Average Error: 45.7 → 45.7
Time: 1.1s
Precision: binary64
\[\frac{\sqrt{ti \cdot ti + 1} - 1}{ti}\]
↓
\[\frac{\sqrt{ti \cdot ti + 1} - 1}{ti}\]
\frac{\sqrt{ti \cdot ti + 1} - 1}{ti}
↓
\frac{\sqrt{ti \cdot ti + 1} - 1}{ti}
double code(double ti) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (ti * ti)) + 1.0)))) - 1.0)) / ti));
}
↓
double code(double ti) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (ti * ti)) + 1.0)))) - 1.0)) / ti));
}

Error

Bits error versus ti

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.7

    \[\frac{\sqrt{ti \cdot ti + 1} - 1}{ti}\]

  2. Final simplification45.7

    \[\leadsto \frac{\sqrt{ti \cdot ti + 1} - 1}{ti}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (ti)
  :name "(/ (- (sqrt (+ (* ti ti) 1)) 1) ti)"
  :precision binary64
  (/ (- (sqrt (+ (* ti ti) 1.0)) 1.0) ti))