Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
Internal Precision: 128
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Initial simplification0.0

    \[\leadsto \frac{1 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

  3. Final simplification0.0

    \[\leadsto \frac{1 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Runtime

Time bar (total: 8.7s)Debug logProfile

start108.0ms

Algorithm
intervals

setup176.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

3.0b
(- 2 (/ 2 (+ 1 t)))
3.0b
(- 2 (/ 2 (+ 1 t)))
3.0b
(- 2 (/ 2 (+ 1 t)))
3.0b
(- 2 (/ 2 (+ 1 t)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
4 → 44
Calls

4 calls. Slowest were:

1.0ms
(- 2 (/ 2 (+ 1 t)))
1.0ms
(- 2 (/ 2 (+ 1 t)))
1.0ms
(- 2 (/ 2 (+ 1 t)))

series61.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

16.0ms
(- 2 (/ 2 (+ 1 t)))
16.0ms
(- 2 (/ 2 (+ 1 t)))
15.0ms
(- 2 (/ 2 (+ 1 t)))

simplify3.4s

Counts
12 → 56
Calls

12 calls. Slowest were:

634.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
610.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
513.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))

prune622.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

herbie shell --seed 2018357 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))