Details

sample265.0ms

Algorithm

intervals

Results

88.0ms	34×	body	2560	valid
87.0ms	81×	body	1280	valid
29.0ms	50×	body	640	valid
17.0ms	22×	body	320	valid
11.0ms	107×	body	80	valid
8.0ms	80×	body	80	nan
6.0ms	1×	body	5120	valid
4.0ms	15×	body	160	valid

simplify945.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
5	2016
4	533
3	154
2	59
1	28
0	10

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.5b

localize17.0ms

Local error

Found 3 expressions with local error:

1.3b	(fma 100 (pow (+ 1 (/ i n)) n) -100)
6.8b	(pow (+ 1 (/ i n)) n)
11.2b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
49×	`*-un-lft-identity`
47×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`div-inv`
4×	`pow1` `unpow-prod-down`
3×	`expm1-log1p-u` `cbrt-undiv` `pow-unpow` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `pow-exp` `associate-/r/` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

3 → 105

Calls

3 calls:

0.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
16.0ms	(pow (+ 1 (/ i n)) n)
11.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series970.0ms

Counts

3 → 9

Calls

3 calls:

309.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
293.0ms	(pow (+ 1 (/ i n)) n)
368.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify1.2s

Counts

114 → 114

Iterations

Iter	Nodes
done	2005
3	2005
2	1605
1	528
0	222

prune516.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize29.0ms

Local error

Found 4 expressions with local error:

3.4b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
6.3b	(log1p (/ i n))
11.0b	(* n (log1p (/ i n)))
11.2b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/l*`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
1.0ms	(log1p (/ i n))
8.0ms	(* n (log1p (/ i n)))
9.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

series962.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
64.0ms	(log1p (/ i n))
81.0ms	(* n (log1p (/ i n)))
495.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

simplify956.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	2000
2	2000
1	636
0	257

prune679.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.8b

localize71.0ms

Local error

Found 4 expressions with local error:

11.0b	(* n (log1p (/ i n)))
17.7b	(cbrt (/ i n))
17.7b	(cbrt (/ i n))
17.7b	(cbrt (/ i n))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
29×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-r` `associate-l` `div-inv`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* n (log1p (/ i n)))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))

series273.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* n (log1p (/ i n)))
74.0ms	(cbrt (/ i n))
70.0ms	(cbrt (/ i n))
66.0ms	(cbrt (/ i n))

simplify929.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2001
4	2001
3	872
2	339
1	176
0	109

prune687.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.8b

localize67.0ms

Local error

Found 4 expressions with local error:

17.7b	(cbrt (/ i n))
17.7b	(cbrt (/ i n))
17.7b	(cbrt (/ i n))
17.7b	(cbrt (/ i n))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (/ i n))
1.0ms	(cbrt (/ i n))
1.0ms	(cbrt (/ i n))
1.0ms	(cbrt (/ i n))

series304.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (/ i n))
71.0ms	(cbrt (/ i n))
72.0ms	(cbrt (/ i n))
79.0ms	(cbrt (/ i n))

simplify871.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	2005
5	2005
4	1250
3	436
2	192
1	115
0	79

prune725.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.8b

regimes222.0ms

Accuracy

38.1% (15.8b remaining)

Error of 29.6b against oracle of 13.8b and baseline of 39.3b

bsearch1.0s

Steps

Iters	Range		Point
7	5.230678463826716e+219	3.866702833130526e+221	2.5555363937413246e+221
10	4.768362289250455e-83	3.133124810475992e-71	5.811229823508011e-78
9	-1.1122790233705282e-302	1.660299618472118e-308	-1.7065727457962e-312
6	-0.13673991589698092	-0.009521407882115243	-0.13295556128930017
6	-5.981261346914101e+64	-9.091852273913624e+63	-1.0933259526011947e+64
7	-1.38761684700311e+113	-8.639618869970432e+110	-6.246516767500982e+112

simplify60.0ms

Iterations

Iter	Nodes
done	123
1	123
0	95

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.6s	2455×	body	1280	valid
2.2s	998×	body	2560	valid
890.0ms	1537×	body	640	valid
651.0ms	3055×	body	80	valid
379.0ms	898×	body	320	valid
231.0ms	2276×	body	80	nan
116.0ms	456×	body	160	valid
13.0ms	3×	body	5120	valid