Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
double f(double x, double y) {
        double r701532 = x;
        double r701533 = r701532 * r701532;
        double r701534 = 2.0;
        double r701535 = r701532 * r701534;
        double r701536 = y;
        double r701537 = r701535 * r701536;
        double r701538 = r701533 + r701537;
        double r701539 = r701536 * r701536;
        double r701540 = r701538 + r701539;
        return r701540;
}
↓
double f(double x, double y) {
        double r701541 = x;
        double r701542 = r701541 * r701541;
        double r701543 = 2.0;
        double r701544 = r701541 * r701543;
        double r701545 = y;
        double r701546 = r701544 * r701545;
        double r701547 = r701542 + r701546;
        double r701548 = r701545 * r701545;
        double r701549 = r701547 + r701548;
        return r701549;
}

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

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))