Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	98×	body	1280	valid
11.0ms	117×	body	80	valid
3.0ms	24×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	3×	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: 17.8b

localize8.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

4.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify2.3s

Counts

18 → 18

Iterations

Iter	Nodes
done	5001
5	3570
4	966
3	326
2	149
1	73
0	36

prune74.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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:

32.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series56.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify739.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	5002
2	695
1	127
0	55

prune136.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
7.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))

series372.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
127.0ms	(cbrt (* (+ N 1.0) N))
109.0ms	(cbrt (* (+ N 1.0) N))
128.0ms	(cbrt (* (+ N 1.0) N))

simplify2.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	3332
2	689
1	210
0	95

prune254.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (* (cbrt (+ N 1.0)) (cbrt N))) (cbrt (* (+ N 1.0) N)))))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `associate-*l/` `add-exp-log` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt N)
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (* (cbrt (+ N 1.0)) (cbrt N))) (cbrt (* (+ N 1.0) N)))))
6.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))

series396.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt N)
7.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (* (cbrt (+ N 1.0)) (cbrt N))) (cbrt (* (+ N 1.0) N)))))
99.0ms	(cbrt (* (+ N 1.0) N))
100.0ms	(cbrt (* (+ N 1.0) N))

simplify1.8s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	3772
2	814
1	250
0	115

prune252.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.3s

Algorithm

intervals

Results

824.0ms	2881×	body	1280	valid
196.0ms	4036×	body	80	valid
83.0ms	625×	body	640	valid
30.0ms	302×	body	320	valid
11.0ms	156×	body	160	valid