Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot y + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(3 \cdot y\right) \cdot y + x \cdot x
double f(double x, double y) {
        double r26549467 = x;
        double r26549468 = r26549467 * r26549467;
        double r26549469 = y;
        double r26549470 = r26549469 * r26549469;
        double r26549471 = r26549468 + r26549470;
        double r26549472 = r26549471 + r26549470;
        double r26549473 = r26549472 + r26549470;
        return r26549473;
}
↓
double f(double x, double y) {
        double r26549474 = 3.0;
        double r26549475 = y;
        double r26549476 = r26549474 * r26549475;
        double r26549477 = r26549476 * r26549475;
        double r26549478 = x;
        double r26549479 = r26549478 * r26549478;
        double r26549480 = r26549477 + r26549479;
        return r26549480;
}

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. Using strategy rm

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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)))