Details

sample33.0ms

Algorithm

intervals

Results

16.0ms	94×	body	1280	valid
5.0ms	132×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.8b	(- (atan (+ 1.0 N)) (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:

5.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify2.0s

Counts

18 → 18

Iterations

Iter	Nodes
done	5000
5	3649
4	1034
3	360
2	151
1	76
0	39

prune101.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.1b	(atan2 1.0 (+ (* N (+ N 1.0)) 1))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series80.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(* N (+ N 1.0))
4.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))

simplify525.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
2	748
1	156
0	56

prune119.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

17.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.2s

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (cbrt N) (cbrt N))
345.0ms	(cbrt N)
295.0ms	(cbrt N)
288.0ms	(cbrt N)

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	727
1	138
0	61

prune373.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.7b	(cbrt (cbrt N))
0.7b	(cbrt (cbrt N))
0.7b	(cbrt (cbrt N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-log-exp`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt (cbrt N))
1.0ms	(cbrt (cbrt N))
1.0ms	(cbrt (cbrt N))

series1.8s

Counts

4 → 12

Calls

4 calls:

575.0ms	(cbrt N)
447.0ms	(cbrt (cbrt N))
409.0ms	(cbrt (cbrt N))
395.0ms	(cbrt (cbrt N))

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
4	2270
3	644
2	187
1	77
0	42

prune343.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.5s

Algorithm

intervals

Results

833.0ms	2802×	body	1280	valid
276.0ms	4130×	body	80	valid
147.0ms	589×	body	640	valid
51.0ms	334×	body	320	valid
15.0ms	145×	body	160	valid