Details

sample50.0ms

Algorithm

intervals

Results

21.0ms	85×	body	1280	valid
7.0ms	130×	body	80	valid
5.0ms	25×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	3×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
7.0ms	(- (atan (+ N 1.0)) (atan N))

series38.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(atan (+ N 1.0))
34.0ms	(- (atan (+ N 1.0)) (atan N))

simplify8.1s

Counts

44 → 44

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	66	624
1	139	506
2	506	416
3	4476	355
done	5000	355

prune106.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 (+ 1.0 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 0) (fma N (+ N 1.0) 1))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

simplify1.0s

Counts

12 → 12

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	36	116
3	60	116
4	84	116
5	118	116
6	187	116
7	362	116
8	1140	116
done	5000	116

prune45.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

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)))

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×	`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))
15.0ms	(* (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)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
4.0ms	(* (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)))
22.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify881.0ms

Counts

102 → 102

Iterations

Useful iterations: done (878.0ms)

Iter	Nodes	Cost
0	63	1755
1	122	1211
2	598	1086
done	5000	1053

prune249.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.8b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.8b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

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

series252.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
16.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
114.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
119.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify810.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	40	765
1	61	733
2	157	647
3	595	641
done	5001	641

prune217.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes37.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	11	8
2	12	8
done	12	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

563.0ms	2853×	body	1280	valid
473.0ms	4034×	body	80	valid
102.0ms	317×	body	320	valid
88.0ms	626×	body	640	valid
14.0ms	170×	body	160	valid