Details

sample61.0ms

Algorithm

intervals

Results

30.0ms	93×	body	1280	valid
9.0ms	133×	body	80	valid
5.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	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: 15.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite15.0ms

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:

3.0ms	(atan (+ N 1.0))
39.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.1s

Counts

28 → 28

Iterations

Useful iterations: 4 (198.0ms)

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

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite32.0ms

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:

31.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify440.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (93.0ms)

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

prune93.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.8b	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series746.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt N)
245.0ms	(cbrt N)
243.0ms	(cbrt N)
7.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))

simplify835.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (221.0ms)

Iter	Nodes	Cost
0	43	398
1	87	386
2	265	298
3	1228	265
done	5000	265

prune161.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
15.0b	(cbrt (* (+ N 1.0) N))
15.0b	(cbrt (* (+ N 1.0) N))
15.0b	(cbrt (* (+ N 1.0) N))

rewrite28.0ms

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)))))
7.0ms	(cbrt (* (+ N 1.0) N))
12.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series347.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
112.0ms	(cbrt (* (+ N 1.0) N))
114.0ms	(cbrt (* (+ N 1.0) N))
113.0ms	(cbrt (* (+ N 1.0) N))

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	95	1024
1	210	1012
2	673	826
3	3165	748
done	5001	694

prune239.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

regimes61.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.4s

Algorithm

intervals

Results

844.0ms	2832×	body	1280	valid
204.0ms	4093×	body	80	valid
112.0ms	619×	body	640	valid
43.0ms	311×	body	320	valid
14.0ms	145×	body	160	valid