Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(2 + x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + x \cdot \left(2 + x\right)
double f(double x, double y) {
        double r470440 = x;
        double r470441 = 2.0;
        double r470442 = r470440 * r470441;
        double r470443 = r470440 * r470440;
        double r470444 = r470442 + r470443;
        double r470445 = y;
        double r470446 = r470445 * r470445;
        double r470447 = r470444 + r470446;
        return r470447;
}
↓
double f(double x, double y) {
        double r470448 = y;
        double r470449 = r470448 * r470448;
        double r470450 = x;
        double r470451 = 2.0;
        double r470452 = r470451 + r470450;
        double r470453 = r470450 * r470452;
        double r470454 = r470449 + r470453;
        return r470454;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot y + x \cdot \left(2 + x\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot y + x \cdot \left(2 + x\right)\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2 x) (* x x)))

  (+ (+ (* x 2) (* x x)) (* y y)))