Average Error: 0.1 → 0.1
Time: 12.4s
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 r410165 = x;
        double r410166 = y;
        double r410167 = r410165 * r410166;
        double r410168 = z;
        double r410169 = r410168 * r410168;
        double r410170 = r410167 + r410169;
        double r410171 = r410170 + r410169;
        double r410172 = r410171 + r410169;
        return r410172;
}
↓
double f(double x, double y, double z) {
        double r410173 = 3.0;
        double r410174 = z;
        double r410175 = r410174 * r410174;
        double r410176 = r410173 * r410175;
        double r410177 = x;
        double r410178 = y;
        double r410179 = r410177 * r410178;
        double r410180 = r410176 + r410179;
        return r410180;
}

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 2019291 
(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)))