Details

sample60.0ms

Algorithm

intervals

Results

29.0ms	95×	body	1280	valid
9.0ms	128×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	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: 15.8b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (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))

series25.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
21.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.3s

Counts

28 → 28

Iterations

Useful iterations: 4 (254.0ms)

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

prune90.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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:

52.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(* (+ N 1.0) N)
7.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify531.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (132.0ms)

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

prune97.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)
0.6b	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))

rewrite6.0ms

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)
2.0ms	(cbrt N)
1.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))

series944.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt N)
334.0ms	(cbrt N)
322.0ms	(cbrt N)
11.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))

simplify926.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (261.0ms)

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

prune216.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`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 → 49

Calls

4 calls:

2.0ms	(cbrt (cbrt N))
3.0ms	(cbrt (cbrt N))
4.0ms	(cbrt (cbrt N))
1.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

381.0ms	(cbrt (cbrt N))
404.0ms	(cbrt (cbrt N))
804.0ms	(cbrt (cbrt N))
10.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N))))))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	53	617
1	100	602
2	254	480
3	1052	447
done	5001	415

prune313.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.5b

regimes71.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b 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

sample1.7s

Algorithm

intervals

Results

920.0ms	2870×	body	1280	valid
310.0ms	4057×	body	80	valid
128.0ms	600×	body	640	valid
82.0ms	149×	body	160	valid
54.0ms	324×	body	320	valid