Average Error: 6.1 → 6.1
Time: 1.2s
Precision: binary64
\[\frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}\]
↓
\[\frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}\]
\frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}
↓
\frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}
double code(double w, double a, double d) {
	return ((double) (((double) (((double) (8.0 * w)) * a)) / ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a))))))))));
}
↓
double code(double w, double a, double d) {
	return ((double) (((double) (((double) (8.0 * w)) * a)) / ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a))))))))));
}

Error

Bits error versus w

Bits error versus a

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.1

    \[\frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}\]

  2. Final simplification6.1

    \[\leadsto \frac{\left(8 \cdot w\right) \cdot a}{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (w a d)
  :name "(/ (* (* 8.0 w) a) (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a)))))"
  :precision binary64
  (/ (* (* 8.0 w) a) (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a))))))