Average Error: 0.1 → 0.1
Time: 3.1s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[3 \cdot \left(z \cdot z\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
3 \cdot \left(z \cdot z\right) + x \cdot y
double f(double x, double y, double z) {
        double r571289 = x;
        double r571290 = y;
        double r571291 = r571289 * r571290;
        double r571292 = z;
        double r571293 = r571292 * r571292;
        double r571294 = r571291 + r571293;
        double r571295 = r571294 + r571293;
        double r571296 = r571295 + r571293;
        return r571296;
}
↓
double f(double x, double y, double z) {
        double r571297 = 3.0;
        double r571298 = z;
        double r571299 = r571298 * r571298;
        double r571300 = r571297 * r571299;
        double r571301 = x;
        double r571302 = y;
        double r571303 = r571301 * r571302;
        double r571304 = r571300 + r571303;
        return r571304;
}

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. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right) + x \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(z \cdot z\right) + x \cdot y\]

Reproduce

herbie shell --seed 2020049 
(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)))