Average Error: 0.1 → 0.1
Time: 22.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[x \cdot y + \left(3 \cdot z\right) \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
x \cdot y + \left(3 \cdot z\right) \cdot z
double f(double x, double y, double z) {
        double r352408 = x;
        double r352409 = y;
        double r352410 = r352408 * r352409;
        double r352411 = z;
        double r352412 = r352411 * r352411;
        double r352413 = r352410 + r352412;
        double r352414 = r352413 + r352412;
        double r352415 = r352414 + r352412;
        return r352415;
}
↓
double f(double x, double y, double z) {
        double r352416 = x;
        double r352417 = y;
        double r352418 = r352416 * r352417;
        double r352419 = 3.0;
        double r352420 = z;
        double r352421 = r352419 * r352420;
        double r352422 = r352421 * r352420;
        double r352423 = r352418 + r352422;
        return r352423;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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)))