Details

sample53.0ms

Algorithm

intervals

Results

23.0ms	89×	body	1280	valid
8.0ms	131×	body	80	valid
5.0ms	25×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

Local error

Found 1 expressions with local error:

1.1b	(- (atan (+ N 1.0)) (atan N))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

10.0ms

(- (atan (+ N 1.0)) (atan N))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(- (atan (+ N 1.0)) (atan N))

simplify3.3s

Counts

18 → 18

Iterations

Useful iterations: 4 (289.0ms)

Iter	Nodes	Cost
0	36	209
1	73	205
2	149	191
3	325	187
4	960	185
5	3446	185
done	5000	185

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

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:

49.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series90.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(* (+ N 1.0) N)
7.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify665.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	55	317
1	127	312
2	694	264
done	5000	264

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 49

Calls

4 calls:

7.0ms	(cbrt (+ N 1.0))
12.0ms	(cbrt (+ N 1.0))
7.0ms	(cbrt (+ N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (+ N 1.0))
162.0ms	(cbrt (+ N 1.0))
146.0ms	(cbrt (+ N 1.0))
6.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	92	906
1	201	876
2	569	733
3	2087	658
done	5001	613

prune789.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.0b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

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))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
20.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
25.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify1.7s

Counts

52 → 52

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	32	698
1	53	646
2	128	570
3	313	570
4	916	570
5	2872	570
done	5002	570

prune253.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.6s

Algorithm

intervals

Results

824.0ms	2907×	body	1280	valid
304.0ms	3989×	body	80	valid
128.0ms	627×	body	640	valid
102.0ms	290×	body	320	valid
21.0ms	187×	body	160	valid