Average Error: 0.1 → 0.1
Time: 4.1s
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 r516523 = x;
        double r516524 = y;
        double r516525 = r516523 * r516524;
        double r516526 = z;
        double r516527 = r516526 * r516526;
        double r516528 = r516525 + r516527;
        double r516529 = r516528 + r516527;
        double r516530 = r516529 + r516527;
        return r516530;
}
↓
double f(double x, double y, double z) {
        double r516531 = x;
        double r516532 = y;
        double r516533 = r516531 * r516532;
        double r516534 = z;
        double r516535 = r516534 * r516534;
        double r516536 = r516533 + r516535;
        double r516537 = r516536 + r516535;
        double r516538 = r516537 + r516535;
        return r516538;
}

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 +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)))