Details

sample46.0ms

Algorithm

intervals

Results

21.0ms	91×	body	1280	valid
7.0ms	124×	body	80	valid
5.0ms	24×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize8.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

6.0ms

(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(- (atan (+ N 1.0)) (atan N))

simplify1.7s

Counts

18 → 18

Iterations

Useful iterations: 4 (185.0ms)

Iter	Nodes	Cost
0	36	209
1	73	205
2	143	191
3	267	187
4	533	185
5	1495	185
done	5000	185

prune38.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 1 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

1.0ms

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

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify4.3s

Counts

10 → 10

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	20	133
1	35	133
2	48	109
3	59	109
4	71	109
5	91	109
6	133	109
7	285	109
8	848	109
9	3642	109
done	5001	109

prune22.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.0ms	(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)))
3.0ms	(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))))

simplify1.6s

Counts

52 → 52

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	32	698
1	50	646
2	72	570
3	99	570
4	143	570
5	251	570
6	549	570
7	1704	570
done	5000	570

prune155.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 46

Calls

4 calls:

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
21.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
27.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify1.5s

Counts

58 → 58

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	32	781
1	50	703
2	72	637
3	99	637
4	143	637
5	251	637
6	549	637
7	1704	637
done	5000	637

prune206.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
done	12	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

713.0ms	2857×	body	1280	valid
638.0ms	4009×	body	80	valid
114.0ms	645×	body	640	valid
42.0ms	321×	body	320	valid
16.0ms	168×	body	160	valid