Average Error: 0.1 → 0.1
Time: 12.4s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + \left(z \cdot z\right) \cdot 3\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + \left(z \cdot z\right) \cdot 3
double f(double x, double y, double z) {
        double r349180 = x;
        double r349181 = y;
        double r349182 = r349180 * r349181;
        double r349183 = z;
        double r349184 = r349183 * r349183;
        double r349185 = r349182 + r349184;
        double r349186 = r349185 + r349184;
        double r349187 = r349186 + r349184;
        return r349187;
}
↓
double f(double x, double y, double z) {
        double r349188 = x;
        double r349189 = y;
        double r349190 = r349188 * r349189;
        double r349191 = z;
        double r349192 = r349191 * r349191;
        double r349193 = 3.0;
        double r349194 = r349192 * r349193;
        double r349195 = r349190 + r349194;
        return r349195;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

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