Average Error: 5.1 → 5.1
Time: 2.5s
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 r512241 = x;
        double r512242 = 1.0;
        double r512243 = y;
        double r512244 = r512243 * r512243;
        double r512245 = r512242 + r512244;
        double r512246 = r512241 * r512245;
        return r512246;
}
↓
double f(double x, double y) {
        double r512247 = x;
        double r512248 = 1.0;
        double r512249 = y;
        double r512250 = r512249 * r512249;
        double r512251 = r512248 + r512250;
        double r512252 = r512247 * r512251;
        return r512252;
}

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))))