Average Error: 0.1 → 0.1
Time: 4.7s
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 r545351 = x;
        double r545352 = y;
        double r545353 = r545351 * r545352;
        double r545354 = z;
        double r545355 = r545354 * r545354;
        double r545356 = r545353 + r545355;
        double r545357 = r545356 + r545355;
        double r545358 = r545357 + r545355;
        return r545358;
}
↓
double f(double x, double y, double z) {
        double r545359 = x;
        double r545360 = y;
        double r545361 = r545359 * r545360;
        double r545362 = z;
        double r545363 = r545362 * r545362;
        double r545364 = r545361 + r545363;
        double r545365 = r545364 + r545363;
        double r545366 = r545365 + r545363;
        return r545366;
}

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 2020081 
(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)))