Average Error: 40.1 → 36.4
Time: 4.2s
Precision: binary64
\[\frac{\left(1 - a\right) - \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}{2 \cdot \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}\]
↓
\[\frac{-1}{2} + \frac{1 - a}{2 \cdot \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}\]
\frac{\left(1 - a\right) - \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}{2 \cdot \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}
↓
\frac{-1}{2} + \frac{1 - a}{2 \cdot \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}
double code(double a, double K) {
	return ((double) (((double) (((double) (1.0 - a)) - ((double) sqrt(((double) (((double) (((double) (1.0 - ((double) (2.0 * a)))) + ((double) (((double) (4.0 * K)) * a)))) + ((double) pow(a, 2.0)))))))) / ((double) (2.0 * ((double) sqrt(((double) (((double) (((double) (1.0 - ((double) (2.0 * a)))) + ((double) (((double) (4.0 * K)) * a)))) + ((double) pow(a, 2.0))))))))));
}
↓
double code(double a, double K) {
	return ((double) (((double) (-1.0 / 2.0)) + ((double) (((double) (1.0 - a)) / ((double) (2.0 * ((double) sqrt(((double) (((double) (((double) (1.0 - ((double) (2.0 * a)))) + ((double) (((double) (4.0 * K)) * a)))) + ((double) pow(a, 2.0))))))))))));
}

Error

Bits error versus a

Bits error versus K

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 40.1

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

  2. Simplified36.4

    \[\leadsto \color{blue}{\frac{-1}{2} + \frac{1 - a}{2 \cdot \sqrt{\left(\left(1 - 2 \cdot a\right) + \left(4 \cdot K\right) \cdot a\right) + {a}^{2}}}}\]

  3. Final simplification36.4

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

Reproduce

herbie shell --seed 2020152 
(FPCore (a K)
  :name "(/ (- (- 1 a) (sqrt (+ (+ (- 1 (* 2 a)) (* (* 4 K) a)) (pow a 2)))) (* 2 (sqrt (+ (+ (- 1 (* 2 a)) (* (* 4 K) a)) (pow a 2)))))"
  :precision binary64
  (/ (- (- 1.0 a) (sqrt (+ (+ (- 1.0 (* 2.0 a)) (* (* 4.0 K) a)) (pow a 2.0)))) (* 2.0 (sqrt (+ (+ (- 1.0 (* 2.0 a)) (* (* 4.0 K) a)) (pow a 2.0))))))