Details

sample57.0ms

Algorithm

intervals

Results

26.0ms	92×	body	1280	valid
8.0ms	122×	body	80	valid
6.0ms	23×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	4×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.3b	(- (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-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series24.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
21.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.0s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	1579
4	611
3	284
2	150
1	76
0	40

prune140.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.0b	(+ 1 (* (+ N 1.0) N))
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

16.0ms	(* (+ N 1.0) N)
5.0ms	(+ 1 (* (+ N 1.0) N))
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series86.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (+ N 1.0) N)
24.0ms	(+ 1 (* (+ N 1.0) N))
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	1520
2	512
1	188
0	73

prune233.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (* (* (cbrt (+ 1 (* (+ N 1.0) N))) (cbrt (+ 1 (* (+ N 1.0) N)))) (cbrt (+ 1 (* (+ N 1.0) N)))))
15.9b	(cbrt (+ 1 (* (+ N 1.0) N)))
15.9b	(cbrt (+ 1 (* (+ N 1.0) N)))
15.9b	(cbrt (+ 1 (* (+ N 1.0) N)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

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

series364.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 1.0 (* (* (cbrt (+ 1 (* (+ N 1.0) N))) (cbrt (+ 1 (* (+ N 1.0) N)))) (cbrt (+ 1 (* (+ N 1.0) N)))))
145.0ms	(cbrt (+ 1 (* (+ N 1.0) N)))
106.0ms	(cbrt (+ 1 (* (+ N 1.0) N)))
103.0ms	(cbrt (+ 1 (* (+ N 1.0) N)))

simplify2.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
4	3297
3	909
2	363
1	152
0	71

prune363.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize27.0ms

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

rewrite16.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 49

Calls

4 calls:

4.0ms	(cbrt (+ N 1.0))
7.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (+ N 1.0))
107.0ms	(cbrt (+ N 1.0))
96.0ms	(cbrt (+ N 1.0))
4.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify2.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
4	4147
3	1335
2	496
1	201
0	92

prune316.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes66.0ms

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

end1.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	2853×	body	1280	valid
213.0ms	4018×	body	80	valid
117.0ms	650×	body	640	valid
78.0ms	327×	body	320	valid
15.0ms	152×	body	160	valid