Average Error: 0.0 → 0.0
Time: 1.5s
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 r560633 = x;
        double r560634 = 2.0;
        double r560635 = r560633 * r560634;
        double r560636 = r560633 * r560633;
        double r560637 = r560635 + r560636;
        double r560638 = y;
        double r560639 = r560638 * r560638;
        double r560640 = r560637 + r560639;
        return r560640;
}
↓
double f(double x, double y) {
        double r560641 = y;
        double r560642 = r560641 * r560641;
        double r560643 = x;
        double r560644 = 2.0;
        double r560645 = r560644 + r560643;
        double r560646 = r560643 * r560645;
        double r560647 = r560642 + r560646;
        return r560647;
}

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 2020036 
(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)))