Details

sample55.0ms

Algorithm

intervals

Results

18.0ms	66×	body	1280	valid
8.0ms	249×	body	80	nan
7.0ms	38×	body	640	valid
6.0ms	122×	body	80	valid
3.0ms	25×	body	320	valid
0.0ms	5×	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

prune2.0ms

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: 31.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

simplify894.0ms

Counts

47 → 47

Iterations

Useful iterations: 4 (457.0ms)

Iter	Nodes	Cost
0	107	516
1	233	490
2	605	445
3	1483	443
4	3925	432
done	5000	432

prune88.0ms

Filtered

33 candidates to 47 candidates (-42.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
0.3b	(/ 0.5 (* N N))
0.4b	(/ 0.3333333333333333 (pow N 3))
12.2b	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
54×	`times-frac`
40×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`add-exp-log` `unpow-prod-down` `cube-prod`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-log-exp`
10×	`difference-of-squares`
6×	`associate-/l*` `sqr-pow`
5×	`cube-mult` `div-exp`
4×	`pow1` `unpow3`
3×	`cbrt-undiv` `frac-add` `distribute-lft-out--`
2×	`sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 131

Calls

4 calls:

32.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
5.0ms	(/ 0.5 (* N N))
6.0ms	(/ 0.3333333333333333 (pow N 3))
22.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms	(/ 0.5 (* N N))
4.0ms	(/ 0.3333333333333333 (pow N 3))
9.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify480.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	213	2088
1	515	1835
2	1853	1733
done	5000	1733

prune199.0ms

Filtered

90 candidates to 143 candidates (-58.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Merged error: 0.0b

Counts

146 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.6b	(log (/ (+ N 1.0) N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/ (+ N 1.0) N)
5.0ms	(log (/ (+ N 1.0) N))

series9.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

simplify471.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	103	713
1	218	680
2	581	625
3	1723	612
done	5000	612

prune88.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (log (/ (+ N 1.0) N)))
2.6b	(log (/ (+ N 1.0) N))
2.6b	(log (/ (+ N 1.0) N))
2.6b	(log (/ (+ N 1.0) N))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
47×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
9×	`distribute-lft-out`
8×	`pow1`
6×	`rem-log-exp`
4×	`cbrt-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-div` `div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 93

Calls

4 calls:

2.0ms	(cbrt (log (/ (+ N 1.0) N)))
5.0ms	(log (/ (+ N 1.0) N))
5.0ms	(log (/ (+ N 1.0) N))
5.0ms	(log (/ (+ N 1.0) N))

series33.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (log (/ (+ N 1.0) N)))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))
7.0ms	(log (/ (+ N 1.0) N))

simplify559.0ms

Counts

105 → 105

Iterations

Useful iterations: 3 (201.0ms)

Iter	Nodes	Cost
0	127	1420
1	280	1338
2	774	1211
3	2260	1150
done	5001	1150

prune252.0ms

Filtered

74 candidates to 105 candidates (-41.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch13.0ms

Steps

Iters	Range		Point
8	901.3230478674768	932371.3337660737	4139.108144936646

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	28
1	23	28
done	23	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

477.0ms	1761×	body	1280	valid
276.0ms	8058×	body	80	nan
225.0ms	1217×	body	640	valid
179.0ms	4113×	body	80	valid
76.0ms	621×	body	320	valid
25.0ms	288×	body	160	valid

Details

sample55.0ms

simplify3.0ms

prune2.0ms

localize7.0ms

rewrite12.0ms

series9.0ms

simplify894.0ms

prune88.0ms

localize13.0ms

rewrite74.0ms

series20.0ms

simplify480.0ms

prune199.0ms

localize5.0ms

rewrite13.0ms

series9.0ms

simplify471.0ms

prune88.0ms

localize9.0ms

rewrite20.0ms

series33.0ms

simplify559.0ms

prune252.0ms

regimes44.0ms

bsearch13.0ms

simplify2.0ms

end0.0ms

sample1.6s

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