Details

sample27.0ms

Algorithm

intervals

Results

12.0ms	90×	body	1280	valid
4.0ms	129×	body	80	valid
2.0ms	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))

series4.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.9s

Counts

28 → 28

Iterations

Useful iterations: 4 (79.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	148	245
3	253	241
4	519	239
5	1334	239
6	4799	239
done	5000	239

prune45.0ms

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

localize7.0ms

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)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.9s

Counts

34 → 34

Iterations

Useful iterations: 3 (161.0ms)

Iter	Nodes	Cost
0	55	317
1	122	313
2	420	267
3	1267	264
4	4448	264
done	5000	264

prune69.0ms

Filtered

23 candidates to 34 candidates (-47.8%)

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))

rewrite30.0ms

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))
6.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (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))

simplify871.0ms

Counts

84 → 84

Iterations

Useful iterations: done (868.0ms)

Iter	Nodes	Cost
0	158	1656
1	366	1545
2	1142	1386
3	3667	1129
done	5001	1113

prune239.0ms

Filtered

70 candidates to 84 candidates (-20.0%)

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

localize10.0ms

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))

rewrite25.0ms

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:

8.0ms	(* (pow (cbrt (* (+ N 1.0) N)) 2) (cbrt (* (+ N 1.0) N)))
4.0ms	(pow (cbrt (* (+ N 1.0) N)) 2)
5.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))

series46.0ms

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))

simplify546.0ms

Counts

88 → 88

Iterations

Useful iterations: done (543.0ms)

Iter	Nodes	Cost
0	166	1596
1	419	1401
2	1538	1194
done	5000	1028

prune190.0ms

Filtered

65 candidates to 88 candidates (-35.4%)

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

regimes44.0ms

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

sample750.0ms

Algorithm

intervals

Results

368.0ms	2812×	body	1280	valid
119.0ms	4111×	body	80	valid
67.0ms	611×	body	640	valid
24.0ms	290×	body	320	valid
11.0ms	176×	body	160	valid

Details

sample27.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series4.0ms

simplify1.9s

prune45.0ms

localize7.0ms

rewrite8.0ms

series7.0ms

simplify1.9s

prune69.0ms

localize10.0ms

rewrite30.0ms

series42.0ms

simplify871.0ms

prune239.0ms

localize10.0ms

rewrite25.0ms

series46.0ms

simplify546.0ms

prune190.0ms

regimes44.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample750.0ms

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