Details

sample49.0ms

Algorithm

intervals

Results

24.0ms	90×	body	1280	valid
8.0ms	137×	body	80	valid
3.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	6×	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

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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))

simplify1.9s

Counts

28 → 28

Iterations

Useful iterations: 4 (193.0ms)

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

prune55.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite22.0ms

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:

21.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* (+ N 1.0) N)
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify348.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (69.0ms)

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

prune73.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.0ms

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:

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

series626.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt N) (cbrt N)) (+ N 1.0)) (cbrt N))))
217.0ms	(cbrt N)
200.0ms	(cbrt N)
200.0ms	(cbrt N)

simplify792.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (274.0ms)

Iter	Nodes	Cost
0	43	398
1	87	386
2	277	298
3	1439	265
done	5000	265

prune133.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))))
13.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))
13.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))
17.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))

simplify11.9s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	64	1843
1	134	1255
2	531	1115
3	4836	1064
done	5000	1064

prune120.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes16.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

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

569.0ms	2904×	body	1280	valid
207.0ms	3996×	body	80	valid
83.0ms	610×	body	640	valid
62.0ms	319×	body	320	valid
13.0ms	171×	body	160	valid