Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left(y \cdot \left(2 \cdot x\right) + y \cdot y\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(y \cdot \left(2 \cdot x\right) + y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r435147 = x;
        double r435148 = y;
        double r435149 = r435147 + r435148;
        double r435150 = r435149 * r435149;
        return r435150;
}
↓
double f(double x, double y) {
        double r435151 = y;
        double r435152 = 2.0;
        double r435153 = x;
        double r435154 = r435152 * r435153;
        double r435155 = r435151 * r435154;
        double r435156 = r435151 * r435151;
        double r435157 = r435155 + r435156;
        double r435158 = r435153 * r435153;
        double r435159 = r435157 + r435158;
        return r435159;
}

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

    \[\leadsto \color{blue}{y \cdot \left(2 \cdot x + y\right) + x \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))