Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[x + \left(y \cdot z\right) \cdot z\]
↓
\[x + z \cdot \left(z \cdot y\right)\]
x + \left(y \cdot z\right) \cdot z
↓
x + z \cdot \left(z \cdot y\right)
double f(double x, double y, double z) {
        double r890024 = x;
        double r890025 = y;
        double r890026 = z;
        double r890027 = r890025 * r890026;
        double r890028 = r890027 * r890026;
        double r890029 = r890024 + r890028;
        return r890029;
}
↓
double f(double x, double y, double z) {
        double r890030 = x;
        double r890031 = z;
        double r890032 = y;
        double r890033 = r890031 * r890032;
        double r890034 = r890031 * r890033;
        double r890035 = r890030 + r890034;
        return r890035;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x + \left(y \cdot z\right) \cdot z\]

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  (+ x (* (* y z) z)))