Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	78×	body	1280	valid
7.0ms	134×	body	80	valid
4.0ms	26×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	5×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.0b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series19.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
16.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.8s

Counts

44 → 44

Iterations

Iter	Nodes
done	5004
4	2193
3	738
2	286
1	139
0	66

prune120.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ 1.0 N) 1)
0.2b	(atan2 1.0 (fma N (+ 1.0 N) 1))

rewrite1.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

2 → 19

Calls

2 calls:

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

series44.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(fma N (+ 1.0 N) 1)
4.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))

simplify2.9s

Counts

25 → 25

Iterations

Iter	Nodes
done	5000
4	2753
3	442
2	121
1	54
0	33

prune101.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (* (* (cbrt (fma N (+ 1.0 N) 1)) (cbrt (fma N (+ 1.0 N) 1))) (cbrt (fma N (+ 1.0 N) 1))))
14.5b	(cbrt (fma N (+ 1.0 N) 1))
14.5b	(cbrt (fma N (+ 1.0 N) 1))
14.5b	(cbrt (fma N (+ 1.0 N) 1))

rewrite3.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (* (* (cbrt (fma N (+ 1.0 N) 1)) (cbrt (fma N (+ 1.0 N) 1))) (cbrt (fma N (+ 1.0 N) 1))))
85.0ms	(cbrt (fma N (+ 1.0 N) 1))
95.0ms	(cbrt (fma N (+ 1.0 N) 1))
90.0ms	(cbrt (fma N (+ 1.0 N) 1))

simplify1.9s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
6	3920
5	1640
4	794
3	424
2	203
1	107
0	58

prune283.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (fma N (+ 1.0 N) 1))
14.5b	(cbrt (fma N (+ 1.0 N) 1))
14.5b	(cbrt (fma N (+ 1.0 N) 1))
14.5b	(cbrt (fma N (+ 1.0 N) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma N (+ 1.0 N) 1))
1.0ms	(cbrt (fma N (+ 1.0 N) 1))
1.0ms	(cbrt (fma N (+ 1.0 N) 1))
1.0ms	(cbrt (fma N (+ 1.0 N) 1))

series354.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (fma N (+ 1.0 N) 1))
87.0ms	(cbrt (fma N (+ 1.0 N) 1))
89.0ms	(cbrt (fma N (+ 1.0 N) 1))
91.0ms	(cbrt (fma N (+ 1.0 N) 1))

simplify1.8s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
6	3695
5	1576
4	767
3	398
2	185
1	92
0	45

prune353.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

644.0ms	2867×	body	1280	valid
192.0ms	4027×	body	80	valid
125.0ms	630×	body	640	valid
36.0ms	319×	body	320	valid
13.0ms	157×	body	160	valid