Details

sample60.0ms

Algorithm

intervals

Results

31.0ms	99×	body	1280	valid
8.0ms	115×	body	80	valid
5.0ms	18×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	14×	body	160	valid

simplify7.0ms

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: 15.6b

localize7.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (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))

series26.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

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

simplify3.0s

Counts

32 → 32

Iterations

Useful iterations: 4 (1.8s)

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

prune53.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite0.0ms

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))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.5s

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

prune29.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.5b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite23.0ms

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

series30.0ms

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))))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify4.2s

Counts

102 → 102

Iterations

Useful iterations: 5 (2.2s)

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

prune165.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 99

Calls

4 calls:

59.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (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)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify2.3s

Counts

111 → 111

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	84	2040
1	171	1055
2	322	962
3	504	944
4	759	944
5	2002	944
done	5001	944

prune167.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.1b

regimes30.0ms

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

sample1.1s

Algorithm

intervals

Results

600.0ms	2879×	body	1280	valid
172.0ms	3986×	body	80	valid
118.0ms	659×	body	640	valid
32.0ms	308×	body	320	valid
13.0ms	168×	body	160	valid