Average Error: 0.1 → 0.1
Time: 16.4s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(3 \cdot z\right) \cdot z + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(3 \cdot z\right) \cdot z + x \cdot y
double f(double x, double y, double z) {
        double r97751038 = x;
        double r97751039 = y;
        double r97751040 = r97751038 * r97751039;
        double r97751041 = z;
        double r97751042 = r97751041 * r97751041;
        double r97751043 = r97751040 + r97751042;
        double r97751044 = r97751043 + r97751042;
        double r97751045 = r97751044 + r97751042;
        return r97751045;
}
↓
double f(double x, double y, double z) {
        double r97751046 = 3.0;
        double r97751047 = z;
        double r97751048 = r97751046 * r97751047;
        double r97751049 = r97751048 * r97751047;
        double r97751050 = x;
        double r97751051 = y;
        double r97751052 = r97751050 * r97751051;
        double r97751053 = r97751049 + r97751052;
        return r97751053;
}

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. Using strategy rm

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(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)))