Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\left(a \cdot a + \left(2 \cdot a\right) \cdot b\right) + b \cdot b\]
↓
\[b \cdot \left(2 \cdot a + b\right) + a \cdot a\]
\left(a \cdot a + \left(2 \cdot a\right) \cdot b\right) + b \cdot b
↓
b \cdot \left(2 \cdot a + b\right) + a \cdot a
double code(double a, double b) {
	return ((double) (((double) (((double) (a * a)) + ((double) (((double) (2.0 * a)) * b)))) + ((double) (b * b))));
}
↓
double code(double a, double b) {
	return ((double) (((double) (b * ((double) (((double) (2.0 * a)) + b)))) + ((double) (a * a))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(a \cdot a + \left(2 \cdot a\right) \cdot b\right) + b \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{b \cdot \left(2 \cdot a + b\right) + a \cdot a}\]

  3. Final simplification0.0

    \[\leadsto b \cdot \left(2 \cdot a + b\right) + a \cdot a\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b)
  :name "(+ (+ (* a a) (* (* 2 a) b)) (* b b))"
  :precision binary64
  (+ (+ (* a a) (* (* 2.0 a) b)) (* b b)))