Average Error: 5.7 → 0.1
Time: 9.5s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot 1 + y \cdot \left(y \cdot x\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot 1 + y \cdot \left(y \cdot x\right)
double f(double x, double y) {
        double r357160 = x;
        double r357161 = 1.0;
        double r357162 = y;
        double r357163 = r357162 * r357162;
        double r357164 = r357161 + r357163;
        double r357165 = r357160 * r357164;
        return r357165;
}
↓
double f(double x, double y) {
        double r357166 = x;
        double r357167 = 1.0;
        double r357168 = r357166 * r357167;
        double r357169 = y;
        double r357170 = r357169 * r357166;
        double r357171 = r357169 * r357170;
        double r357172 = r357168 + r357171;
        return r357172;
}

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

Original5.7
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.7

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

  3. Applied distribute-lft-in5.7

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

  4. Simplified5.7

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

  6. Applied associate-*l*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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))))