Details

sample54.0ms

Algorithm

intervals

Results

27.0ms	102×	body	1280	valid
7.0ms	113×	body	80	valid
6.0ms	28×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.4b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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))
6.0ms	(- (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))

simplify1.8s

Counts

28 → 28

Iterations

Useful iterations: 4 (218.0ms)

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

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

30.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (+ N 1.0) N)
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.5s

Counts

34 → 34

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	356	264
3	1001	264
4	4336	264
done	5002	264

prune66.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.5b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
17.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.4b	(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))))

series45.0ms

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)))))
21.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify4.5s

Counts

94 → 94

Iterations

Useful iterations: 5 (2.6s)

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

prune184.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
17.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
18.0b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
18.0b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
130.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
134.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify2.9s

Counts

54 → 54

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	41	781
1	65	747
2	94	657
3	152	621
4	460	621
5	3380	621
done	5001	621

prune214.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes53.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.3s

Algorithm

intervals

Results

716.0ms	2890×	body	1280	valid
203.0ms	3999×	body	80	valid
140.0ms	655×	body	640	valid
39.0ms	302×	body	320	valid
17.0ms	154×	body	160	valid