Average Error: 5.3 → 0.1
Time: 13.8s
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 r290035 = x;
        double r290036 = 1.0;
        double r290037 = y;
        double r290038 = r290037 * r290037;
        double r290039 = r290036 + r290038;
        double r290040 = r290035 * r290039;
        return r290040;
}
↓
double f(double x, double y) {
        double r290041 = 1.0;
        double r290042 = x;
        double r290043 = r290041 * r290042;
        double r290044 = y;
        double r290045 = r290042 * r290044;
        double r290046 = r290044 * r290045;
        double r290047 = r290043 + r290046;
        return r290047;
}

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

Original5.3
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.3

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

  3. Applied distribute-lft-in5.3

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

  4. Simplified5.3

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

  5. Simplified5.3

    \[\leadsto 1 \cdot x + \color{blue}{\left(y \cdot y\right) \cdot x}\]
  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 2019306 +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))))