Details

sample60.0ms

Algorithm

intervals

Results

27.0ms	85×	body	1280	valid
9.0ms	130×	body	80	valid
6.0ms	25×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

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: 16.9b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:

1.0ms	(atan (+ N 1.0))
6.0ms	(- (atan (+ N 1.0)) (atan N))

series32.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
30.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.2s

Counts

28 → 28

Iterations

Useful iterations: 4 (230.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	151	245
3	326	241
4	966	239
5	3321	239
done	5001	239

prune140.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite46.0ms

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:

44.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify502.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	55	317
1	127	312
2	694	264
done	5000	264

prune145.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
13.8b	(cbrt (* (+ N 1.0) N))
13.8b	(cbrt (* (+ N 1.0) N))
13.8b	(cbrt (* (+ N 1.0) N))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

33.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
15.0ms	(cbrt (* (+ N 1.0) N))
21.0ms	(cbrt (* (+ N 1.0) N))
14.0ms	(cbrt (* (+ N 1.0) N))

series555.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
154.0ms	(cbrt (* (+ N 1.0) N))
121.0ms	(cbrt (* (+ N 1.0) N))
129.0ms	(cbrt (* (+ N 1.0) N))

simplify740.0ms

Counts

84 → 84

Iterations

Useful iterations: done (736.0ms)

Iter	Nodes	Cost
0	152	1527
1	383	1427
2	1580	1328
done	5000	1215

prune481.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (* (+ N 1.0) N))
13.8b	(cbrt (* (+ N 1.0) N))
13.8b	(cbrt (* (+ N 1.0) N))
13.8b	(cbrt (* N (+ N 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))
14.0ms	(cbrt (* (+ N 1.0) N))
13.0ms	(cbrt (* N (+ N 1.0)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (* (+ N 1.0) N))
117.0ms	(cbrt (* (+ N 1.0) N))
122.0ms	(cbrt (* (+ N 1.0) N))
124.0ms	(cbrt (* N (+ N 1.0)))

simplify2.3s

Counts

56 → 56

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	95	988
1	212	972
2	735	924
3	3697	784
done	5002	724

prune454.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes60.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.3s

Algorithm

intervals

Results

684.0ms	2853×	body	1280	valid
216.0ms	4034×	body	80	valid
136.0ms	626×	body	640	valid
38.0ms	317×	body	320	valid
15.0ms	170×	body	160	valid