Details

sample185.0ms

Algorithm

intervals

Results

76.0ms	100×	body	1280	valid
52.0ms	32×	body	2560	valid
22.0ms	49×	body	640	valid
6.0ms	84×	body	80	valid
5.0ms	27×	body	320	valid
3.0ms	68×	body	80	nan
2.0ms	17×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	58	15
3	137	15
4	328	15
5	1007	15
6	4131	15
done	5000	15

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: 48.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b	(pow (+ 1.0 (/ i n)) n)
10.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
16.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
18.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series217.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
41.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms	(pow (+ 1.0 (/ i n)) n)
72.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify904.0ms

Counts

293 → 293

Iterations

Useful iterations: 2 (327.0ms)

Iter	Nodes	Cost
0	437	6469
1	1237	6166
2	4457	5908
done	5000	5908

prune659.0ms

Filtered

233 candidates to 293 candidates (-25.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	7	294

Merged error: 21.2b

Counts

294 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
12.1b	(* (log 1.0) (pow i 2))
20.3b	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
109×	`add-sqr-sqrt`
88×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`unswap-sqr`
10×	`associate-l`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 194

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
20.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
9.0ms	(* (log 1.0) (pow i 2))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

series66.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
28.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
14.0ms	(* (log 1.0) (pow i 2))
21.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

simplify822.0ms

Counts

206 → 206

Iterations

Useful iterations: done (813.0ms)

Iter	Nodes	Cost
0	328	6640
1	896	6463
2	3814	5986
done	5001	5978

prune831.0ms

Filtered

159 candidates to 206 candidates (-29.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	202	11	213

Merged error: 9.5b

Counts

213 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2))))
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) n))
11.5b	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
12.1b	(* (log 1.0) (pow i 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`times-frac` `associate-r` `add-log-exp`
8×	`prod-exp`
7×	`associate-l`
6×	`cbrt-unprod`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `sum-log` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2))))
12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) n))
12.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
7.0ms	(* (log 1.0) (pow i 2))

series65.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2))))
23.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) n))
19.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
15.0ms	(* (log 1.0) (pow i 2))

simplify600.0ms

Counts

104 → 104

Iterations

Useful iterations: done (596.0ms)

Iter	Nodes	Cost
0	193	2813
1	528	2752
2	2107	2362
done	5000	2347

prune300.0ms

Filtered

68 candidates to 104 candidates (-52.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 9.5b

Counts

115 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n)))
0.2b	(/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n))
11.5b	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
12.1b	(* (log 1.0) (pow i 2))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
426×	`add-sqr-sqrt`
397×	`*-un-lft-identity`
395×	`add-cube-cbrt`
182×	`associate-r`
65×	`add-exp-log`
57×	`div-inv`
38×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
12×	`prod-exp`
11×	`unswap-sqr`
7×	`pow1` `associate-l`
6×	`cbrt-unprod`
4×	`unpow-prod-down` `rec-exp` `1-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `associate-*r/` `pow-prod-down` `pow-exp` `log-pow` `flip--`

Counts

4 → 486

Calls

4 calls:

49.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n)))
20.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n))
12.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
7.0ms	(* (log 1.0) (pow i 2))

series80.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n)))
21.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) (/ 1 n))
16.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
14.0ms	(* (log 1.0) (pow i 2))

simplify533.0ms

Counts

498 → 498

Iterations

Useful iterations: done (501.0ms)

Iter	Nodes	Cost
0	700	22239
1	2123	21148
done	5000	20488

prune2.8s

Filtered

341 candidates to 498 candidates (-46.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	498	11	509

Merged error: 9.5b

Counts

509 → 11

regimes211.0ms

Accuracy

64.1% (6.4b remaining)

Error of 17.3b against oracle of 10.9b and baseline of 28.8b

bsearch210.0ms

Steps

Iters	Range		Point
11	8.13869889177149e+213	1.748637164400731e+238	1.8422380825896938e+236
9	3.068084326862795e-12	6.274218779895055e-05	5.681068722470438e-05
9	-7.954226809062042e-32	-6.675104844668032e-38	-7.856997819585396e-32

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	107
1	68	107
done	68	107

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	2949×	body	1280	valid
1.6s	1014×	body	2560	valid
614.0ms	1720×	body	640	valid
192.0ms	876×	body	320	valid
169.0ms	2399×	body	80	valid
107.0ms	2296×	body	80	nan
69.0ms	482×	body	160	valid
22.0ms	8×	body	5120	valid

Details

sample185.0ms

simplify1.4s

prune3.0ms

localize9.0ms

rewrite95.0ms

series217.0ms

simplify904.0ms

prune659.0ms

localize17.0ms

rewrite60.0ms

series66.0ms

simplify822.0ms

prune831.0ms

localize17.0ms

rewrite41.0ms

series65.0ms

simplify600.0ms

prune300.0ms

localize18.0ms

rewrite128.0ms

series80.0ms

simplify533.0ms

prune2.8s

regimes211.0ms

bsearch210.0ms

simplify5.0ms

end0.0ms

sample5.3s

Profiling