Average Error: 5.2 → 0.1
Time: 14.3s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[1 \cdot x + y \cdot \left(x \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
1 \cdot x + y \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r437948 = x;
        double r437949 = 1.0;
        double r437950 = y;
        double r437951 = r437950 * r437950;
        double r437952 = r437949 + r437951;
        double r437953 = r437948 * r437952;
        return r437953;
}
↓
double f(double x, double y) {
        double r437954 = 1.0;
        double r437955 = x;
        double r437956 = r437954 * r437955;
        double r437957 = y;
        double r437958 = r437955 * r437957;
        double r437959 = r437957 * r437958;
        double r437960 = r437956 + r437959;
        return r437960;
}

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

    \[x \cdot \left(1 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.2

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]

  4. Simplified5.2

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(y \cdot y\right)\]

  5. Simplified5.2

    \[\leadsto 1 \cdot x + \color{blue}{\left(y \cdot y\right) \cdot x}\]
  6. Using strategy rm

  7. Applied associate-*l*0.1

    \[\leadsto 1 \cdot x + \color{blue}{y \cdot \left(y \cdot x\right)}\]

  8. Simplified0.1

    \[\leadsto 1 \cdot x + y \cdot \color{blue}{\left(x \cdot y\right)}\]

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +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))))