Average Error: 0.1 → 0.1
Time: 19.6s
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 r356900 = x;
        double r356901 = y;
        double r356902 = r356900 * r356901;
        double r356903 = z;
        double r356904 = r356903 * r356903;
        double r356905 = r356902 + r356904;
        double r356906 = r356905 + r356904;
        double r356907 = r356906 + r356904;
        return r356907;
}
↓
double f(double x, double y, double z) {
        double r356908 = x;
        double r356909 = y;
        double r356910 = r356908 * r356909;
        double r356911 = 3.0;
        double r356912 = z;
        double r356913 = r356911 * r356912;
        double r356914 = r356913 * r356912;
        double r356915 = r356910 + r356914;
        return r356915;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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)))