Average Error: 0.0 → 0.0
Time: 14.2s
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 r439477 = x;
        double r439478 = r439477 * r439477;
        double r439479 = 2.0;
        double r439480 = r439477 * r439479;
        double r439481 = y;
        double r439482 = r439480 * r439481;
        double r439483 = r439478 + r439482;
        double r439484 = r439481 * r439481;
        double r439485 = r439483 + r439484;
        return r439485;
}
↓
double f(double x, double y) {
        double r439486 = x;
        double r439487 = r439486 * r439486;
        double r439488 = 2.0;
        double r439489 = r439486 * r439488;
        double r439490 = y;
        double r439491 = r439489 * r439490;
        double r439492 = r439487 + r439491;
        double r439493 = r439490 * r439490;
        double r439494 = r439492 + r439493;
        return r439494;
}

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 2019323 
(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)))