Details

sample45.0ms

Algorithm

intervals

Results

19.0ms	87×	body	1280	valid
7.0ms	129×	body	80	valid
4.0ms	22×	body	640	valid
2.0ms	15×	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: 16.9b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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

series16.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
14.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.6s

Counts

28 → 28

Iterations

Useful iterations: 4 (262.0ms)

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

prune64.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

2 → 18

Calls

2 calls:

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

series36.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ 1 (* (+ N 1.0) N))
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify745.0ms

Counts

24 → 24

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	41	305
1	119	292
2	690	248
done	5000	248

prune105.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))))
0.6b	(atan2 1.0 (* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N)))))
13.6b	(sqrt (+ 1 (* (+ N 1.0) N)))
13.6b	(sqrt (+ 1 (* (+ N 1.0) N)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`flip3-+` `swap-sqr` `flip-+`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

52.0ms	(* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))))
0.0ms	(atan2 1.0 (* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N)))))
6.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
6.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))))
4.0ms	(atan2 1.0 (* (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N)))))
55.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
51.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	104	2105
1	242	1389
2	1266	1255
done	5000	1228

prune358.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (* (* (sqrt (sqrt (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (+ 1 (* (+ N 1.0) N))))) (sqrt (+ 1 (* (+ N 1.0) N)))))
13.6b	(sqrt (+ 1 (* (+ N 1.0) N)))
13.6b	(sqrt (+ 1 (* (+ N 1.0) N)))
13.6b	(sqrt (+ 1 (* (+ N 1.0) N)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

0.0ms	(atan2 1.0 (* (* (sqrt (sqrt (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (+ 1 (* (+ N 1.0) N))))) (sqrt (+ 1 (* (+ N 1.0) N)))))
10.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
12.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
13.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 1.0 (* (* (sqrt (sqrt (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (+ 1 (* (+ N 1.0) N))))) (sqrt (+ 1 (* (+ N 1.0) N)))))
74.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
43.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))
53.0ms	(sqrt (+ 1 (* (+ N 1.0) N)))

simplify722.0ms

Counts

64 → 64

Iterations

Useful iterations: done (720.0ms)

Iter	Nodes	Cost
0	62	1057
1	144	845
2	638	691
done	5001	685

prune267.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes34.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	9	19
1	14	19
done	14	19

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	2816×	body	1280	valid
265.0ms	4082×	body	80	valid
121.0ms	605×	body	640	valid
51.0ms	330×	body	320	valid
18.0ms	167×	body	160	valid