Average Error: 0.1 → 0.1
Time: 2.7s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + \left(3 \cdot z\right) \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + \left(3 \cdot z\right) \cdot z
double f(double x, double y, double z) {
        double r496974 = x;
        double r496975 = y;
        double r496976 = r496974 * r496975;
        double r496977 = z;
        double r496978 = r496977 * r496977;
        double r496979 = r496976 + r496978;
        double r496980 = r496979 + r496978;
        double r496981 = r496980 + r496978;
        return r496981;
}
↓
double f(double x, double y, double z) {
        double r496982 = x;
        double r496983 = y;
        double r496984 = r496982 * r496983;
        double r496985 = 3.0;
        double r496986 = z;
        double r496987 = r496985 * r496986;
        double r496988 = r496987 * r496986;
        double r496989 = r496984 + r496988;
        return r496989;
}

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. Using strategy rm

  3. Applied associate-+l+0.1

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

  4. Simplified0.1

    \[\leadsto \left(x \cdot y + z \cdot z\right) + \color{blue}{z \cdot \left(z + z\right)}\]
  5. Using strategy rm

  6. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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)))