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 r517281 = x;
        double r517282 = y;
        double r517283 = r517281 * r517282;
        double r517284 = z;
        double r517285 = r517284 * r517284;
        double r517286 = r517283 + r517285;
        double r517287 = r517286 + r517285;
        double r517288 = r517287 + r517285;
        return r517288;
}
↓
double f(double x, double y, double z) {
        double r517289 = x;
        double r517290 = y;
        double r517291 = r517289 * r517290;
        double r517292 = z;
        double r517293 = r517292 * r517292;
        double r517294 = r517291 + r517293;
        double r517295 = r517294 + r517293;
        double r517296 = r517295 + r517293;
        return r517296;
}

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 2019354 
(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)))