Average Error: 0.1 → 0.1
Time: 2.5s
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 r515266 = x;
        double r515267 = y;
        double r515268 = r515266 * r515267;
        double r515269 = z;
        double r515270 = r515269 * r515269;
        double r515271 = r515268 + r515270;
        double r515272 = r515271 + r515270;
        double r515273 = r515272 + r515270;
        return r515273;
}
↓
double f(double x, double y, double z) {
        double r515274 = x;
        double r515275 = y;
        double r515276 = r515274 * r515275;
        double r515277 = z;
        double r515278 = r515277 * r515277;
        double r515279 = r515276 + r515278;
        double r515280 = r515279 + r515278;
        double r515281 = r515280 + r515278;
        return r515281;
}

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 2020056 
(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)))