Details

sample38.0ms

Algorithm

intervals

Results

16.0ms	77×	body	1280	valid
7.0ms	137×	body	80	valid
5.0ms	28×	body	640	valid
1.0ms	10×	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: 15.3b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

7.0ms

(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(- (atan (+ N 1.0)) (atan N))

simplify4.5s

Counts

32 → 32

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	62	552
1	128	439
2	293	352
3	1027	291
4	3993	280
done	5000	280

prune60.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

simplify2.3s

Counts

12 → 12

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	15	132
1	21	132
2	32	116
3	56	116
4	68	116
5	78	116
6	99	116
7	168	116
8	435	116
9	1843	116
done	5001	116

prune36.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite38.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
27.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
20.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
23.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify4.9s

Counts

102 → 102

Iterations

Useful iterations: 5 (2.8s)

Iter	Nodes	Cost
0	63	1755
1	95	1200
2	212	1086
3	420	1041
4	858	1009
5	4816	982
done	5002	982

prune180.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.3s

Counts

60 → 60

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	29	686
1	38	638
2	60	592
3	97	592
4	143	592
5	244	592
6	529	592
7	1652	592
done	5000	592

prune195.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8
done	9	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

869.0ms	2902×	body	1280	valid
153.0ms	4008×	body	80	valid
91.0ms	632×	body	640	valid
66.0ms	313×	body	320	valid
12.0ms	145×	body	160	valid