Average Error: 5.8 → 5.8
Time: 8.6s
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 r314231 = x;
        double r314232 = 1.0;
        double r314233 = y;
        double r314234 = r314233 * r314233;
        double r314235 = r314232 + r314234;
        double r314236 = r314231 * r314235;
        return r314236;
}
↓
double f(double x, double y) {
        double r314237 = x;
        double r314238 = 1.0;
        double r314239 = y;
        double r314240 = r314239 * r314239;
        double r314241 = r314238 + r314240;
        double r314242 = r314237 * r314241;
        return r314242;
}

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 +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))))