Details

sample298.0ms

Algorithm

intervals

Results

109.0ms	80×	body	1280	valid
93.0ms	34×	body	2560	valid
36.0ms	40×	body	640	valid
10.0ms	28×	body	320	valid
9.0ms	88×	body	80	valid
5.0ms	57×	body	80	nan
5.0ms	19×	body	160	valid

simplify7.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
6	3302
5	836
4	309
3	135
2	59
1	25
0	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize120.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.9s

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`
4×	`insert-posit16`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `distribute-lft-out`

Counts

4 → 285

Calls

4 calls:

687.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
431.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
40.0ms	(pow (+ 1.0 (/ i n)) n)
730.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.4s

Counts

4 → 12

Calls

4 calls:

775.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
474.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
364.0ms	(pow (+ 1.0 (/ i n)) n)
783.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify7.0s

Counts

297 → 297

Iterations

Iter	Nodes
done	5001
2	4691
1	1394
0	441

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize107.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (exp (- (pow (+ (/ i n) 1.0) n) 1.0)))
1.7b	(- (pow (+ (/ i n) 1.0) n) 1.0)
6.1b	(pow (+ (/ i n) 1.0) n)
11.4b	(/ (log (exp (- (pow (+ (/ i n) 1.0) n) 1.0))) (/ i n))

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
200×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
120×	`log-pow` `add-cube-cbrt`
105×	`exp-prod`
48×	`difference-of-squares`
20×	`pow1` `unpow-prod-down`
17×	`sqr-pow`
16×	`distribute-lft-out--`
13×	`associate-/r*` `div-inv`
11×	`associate-/l*`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`log-prod`
4×	`insert-posit16`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`log-div` `sub-neg` `exp-diff` `exp-sum`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `flip3--` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `associate-/r/` `flip--` `distribute-lft-out`

Counts

4 → 243

Calls

4 calls:

810.0ms	(log (exp (- (pow (+ (/ i n) 1.0) n) 1.0)))
374.0ms	(- (pow (+ (/ i n) 1.0) n) 1.0)
61.0ms	(pow (+ (/ i n) 1.0) n)
2.6s	(/ (log (exp (- (pow (+ (/ i n) 1.0) n) 1.0))) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

378.0ms	(log (exp (- (pow (+ (/ i n) 1.0) n) 1.0)))
381.0ms	(- (pow (+ (/ i n) 1.0) n) 1.0)
295.0ms	(pow (+ (/ i n) 1.0) n)
646.0ms	(/ (log (exp (- (pow (+ (/ i n) 1.0) n) 1.0))) (/ i n))

simplify4.7s

Counts

255 → 255

Iterations

Iter	Nodes
done	5009
2	3401
1	1179
0	432

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize218.0ms

Local error

Found 4 expressions with local error:

6.1b	(pow (+ (/ i n) 1.0) n)
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
29×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `pow1/3` `div-inv`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

44.0ms	(pow (+ (/ i n) 1.0) n)
5.0ms	(cbrt (/ i n))
5.0ms	(cbrt (/ i n))
5.0ms	(cbrt (/ i n))

series610.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(pow (+ (/ i n) 1.0) n)
105.0ms	(cbrt (/ i n))
104.0ms	(cbrt (/ i n))
104.0ms	(cbrt (/ i n))

simplify4.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5032
4	3519
3	972
2	401
1	205
0	113

prune968.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize267.0ms

Local error

Found 4 expressions with local error:

17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `div-inv` `add-log-exp`

Counts

4 → 92

Calls

4 calls:

5.0ms	(cbrt (/ i n))
5.0ms	(cbrt (/ i n))
5.0ms	(cbrt (/ i n))
5.0ms	(cbrt (/ i n))

series419.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (/ i n))
104.0ms	(cbrt (/ i n))
104.0ms	(cbrt (/ i n))
105.0ms	(cbrt (/ i n))

simplify3.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
5	3179
4	1084
3	382
2	188
1	113
0	77

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

regimes293.0ms

Accuracy

50.7% (10.6b remaining)

Error of 32.5b against oracle of 21.8b and baseline of 43.4b

bsearch527.0ms

Steps

Iters	Range		Point
11	7.945801709345076e-185	1.988988581640589e-154	7.680781589380277e-180
11	-3.4461486957845398e-239	-1.7934479232057028e-258	-1.8097259091280393e-258
8	-1763.0658270955876	-0.28008678268591264	-1.999963205744506
4	-1.5125315820373007e+85	-8.927875500473959e+84	-1.260760569041402e+85

simplify40.0ms

Iterations

Iter	Nodes
done	75
1	75
0	58

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.4s	2486×	body	1280	valid
2.2s	993×	body	2560	valid
759.0ms	1615×	body	640	valid
545.0ms	3065×	body	80	valid
218.0ms	842×	body	320	valid
129.0ms	2210×	body	80	nan
125.0ms	449×	body	160	valid
24.0ms	7×	body	5120	valid