Details

sample50.0ms

Algorithm

intervals

Results

27.0ms	98×	body	1280	valid
6.0ms	120×	body	80	valid
5.0ms	25×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

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: 16.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite11.0ms

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))
8.0ms	(- (atan (+ N 1.0)) (atan N))

series23.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
20.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.5s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	3795
4	981
3	326
2	151
1	76
0	40

prune118.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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:

8.0ms	(+ 1 (* (+ N 1.0) N))
16.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series102.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ 1 (* (+ N 1.0) N))
70.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5002
2	1287
1	197
0	73

prune274.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
16.2b	(cbrt (* (+ N 1.0) N))
16.2b	(cbrt (* (+ N 1.0) N))
16.2b	(cbrt (* (+ N 1.0) N))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `associate-*r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

17.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
6.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))
13.0ms	(cbrt (* (+ N 1.0) N))

series512.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
138.0ms	(cbrt (* (+ N 1.0) N))
109.0ms	(cbrt (* (+ N 1.0) N))
122.0ms	(cbrt (* (+ N 1.0) N))

simplify1.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1583
1	380
0	152

prune598.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
9.0ms	(* (cbrt N) (cbrt N))

series1.1s

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt N)
236.0ms	(cbrt N)
267.0ms	(cbrt N)
303.0ms	(* (cbrt N) (cbrt N))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	723
1	138
0	61

prune400.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2776×	body	1280	valid
218.0ms	4138×	body	80	valid
161.0ms	626×	body	640	valid
52.0ms	313×	body	320	valid
16.0ms	147×	body	160	valid