Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	85×	body	1280	valid
6.0ms	148×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1)) (atan N))

rewrite7.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 30

Calls

1 calls:

6.0ms

(- (atan (+ N 1)) (atan N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(- (atan (+ N 1)) (atan N))

simplify2.4s

Counts

33 → 33

Iterations

Iter	Nodes
done	5002
4	2213
3	777
2	288
1	136
0	62

prune96.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b	(atan2 1 (fma N (+ 1 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify3.2s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
9	1660
8	834
7	554
6	378
5	223
4	133
3	62
2	37
1	25
0	18

prune58.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.5b	(atan2 1 (fma N (+ 1 N) 1))
0.5b	(log1p (atan2 1 (fma N (+ 1 N) 1)))
0.6b	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`expm1-log1p-u`
3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

3 → 34

Calls

3 calls:

0.0ms	(atan2 1 (fma N (+ 1 N) 1))
0.0ms	(log1p (atan2 1 (fma N (+ 1 N) 1)))
0.0ms	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))

series191.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan2 1 (fma N (+ 1 N) 1))
79.0ms	(log1p (atan2 1 (fma N (+ 1 N) 1)))
109.0ms	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))

simplify2.5s

Counts

43 → 43

Iterations

Iter	Nodes
done	5003
9	3273
8	1315
7	744
6	479
5	308
4	190
3	106
2	74
1	57
0	41

prune155.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))
13.2b	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
13.2b	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
13.2b	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 54

Calls

4 calls:

0.0ms	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))
1.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
1.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
5.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(expm1 (log1p (atan2 1 (fma N (+ 1 N) 1))))
220.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
250.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))
250.0ms	(cbrt (expm1 (log1p (atan2 1 (fma N (+ 1 N) 1)))))

simplify2.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5042
5	2226
4	687
3	220
2	99
1	51
0	35

prune264.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes69.0ms

Accuracy

0% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	7

end0.0ms

sample1.2s

Algorithm

intervals

Results

682.0ms	2867×	body	1280	valid
268.0ms	4022×	body	80	valid
131.0ms	613×	body	640	valid
44.0ms	339×	body	320	valid
15.0ms	159×	body	160	valid