Average Error: 45.3 → 45.3
Time: 2.3s
Precision: binary64
\[\frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}\]
↓
\[\frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}\]
\frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}
↓
\frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}
double code(double a, double b) {
	return ((double) (((double) (((double) (a + b)) + ((double) sqrt(((double) (((double) (((double) pow(b, 2.0)) + ((double) (b * a)))) + ((double) pow(a, 2.0)))))))) / a));
}
↓
double code(double a, double b) {
	return ((double) (((double) (((double) (a + b)) + ((double) sqrt(((double) (((double) (((double) pow(b, 2.0)) + ((double) (b * a)))) + ((double) pow(a, 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 45.3

    \[\frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}\]

  2. Final simplification45.3

    \[\leadsto \frac{\left(a + b\right) + \sqrt{\left({b}^{2} + b \cdot a\right) + {a}^{2}}}{a}\]

Reproduce

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