Average Error: 0.1 → 0.1
Time: 3.9s
Precision: 64
\[x + \left(y \cdot z\right) \cdot z\]
↓
\[x + \left(y \cdot z\right) \cdot z\]
x + \left(y \cdot z\right) \cdot z
↓
x + \left(y \cdot z\right) \cdot z
double f(double x, double y, double z) {
        double r16852 = x;
        double r16853 = y;
        double r16854 = z;
        double r16855 = r16853 * r16854;
        double r16856 = r16855 * r16854;
        double r16857 = r16852 + r16856;
        return r16857;
}
↓
double f(double x, double y, double z) {
        double r16858 = x;
        double r16859 = y;
        double r16860 = z;
        double r16861 = r16859 * r16860;
        double r16862 = r16861 * r16860;
        double r16863 = r16858 + r16862;
        return r16863;
}

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

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))