Average Error: 0.0 → 0.0
Time: 6.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot \left(y + 2 \cdot x\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot \left(y + 2 \cdot x\right) + x \cdot x
double f(double x, double y) {
        double r684197 = x;
        double r684198 = y;
        double r684199 = r684197 + r684198;
        double r684200 = r684199 * r684199;
        return r684200;
}
↓
double f(double x, double y) {
        double r684201 = y;
        double r684202 = 2.0;
        double r684203 = x;
        double r684204 = r684202 * r684203;
        double r684205 = r684201 + r684204;
        double r684206 = r684201 * r684205;
        double r684207 = r684203 * r684203;
        double r684208 = r684206 + r684207;
        return r684208;
}

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

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(y + 2 \cdot x\right) + x \cdot x}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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