Average Error: 0.1 → 0.1
Time: 13.6s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(y \cdot 3\right) + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot \left(y \cdot 3\right) + x \cdot x
double f(double x, double y) {
        double r25022568 = x;
        double r25022569 = r25022568 * r25022568;
        double r25022570 = y;
        double r25022571 = r25022570 * r25022570;
        double r25022572 = r25022569 + r25022571;
        double r25022573 = r25022572 + r25022571;
        double r25022574 = r25022573 + r25022571;
        return r25022574;
}
↓
double f(double x, double y) {
        double r25022575 = y;
        double r25022576 = 3.0;
        double r25022577 = r25022575 * r25022576;
        double r25022578 = r25022575 * r25022577;
        double r25022579 = x;
        double r25022580 = r25022579 * r25022579;
        double r25022581 = r25022578 + r25022580;
        return r25022581;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right)\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {y}^{2}} + x \cdot x\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"

  :herbie-target
  (+ (* x x) (* y (+ y (+ y y))))

  (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))