Average Error: 5.3 → 0.1
Time: 12.5s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[1 \cdot x + y \cdot \left(y \cdot x\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
1 \cdot x + y \cdot \left(y \cdot x\right)
double f(double x, double y) {
        double r387860 = x;
        double r387861 = 1.0;
        double r387862 = y;
        double r387863 = r387862 * r387862;
        double r387864 = r387861 + r387863;
        double r387865 = r387860 * r387864;
        return r387865;
}
↓
double f(double x, double y) {
        double r387866 = 1.0;
        double r387867 = x;
        double r387868 = r387866 * r387867;
        double r387869 = y;
        double r387870 = r387869 * r387867;
        double r387871 = r387869 * r387870;
        double r387872 = r387868 + r387871;
        return r387872;
}

Error

Bits error versus x

Bits error versus y

Try it out

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 +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))))