Details

sample50.0ms

Algorithm

intervals

Results

22.0ms	90×	body	1280	valid
7.0ms	125×	body	80	valid
5.0ms	24×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

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: 16.5b

localize18.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite14.0ms

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:

11.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify2.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
4	2162
3	737
2	287
1	136
0	62

prune133.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

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 (fma N (+ 1.0 N) 1))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify2.8s

Counts

12 → 12

Iterations

Iter	Nodes
done	5001
9	1219
8	427
7	205
6	131
5	101
4	82
3	61
2	37
1	25
0	18

prune53.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ 1.0 N) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
14.1b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.1b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite25.0ms

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 (+ 1.0 N) 1))
19.0ms	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
3.0ms	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
21.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
23.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify3.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
4	3998
3	669
2	252
1	122
0	67

prune285.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ 1.0 N) 1))
14.1b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.1b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.1b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
4.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
7	1528
6	608
5	256
4	151
3	106
2	69
1	46
0	33

prune240.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample1.2s

Algorithm

intervals

Results

643.0ms	2811×	body	1280	valid
235.0ms	4101×	body	80	valid
96.0ms	626×	body	640	valid
37.0ms	315×	body	320	valid
13.0ms	147×	body	160	valid