Details

sample61.0ms

Algorithm

intervals

Results

29.0ms	85×	body	1280	valid
10.0ms	130×	body	80	valid
8.0ms	27×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

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: 15.8b

localize10.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (atan (+ N 1)) (atan N))

rewrite8.0ms

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:

7.0ms

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

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify2.2s

Counts

33 → 33

Iterations

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

prune103.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ 1 N) 1)
0.4b	(atan2 1 (fma N (+ 1 N) 1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`fma-udef`

Counts

2 → 21

Calls

2 calls:

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

series29.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(fma N (+ 1 N) 1)
4.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify1.3s

Counts

27 → 27

Iterations

Iter	Nodes
done	5001
4	1226
3	278
2	89
1	53
0	33

prune88.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1 (fma N (+ 1 N) 1))
0.6b	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

rewrite19.0ms

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` `insert-posit16` `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 → 94

Calls

4 calls:

0.0ms	(atan2 1 (fma N (+ 1 N) 1))
14.0ms	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
2.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify3.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
4	4096
3	679
2	259
1	123
0	69

prune274.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1 (fma N (+ 1 N) 1))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

rewrite5.0ms

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:

0.0ms	(atan2 1 (fma N (+ 1 N) 1))
1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
2.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (fma N (+ 1 N) 1))
16.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify1.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
7	2054
6	830
5	383
4	207
3	110
2	70
1	47
0	34

prune220.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.4b

regimes37.0ms

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	8
1	8
0	5

end0.0ms

sample1.1s

Algorithm

intervals

Results

607.0ms	2765×	body	1280	valid
200.0ms	4107×	body	80	valid
171.0ms	665×	body	640	valid
38.0ms	328×	body	320	valid
11.0ms	135×	body	160	valid