134 * r532134;
        double r532136 = r532133 + r532135;
        double r532137 = r532132 * r532136;
        return r532137;
}
↓
double f(double x, double y) {
        double r532138 = x;
        double r532139 = 1.0;
        double r532140 = y;
        double r532141 = r532140 * r532140;
        double r532142 = r532139 + r532141;
        double r532143 = r532138 * r532142;
        return r532143;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

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

  2. Final simplification5.1

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

Reproduce

herbie shell --seed 2020036 
(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))))