Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	93×	body	1280	valid
5.0ms	118×	body	80	valid
4.0ms	26×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.3b	(- (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))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series15.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.9s

Counts

28 → 28

Iterations

Useful iterations: 4 (169.0ms)

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

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(* (+ N 1.0) N)
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.7s

Counts

34 → 34

Iterations

Useful iterations: 2 (82.0ms)

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

prune65.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series937.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (cbrt N) (cbrt N))
233.0ms	(cbrt N)
222.0ms	(cbrt N)
224.0ms	(cbrt N)

simplify4.1s

Counts

85 → 85

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	61	524
1	115	417
2	319	397
3	1092	379
4	4427	374
done	5001	364

prune272.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
43.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ N 1.0))
93.0ms	(cbrt (+ N 1.0))
92.0ms	(cbrt (+ N 1.0))
113.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

simplify1.3s

Counts

107 → 107

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	139	1485
1	307	1358
2	772	1288
3	1885	1148
done	5000	1116

prune351.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes25.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

626.0ms	2858×	body	1280	valid
223.0ms	4064×	body	80	valid
84.0ms	613×	body	640	valid
32.0ms	297×	body	320	valid
13.0ms	168×	body	160	valid