Details

sample45.0ms

Algorithm

intervals

Results

20.0ms	87×	body	1280	valid
7.0ms	136×	body	80	valid
3.0ms	14×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

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: 16.5b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

series42.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(atan (+ N 1.0))
39.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.0s

Counts

28 → 28

Iterations

Useful iterations: 4 (167.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	145	245
3	270	241
4	534	239
5	1497	239
done	5000	239

prune77.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

24.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (+ N 1.0) N)
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify4.5s

Counts

34 → 34

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	356	264
3	1001	264
4	4336	264
done	5002	264

prune85.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
12.9b	(cbrt (* (+ N 1.0) N))
12.9b	(cbrt (* (+ N 1.0) N))
12.9b	(cbrt (* (+ N 1.0) N))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
14.0ms	(cbrt (* (+ N 1.0) N))
15.0ms	(cbrt (* (+ N 1.0) N))
22.0ms	(cbrt (* (+ N 1.0) N))

series441.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
129.0ms	(cbrt (* (+ N 1.0) N))
141.0ms	(cbrt (* (+ N 1.0) N))
161.0ms	(cbrt (* (+ N 1.0) N))

simplify2.7s

Counts

52 → 52

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	95	1024
1	210	1012
2	482	826
3	1284	697
4	4474	631
done	5000	631

prune234.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (* (cbrt (+ N 1.0)) (cbrt N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
0.6b	(cbrt N)
12.9b	(cbrt (* (+ N 1.0) N))
12.9b	(cbrt (* (+ N 1.0) N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

5×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `associate-*l/` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt (+ N 1.0)) (cbrt N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
1.0ms	(cbrt N)
8.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))

series550.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt (+ N 1.0)) (cbrt N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
250.0ms	(cbrt N)
132.0ms	(cbrt (* (+ N 1.0) N))
161.0ms	(cbrt (* (+ N 1.0) N))

simplify1.2s

Counts

52 → 52

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	115	852
1	248	840
2	576	754
3	1514	675
done	5001	637

prune578.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes23.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	21	25
done	21	25

end0.0ms

sample1.3s

Algorithm

intervals

Results

686.0ms	2814×	body	1280	valid
266.0ms	4093×	body	80	valid
107.0ms	615×	body	640	valid
42.0ms	324×	body	320	valid
14.0ms	154×	body	160	valid