Details

sample43.0ms

Algorithm

intervals

Results

21.0ms	95×	body	1280	valid
6.0ms	125×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.8b	(- (atan (+ N 1.0)) (atan N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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))
10.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify7.8s

Counts

44 → 44

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	66	624
1	139	506
2	506	416
3	4476	355
done	5000	355

prune78.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

simplify1.3s

Counts

12 → 12

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	36	116
3	60	116
4	84	116
5	118	116
6	187	116
7	362	116
8	1140	116
done	5000	116

prune32.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.3b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.3b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.3b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

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

series374.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
126.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
115.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
129.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.8s

Counts

60 → 60

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	28	765
1	43	753
2	101	647
3	271	638
4	1312	638
done	5001	638

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

14.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.3b	(cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))
15.3b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.3b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
8.0ms	(cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
150.0ms	(cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))
148.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
116.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify721.0ms

Counts

64 → 64

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	44	935
1	66	768
2	160	689
3	649	680
done	5001	680

prune161.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	11	8
2	12	8
done	12	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

666.0ms	2885×	body	1280	valid
202.0ms	4024×	body	80	valid
93.0ms	631×	body	640	valid
35.0ms	302×	body	320	valid
32.0ms	158×	body	160	valid