Average Error: 5.4 → 5.4
Time: 14.6s
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 r331119 = x;
        double r331120 = 1.0;
        double r331121 = y;
        double r331122 = r331121 * r331121;
        double r331123 = r331120 + r331122;
        double r331124 = r331119 * r331123;
        return r331124;
}
↓
double f(double x, double y) {
        double r331125 = x;
        double r331126 = 1.0;
        double r331127 = y;
        double r331128 = r331127 * r331127;
        double r331129 = r331126 + r331128;
        double r331130 = r331125 * r331129;
        return r331130;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019323 +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))))