Details

sample180.0ms

Algorithm

intervals

Results

79.0ms	100×	body	1280	valid
50.0ms	32×	body	2560	valid
18.0ms	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

simplify2.8s

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	319	15
5	939	15
6	3737	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))

rewrite94.0ms

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:

39.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (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))

series212.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
38.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms	(pow (+ 1.0 (/ i n)) n)
72.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.4s

Counts

293 → 293

Iterations

Useful iterations: 2 (771.0ms)

Iter	Nodes	Cost
0	437	6469
1	1223	6125
2	3766	5875
done	5001	5875

prune624.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

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

localize20.0ms

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))

rewrite56.0ms

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)))
6.0ms	(* (log 1.0) (pow i 2))
14.0ms	(/ (- (+ (* 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))
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)))
14.0ms	(* (log 1.0) (pow i 2))
26.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

simplify1.2s

Counts

206 → 206

Iterations

Useful iterations: 2 (637.0ms)

Iter	Nodes	Cost
0	328	6640
1	886	6434
2	3189	5972
done	5000	5972

prune789.0ms

Filtered

155 candidates to 206 candidates (-32.9%)

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

localize20.0ms

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))

rewrite40.0ms

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))

series62.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2))))
26.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i) n))
16.0ms	(/ (- (+ (* 1.0 i) (+ (* (log 1.0) n) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) i)
13.0ms	(* (log 1.0) (pow i 2))

simplify991.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	193	2813
1	525	2744
2	1919	2353
done	5001	2353

prune294.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 9.5b

Counts

115 → 11

localize20.0ms

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))

rewrite127.0ms

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:

55.0ms	(* 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)))
17.0ms	(/ (/ (- (+ (* 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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

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) (/ 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)
26.0ms	(* (log 1.0) (pow i 2))

simplify1.1s

Counts

498 → 498

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	700	22239
1	2105	20449
done	5000	20255

prune2.2s

Filtered

291 candidates to 498 candidates (-71.1%)

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

regimes204.0ms

Accuracy

64.1% (6.4b remaining)

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

bsearch205.0ms

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

sample5.2s

Algorithm

intervals

Results

2.1s	2949×	body	1280	valid
1.6s	1014×	body	2560	valid
592.0ms	1720×	body	640	valid
185.0ms	876×	body	320	valid
155.0ms	2399×	body	80	valid
100.0ms	2296×	body	80	nan
65.0ms	482×	body	160	valid
21.0ms	8×	body	5120	valid

Details

sample180.0ms

simplify2.8s

prune3.0ms

localize9.0ms

rewrite94.0ms

series212.0ms

simplify1.4s

prune624.0ms

localize20.0ms

rewrite56.0ms

series66.0ms

simplify1.2s

prune789.0ms

localize20.0ms

rewrite40.0ms

series62.0ms

simplify991.0ms

prune294.0ms

localize20.0ms

rewrite127.0ms

series87.0ms

simplify1.1s

prune2.2s

regimes204.0ms

bsearch205.0ms

simplify5.0ms

end0.0ms

sample5.2s

Profiling