Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
Internal Precision: 128
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]

  2. Final simplification0.0

    \[\leadsto \frac{1}{x - 1} + \frac{x}{x + 1}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))

Details

Time bar (total: 9.5s)Debug log

sample38.0ms

Algorithm
intervals

simplify10.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

10.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
0.0b
(/ 1 (- x 1))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

5.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
1.0ms
(/ 1 (- x 1))
1.0ms
(/ x (+ x 1))

series40.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

23.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
10.0ms
(/ x (+ x 1))
6.0ms
(/ 1 (- x 1))

simplify594.0ms

Counts
25 → 56
Calls

25 calls. Slowest were:

108.0ms
(+ (* 1 (+ x 1)) (* (- x 1) x))
66.0ms
(- (+ x (+ (pow x 2) 1)))
65.0ms
(- (+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 1)))

prune459.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

14.8b
(/ (+ 1 (* x x)) (* (- x 1) (+ x 1)))
0.0b
(* (- x 1) (+ x 1))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 58
Calls

2 calls. Slowest were:

7.0ms
(/ (+ 1 (* x x)) (* (- x 1) (+ x 1)))
4.0ms
(* (- x 1) (+ x 1))

series55.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

28.0ms
(* (- x 1) (+ x 1))
26.0ms
(/ (+ 1 (* x x)) (* (- x 1) (+ x 1)))

simplify6.4s

Counts
51 → 64
Calls

51 calls. Slowest were:

802.0ms
(* (* (* (- x 1) (- x 1)) (- x 1)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
551.0ms
(* (- (* x x) (* 1 1)) (+ x 1))
527.0ms
(- (log (+ 1 (* x x))) (log (* (- x 1) (+ x 1))))

prune507.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals