Average Error: 0.1 → 0.1
Time: 4.0s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r485045 = x;
        double r485046 = y;
        double r485047 = r485045 * r485046;
        double r485048 = z;
        double r485049 = r485048 * r485048;
        double r485050 = r485047 + r485049;
        double r485051 = r485050 + r485049;
        double r485052 = r485051 + r485049;
        return r485052;
}
↓
double f(double x, double y, double z) {
        double r485053 = x;
        double r485054 = y;
        double r485055 = r485053 * r485054;
        double r485056 = z;
        double r485057 = r485056 * r485056;
        double r485058 = r485055 + r485057;
        double r485059 = r485058 + r485057;
        double r485060 = r485059 + r485057;
        return r485060;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))