Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + \left(x \cdot x + 2 \cdot x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + \left(x \cdot x + 2 \cdot x\right)
double f(double x, double y) {
        double r20141304 = x;
        double r20141305 = 2.0;
        double r20141306 = r20141304 * r20141305;
        double r20141307 = r20141304 * r20141304;
        double r20141308 = r20141306 + r20141307;
        double r20141309 = y;
        double r20141310 = r20141309 * r20141309;
        double r20141311 = r20141308 + r20141310;
        return r20141311;
}
↓
double f(double x, double y) {
        double r20141312 = y;
        double r20141313 = r20141312 * r20141312;
        double r20141314 = x;
        double r20141315 = r20141314 * r20141314;
        double r20141316 = 2.0;
        double r20141317 = r20141316 * r20141314;
        double r20141318 = r20141315 + r20141317;
        double r20141319 = r20141313 + r20141318;
        return r20141319;
}

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. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))