Details

sample86.0ms

Algorithm

intervals

Results

36.0ms	79×	body	1280	valid
14.0ms	134×	body	80	valid
10.0ms	26×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize46.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(atan (+ N 1.0))
29.0ms	(- (atan (+ N 1.0)) (atan N))

series40.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(atan (+ N 1.0))
33.0ms	(- (atan (+ N 1.0)) (atan N))

simplify5.7s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	2151
3	731
2	279
1	141
0	68

prune448.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize46.0ms

Local error

Found 1 expressions with local error:

0.9b	(atan2 1.0 (fma N (+ 1.0 N) 1))

rewrite2.0ms

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:

1.0ms

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

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

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

simplify11.2s

Counts

13 → 13

Iterations

Iter	Nodes
done	5010
10	3647
9	1229
8	744
7	431
6	130
5	94
4	82
3	62
2	38
1	26
0	19

prune127.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize67.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1.0 (fma N (+ 1.0 N) 1))
0.9b	(atan2 1.0 (fma N (+ 1.0 N) 1))
13.0b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
13.0b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite13.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 52

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
1.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
4.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
5.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
6.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
32.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
29.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify3.5s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
7	1614
6	625
5	250
4	152
3	108
2	71
1	48
0	35

prune442.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize101.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1.0 (fma N (+ 1.0 N) 1))
13.0b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
13.0b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
13.0b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite14.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

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

series94.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
29.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
27.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
30.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify3.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
7	1614
6	625
5	250
4	152
3	108
2	71
1	48
0	35

prune489.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes88.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	2937×	body	1280	valid
279.0ms	3972×	body	80	valid
131.0ms	615×	body	640	valid
53.0ms	327×	body	320	valid
17.0ms	149×	body	160	valid