Average Error: 0.1 → 0.1
Time: 3.7s
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 r560102 = x;
        double r560103 = y;
        double r560104 = r560102 * r560103;
        double r560105 = z;
        double r560106 = r560105 * r560105;
        double r560107 = r560104 + r560106;
        double r560108 = r560107 + r560106;
        double r560109 = r560108 + r560106;
        return r560109;
}
↓
double f(double x, double y, double z) {
        double r560110 = 3.0;
        double r560111 = z;
        double r560112 = r560110 * r560111;
        double r560113 = r560112 * r560111;
        double r560114 = x;
        double r560115 = y;
        double r560116 = r560114 * r560115;
        double r560117 = r560113 + r560116;
        return r560117;
}

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 2020036 
(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)))