Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[3 \cdot \left(z \cdot z\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
3 \cdot \left(z \cdot z\right) + x \cdot y
double f(double x, double y, double z) {
        double r391269 = x;
        double r391270 = y;
        double r391271 = r391269 * r391270;
        double r391272 = z;
        double r391273 = r391272 * r391272;
        double r391274 = r391271 + r391273;
        double r391275 = r391274 + r391273;
        double r391276 = r391275 + r391273;
        return r391276;
}
↓
double f(double x, double y, double z) {
        double r391277 = 3.0;
        double r391278 = z;
        double r391279 = r391278 * r391278;
        double r391280 = r391277 * r391279;
        double r391281 = x;
        double r391282 = y;
        double r391283 = r391281 * r391282;
        double r391284 = r391280 + r391283;
        return r391284;
}

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. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right) + x \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(z \cdot z\right) + x \cdot y\]

Reproduce

herbie shell --seed 2019308 
(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)))