Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
Cost: 704
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(x + y\right) + y \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(x + y\right) + y \cdot \left(x + y\right)
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (+ (* x (+ x y)) (* y (+ x y))))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return (x * (x + y)) + (y * (x + y));
}

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

Alternatives

Alternative 1
Error0.0
Cost704
\[x \cdot x + y \cdot \left(x + \left(x + y\right)\right)\]
Alternative 2
Error0.0
Cost448
\[\left(x + y\right) \cdot \left(x + y\right)\]
Alternative 3
Error13.0
Cost785
\[\begin{array}{l} \mathbf{if}\;y \leq -1.4427194837061562 \cdot 10^{-59} \lor \neg \left(y \leq 2.120345883241027 \cdot 10^{-85} \lor \neg \left(y \leq 4.468379801304094 \cdot 10^{-46}\right) \land y \leq 59798.966583764915\right):\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]
Alternative 4
Error28.4
Cost192
\[x \cdot x\]
Alternative 5
Error55.3
Cost64
\[0\]
Alternative 6
Error60.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(x + y\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in_binary64_187830.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2.0 (* y x))))

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