Average Error: 28.8 → 8.2
Time: 2.2s
Precision: binary64
\[\left(a + b\right) \cdot \left(a + b\right) - \left(\left(a \cdot a + \left(2 \cdot a\right) \cdot b\right) + b \cdot b\right)\]
↓
\[a \cdot b + b \cdot \left(a - 2 \cdot a\right)\]
\left(a + b\right) \cdot \left(a + b\right) - \left(\left(a \cdot a + \left(2 \cdot a\right) \cdot b\right) + b \cdot b\right)
↓
a \cdot b + b \cdot \left(a - 2 \cdot a\right)
double code(double a, double b) {
	return ((double) (((double) (((double) (a + b)) * ((double) (a + b)))) - ((double) (((double) (((double) (a * a)) + ((double) (((double) (2.0 * a)) * b)))) + ((double) (b * b))))));
}
↓
double code(double a, double b) {
	return ((double) (((double) (a * b)) + ((double) (b * ((double) (a - ((double) (2.0 * 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 28.8

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

  2. Simplified8.2

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

  3. Final simplification8.2

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

Reproduce

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