Details

sample39.0ms

Algorithm

intervals

Results

20.0ms	97×	body	1280	valid
6.0ms	131×	body	80	valid
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	292
1	9	292
2	10	292
done	10	292

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.2b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
7.0ms	(- (atan (+ N 1.0)) (atan N))

series20.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
17.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.4s

Counts

28 → 28

Iterations

Useful iterations: 4 (256.0ms)

Iter	Nodes	Cost
0	40	9184
1	76	8813
2	150	8813
3	284	8773
4	611	8732
5	1579	8732
done	5000	8732

prune84.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

1 → 7

Calls

1 calls:

0.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.8s

Counts

10 → 10

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	3763
1	35	3250
2	49	3130
3	74	3130
4	109	3130
5	202	3130
6	355	3130
7	694	3130
8	1560	3130
9	4316	3130
done	5000	3130

prune43.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
16.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
11.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify86.0ms

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	64	36297
1	128	30595