Average Error: 5.2 → 0.1
Time: 10.8s
Precision: 64
\[x \cdot \left(1.0 + y \cdot y\right)\]
↓
\[y \cdot \left(y \cdot x\right) + x \cdot 1.0\]
x \cdot \left(1.0 + y \cdot y\right)
↓
y \cdot \left(y \cdot x\right) + x \cdot 1.0
double f(double x, double y) {
        double r24934143 = x;
        double r24934144 = 1.0;
        double r24934145 = y;
        double r24934146 = r24934145 * r24934145;
        double r24934147 = r24934144 + r24934146;
        double r24934148 = r24934143 * r24934147;
        return r24934148;
}
↓
double f(double x, double y) {
        double r24934149 = y;
        double r24934150 = x;
        double r24934151 = r24934149 * r24934150;
        double r24934152 = r24934149 * r24934151;
        double r24934153 = 1.0;
        double r24934154 = r24934150 * r24934153;
        double r24934155 = r24934152 + r24934154;
        return r24934155;
}

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

Original5.2
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.2

    \[x \cdot \left(1.0 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.2

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(y \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

    \[\leadsto x \cdot 1.0 + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  6. Final simplification0.1

    \[\leadsto y \cdot \left(y \cdot x\right) + x \cdot 1.0\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))