Average Error: 0.1 → 0.1
Time: 6.2s
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 r100 = x;
        double r101 = y;
        double r102 = z;
        double r103 = r101 * r102;
        double r104 = r103 * r102;
        double r105 = r100 + r104;
        return r105;
}
↓
double f(double x, double y, double z) {
        double r106 = x;
        double r107 = y;
        double r108 = z;
        double r109 = r107 * r108;
        double r110 = r109 * r108;
        double r111 = r106 + r110;
        return r111;
}

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 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))