Average Error: 0.1 → 0.1
Time: 8.9s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r534049 = x;
        double r534050 = y;
        double r534051 = r534049 * r534050;
        double r534052 = z;
        double r534053 = r534052 * r534052;
        double r534054 = r534051 + r534053;
        double r534055 = r534054 + r534053;
        double r534056 = r534055 + r534053;
        return r534056;
}
↓
double f(double x, double y, double z) {
        double r534057 = x;
        double r534058 = y;
        double r534059 = r534057 * r534058;
        double r534060 = z;
        double r534061 = r534060 * r534060;
        double r534062 = r534059 + r534061;
        double r534063 = r534062 + r534061;
        double r534064 = r534063 + r534061;
        return r534064;
}

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

Target

Original0.1
Target0.1
Herbie0.1
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))