Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	89×	body	1280	valid
5.0ms	130×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `diff-atan` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

6.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify5.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	4363
2	503
1	136
0	62

prune93.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify2.9s

Counts

12 → 12

Iterations

Iter	Nodes
done	5000
9	4998
8	1072
7	474
6	301
5	215
4	142
3	101
2	52
1	30
0	20

prune48.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize16.0ms

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))))
13.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(* (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)))

series33.0ms

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

simplify645.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	600
1	122
0	63

prune317.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma (+ N 1.0) N 1))
0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))
13.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.9b	(sqrt (atan2 1.0 (fma (+ N 1.0) N 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `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 1.0) N 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 1.0) N 1)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma (+ N 1.0) N 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 1.0) N 1)))

simplify1.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
5	2922
4	1014
3	319
2	150
1	71
0	51

prune297.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes49.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
2	11
1	10
0	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

731.0ms	2873×	body	1280	valid
177.0ms	4029×	body	80	valid
122.0ms	589×	body	640	valid
46.0ms	344×	body	320	valid
18.0ms	165×	body	160	valid