Average Error: 5.4 → 5.4
Time: 5.9s
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 r2070 = x;
        double r2071 = 1.0;
        double r2072 = y;
        double r2073 = r2072 * r2072;
        double r2074 = r2071 + r2073;
        double r2075 = r2070 * r2074;
        return r2075;
}
↓
double f(double x, double y) {
        double r2076 = x;
        double r2077 = 1.0;
        double r2078 = y;
        double r2079 = r2078 * r2078;
        double r2080 = r2077 + r2079;
        double r2081 = r2076 * r2080;
        return r2081;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie5.4
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

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

  2. Final simplification5.4

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

Reproduce

herbie shell --seed 2020025 +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))))