Details

sample27.0ms

Algorithm

intervals

Results

11.0ms	86×	body	1280	valid
4.0ms	130×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	4×	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: 15.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.7b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

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

series13.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.2s

Counts

28 → 28

Iterations

Useful iterations: 4 (127.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	145	245
3	270	241
4	534	239
5	1497	239
done	5000	239

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 1 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

0.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.7s

Counts

10 → 10

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	133
1	35	133
2	48	109
3	59	109
4	71	109
5	91	109
6	133	109
7	285	109
8	848	109
9	3642	109
done	5001	109

prune20.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
20.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify4.4s

Counts

94 → 94

Iterations

Useful iterations: 5 (2.4s)

Iter	Nodes	Cost
0	64	1843
1	104	1267
2	216	1115
3	409	1064
4	838	1028
5	4762	998
done	5000	998

prune163.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	32	698
1	50	646
2	72	570
3	99	570
4	143	570
5	251	570
6	549	570
7	1704	570
done	5000	570

prune138.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.5b

regimes25.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
done	12	9

end0.0ms

sample739.0ms

Algorithm

intervals

Results

368.0ms	2795×	body	1280	valid
126.0ms	4077×	body	80	valid
68.0ms	646×	body	640	valid
30.0ms	329×	body	320	valid
9.0ms	153×	body	160	valid