Average Error: 0.0 → 0.0
Time: 4.0s
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 r483647 = x;
        double r483648 = 2.0;
        double r483649 = r483647 * r483648;
        double r483650 = r483647 * r483647;
        double r483651 = r483649 + r483650;
        double r483652 = y;
        double r483653 = r483652 * r483652;
        double r483654 = r483651 + r483653;
        return r483654;
}
↓
double f(double x, double y) {
        double r483655 = y;
        double r483656 = r483655 * r483655;
        double r483657 = x;
        double r483658 = 2.0;
        double r483659 = r483658 + r483657;
        double r483660 = r483657 * r483659;
        double r483661 = r483656 + r483660;
        return r483661;
}

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 2020100 
(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)))