Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	90×	body	1280	valid
4.0ms	129×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series3.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.7s

Counts

28 → 28

Iterations

Useful iterations: 4 (76.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	148	245
3	250	241
4	484	239
5	1214	239
6	4480	239
done	5000	239

prune41.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	1	29

Merged error: 0.2b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite8.0ms

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:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.0s

Counts

34 → 34

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	55	317
1	122	312
2	370	264
3	1302	264
4	3688	264
done	5000	264

prune69.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	5	35

Merged error: 0.2b

Counts

35 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
15.5b	(cbrt (* (+ N 1.0) N))
15.5b	(cbrt (* (+ N 1.0) N))
15.5b	(cbrt (* (+ N 1.0) N))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
5.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))

series43.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
10.0ms	(cbrt (* (+ N 1.0) N))
10.0ms	(cbrt (* (+ N 1.0) N))
10.0ms	(cbrt (* (+ N 1.0) N))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (326.0ms)

Iter	Nodes	Cost
0	158	1656
1	366	1540
2	1122	1386
3	3534	1113
done	5000	1113

prune252.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	83	6	89

Merged error: 0.1b

Counts

89 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (cbrt (* (+ N 1.0) N)) 2) (cbrt (* (+ N 1.0) N)))
0.4b	(pow (cbrt (* (+ N 1.0) N)) 2)
15.5b	(cbrt (* (+ N 1.0) N))
15.5b	(cbrt (* (+ N 1.0) N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`add-cube-cbrt` `unpow-prod-down` `-un-lft-identity` `associate-l*`
6×	`pow1` `cbrt-div` `associate-*l/`
5×	`cbrt-prod` `add-cbrt-cube`
4×	`associate-r` `unpow2` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `flip3-+` `pow1/3` `prod-exp` `flip-+` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `associate-*r/` `pow-exp`
1×	`pow-plus` `pow3` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (pow (cbrt (* (+ N 1.0) N)) 2) (cbrt (* (+ N 1.0) N)))
4.0ms	(pow (cbrt (* (+ N 1.0) N)) 2)
7.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (pow (cbrt (* (+ N 1.0) N)) 2) (cbrt (* (+ N 1.0) N)))
16.0ms	(pow (cbrt (* (+ N 1.0) N)) 2)
10.0ms	(cbrt (* (+ N 1.0) N))
10.0ms	(cbrt (* (+ N 1.0) N))

simplify401.0ms

Counts

88 → 88

Iterations

Useful iterations: done (398.0ms)

Iter	Nodes	Cost
0	166	1596
1	419	1340
2	1430	1150
done	5000	1008

prune212.0ms

Filtered

69 candidates to 88 candidates (-27.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Merged error: 0.1b

Counts

94 → 6

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample800.0ms

Algorithm

intervals

Results

395.0ms	2812×	body	1280	valid
126.0ms	4111×	body	80	valid
72.0ms	611×	body	640	valid
25.0ms	290×	body	320	valid
11.0ms	176×	body	160	valid

Details

sample29.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify1.7s

prune41.0ms

localize6.0ms

rewrite8.0ms

series10.0ms

simplify1.0s

prune69.0ms

localize10.0ms

rewrite28.0ms

series43.0ms

simplify1.1s

prune252.0ms

localize11.0ms

rewrite29.0ms

series45.0ms

simplify401.0ms

prune212.0ms

regimes45.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample800.0ms

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