Average Error: 0.1 → 0.1
Time: 19.2s
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 r338344 = x;
        double r338345 = y;
        double r338346 = r338344 * r338345;
        double r338347 = z;
        double r338348 = r338347 * r338347;
        double r338349 = r338346 + r338348;
        double r338350 = r338349 + r338348;
        double r338351 = r338350 + r338348;
        return r338351;
}
↓
double f(double x, double y, double z) {
        double r338352 = x;
        double r338353 = y;
        double r338354 = r338352 * r338353;
        double r338355 = z;
        double r338356 = r338355 * r338355;
        double r338357 = r338354 + r338356;
        double r338358 = r338357 + r338356;
        double r338359 = r338358 + r338356;
        return r338359;
}

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 2019303 +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)))