Average Error: 16.8 → 16.8
Time: 717.0ms
Precision: binary64
\[\frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1\]
↓
\[\frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1\]
\frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1
↓
\frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1
double code(double a) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (a + 1000.0)) + 1.0)) * ((double) (((double) (a + 1000.0)) - 1.0)))) / a)) / 1000.0)) / 2.0)) - 1.0));
}
↓
double code(double a) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (a + 1000.0)) + 1.0)) * ((double) (((double) (a + 1000.0)) - 1.0)))) / a)) / 1000.0)) / 2.0)) - 1.0));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.8

    \[\frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1\]

  2. Final simplification16.8

    \[\leadsto \frac{\frac{\frac{\left(\left(a + 10^{3}\right) + 1\right) \cdot \left(\left(a + 10^{3}\right) - 1\right)}{a}}{10^{3}}}{2} - 1\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a)
  :name "(- (/ (/ (/ (* (+ (+ a 1000) 1) (- (+ a 1000) 1)) a) 1000) 2) 1)"
  :precision binary64
  (- (/ (/ (/ (* (+ (+ a 1000.0) 1.0) (- (+ a 1000.0) 1.0)) a) 1000.0) 2.0) 1.0))