Average Error: 0.1 → 0.1
Time: 20.2s
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 r623943 = x;
        double r623944 = y;
        double r623945 = r623943 * r623944;
        double r623946 = z;
        double r623947 = r623946 * r623946;
        double r623948 = r623945 + r623947;
        double r623949 = r623948 + r623947;
        double r623950 = r623949 + r623947;
        return r623950;
}
↓
double f(double x, double y, double z) {
        double r623951 = x;
        double r623952 = y;
        double r623953 = r623951 * r623952;
        double r623954 = z;
        double r623955 = r623954 * r623954;
        double r623956 = r623953 + r623955;
        double r623957 = r623956 + r623955;
        double r623958 = r623957 + r623955;
        return r623958;
}

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 2020046 
(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)))