Average Error: 0.0 → 0.0
Time: 2.5s
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 r567630 = x;
        double r567631 = 2.0;
        double r567632 = r567630 * r567631;
        double r567633 = r567630 * r567630;
        double r567634 = r567632 + r567633;
        double r567635 = y;
        double r567636 = r567635 * r567635;
        double r567637 = r567634 + r567636;
        return r567637;
}
↓
double f(double x, double y) {
        double r567638 = y;
        double r567639 = r567638 * r567638;
        double r567640 = x;
        double r567641 = 2.0;
        double r567642 = r567641 + r567640;
        double r567643 = r567640 * r567642;
        double r567644 = r567639 + r567643;
        return r567644;
}

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 2020089 
(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)))