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 r532194 = x;
        double r532195 = 1.0;
        double r532196 = y;
        double r532197 = r532196 * r532196;
        double r532198 = r532195 + r532197;
        double r532199 = r532194 * r532198;
        return r532199;
}
↓
double f(double x, double y) {
        double r532200 = x;
        double r532201 = 1.0;
        double r532202 = y;
        double r532203 = r532202 * r532202;
        double r532204 = r532201 + r532203;
        double r532205 = r532200 * r532204;
        return r532205;
}

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 2020062 
(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))))