Average Error: 0.1 → 0.1
Time: 9.0s
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 r613299 = x;
        double r613300 = y;
        double r613301 = r613299 * r613300;
        double r613302 = z;
        double r613303 = r613302 * r613302;
        double r613304 = r613301 + r613303;
        double r613305 = r613304 + r613303;
        double r613306 = r613305 + r613303;
        return r613306;
}
↓
double f(double x, double y, double z) {
        double r613307 = x;
        double r613308 = y;
        double r613309 = r613307 * r613308;
        double r613310 = z;
        double r613311 = r613310 * r613310;
        double r613312 = r613309 + r613311;
        double r613313 = r613312 + r613311;
        double r613314 = r613313 + r613311;
        return r613314;
}

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)))