Average Error: 0.0 → 0.0
Time: 4.4s
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 r484440 = x;
        double r484441 = 2.0;
        double r484442 = r484440 * r484441;
        double r484443 = r484440 * r484440;
        double r484444 = r484442 + r484443;
        double r484445 = y;
        double r484446 = r484445 * r484445;
        double r484447 = r484444 + r484446;
        return r484447;
}
↓
double f(double x, double y) {
        double r484448 = y;
        double r484449 = r484448 * r484448;
        double r484450 = x;
        double r484451 = 2.0;
        double r484452 = r484451 + r484450;
        double r484453 = r484450 * r484452;
        double r484454 = r484449 + r484453;
        return r484454;
}

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 2020049 
(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)))