Average Error: 0.0 → 0.0
Time: 1.2s
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 r467538 = x;
        double r467539 = 2.0;
        double r467540 = r467538 * r467539;
        double r467541 = r467538 * r467538;
        double r467542 = r467540 + r467541;
        double r467543 = y;
        double r467544 = r467543 * r467543;
        double r467545 = r467542 + r467544;
        return r467545;
}
↓
double f(double x, double y) {
        double r467546 = y;
        double r467547 = r467546 * r467546;
        double r467548 = x;
        double r467549 = 2.0;
        double r467550 = r467549 + r467548;
        double r467551 = r467548 * r467550;
        double r467552 = r467547 + r467551;
        return r467552;
}

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 2020062 
(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)))