Average Error: 5.5 → 5.5
Time: 3.0s
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 r395155 = x;
        double r395156 = 1.0;
        double r395157 = y;
        double r395158 = r395157 * r395157;
        double r395159 = r395156 + r395158;
        double r395160 = r395155 * r395159;
        return r395160;
}
↓
double f(double x, double y) {
        double r395161 = x;
        double r395162 = 1.0;
        double r395163 = y;
        double r395164 = r395163 * r395163;
        double r395165 = r395162 + r395164;
        double r395166 = r395161 * r395165;
        return r395166;
}

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 2020001 +o rules:numerics
(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))))