Average Error: 5.5 → 5.5
Time: 971.0ms
Precision: binary64
\[\frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}\]
↓
\[\frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}\]
\frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}
↓
\frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}
double code(double a, double b) {
	return ((double) (((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * a)) * b)))))))) / 2.0));
}
↓
double code(double a, double b) {
	return ((double) (((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * a)) * b)))))))) / 2.0));
}

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 5.5

    \[\frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}\]

  2. Final simplification5.5

    \[\leadsto \frac{1 + \sqrt{1 - \left(4 \cdot a\right) \cdot b}}{2}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(/ (+ 1.0 (sqrt (- 1.0 (* (* 4.0 a) b)))) 2.0)"
  :precision binary64
  (/ (+ 1.0 (sqrt (- 1.0 (* (* 4.0 a) b)))) 2.0))