Details

sample157.0ms

Algorithm

intervals

Results

61.0ms	30×	body	2560	valid
53.0ms	75×	body	1280	valid
14.0ms	48×	body	640	valid
5.0ms	107×	body	80	valid
4.0ms	1×	body	5120	valid
4.0ms	23×	body	320	valid
3.0ms	84×	body	80	nan
1.0ms	15×	body	160	valid

simplify2.7s

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	327	15
5	998	15
6	4177	15
done	5000	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b	(pow (+ 1.0 (/ i n)) n)
10.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite637.0ms

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:

258.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
119.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms	(pow (+ 1.0 (/ i n)) n)
229.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

376.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
257.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms	(pow (+ 1.0 (/ i n)) n)
362.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify416.0ms

Counts

293 → 293

Iterations

Useful iterations: done (406.0ms)

Iter	Nodes	Cost
0	437	6469
1	1235	6125
done	5001	6097

prune814.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
0.1b	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b	(pow (+ 1.0 (/ i n)) n)

rewrite580.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`associate-l`
22×	`times-frac`
19×	`add-exp-log` `add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`pow1` `difference-of-squares`
8×	`unpow-prod-down`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sqr-pow`
4×	`associate-r` `pow-prod-down` `distribute-lft-out--`
3×	`pow-unpow`
2×	`cbrt-undiv` `div-exp` `associate-l/` `-commutative` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `associate-*r/` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

186.0ms	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
257.0ms	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
120.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

380.0ms	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
358.0ms	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
255.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms	(pow (+ 1.0 (/ i n)) n)

simplify799.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (170.0ms)

Iter	Nodes	Cost
0	210	1888
1	539	1822
2	2071	1606
done	5001	1606

prune273.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`times-frac` `add-log-exp`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
4×	`unpow-prod-down` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `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 → 98

Calls

4 calls:

9.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
110.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
138.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series542.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
212.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
141.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
143.0ms	(* (pow i 2) (log 1.0))

simplify947.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	210	2896
1	544	2825
2	2228	2419
done	5000	2419

prune311.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
22×	`add-cbrt-cube`
20×	`associate-r`
19×	`times-frac`
12×	`pow1` `associate-l`
10×	`prod-exp`
8×	`cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*r/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*l/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

133.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
153.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
135.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series609.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
204.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
128.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
136.0ms	(* (pow i 2) (log 1.0))

simplify949.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (193.0ms)

Iter	Nodes	Cost
0	218	3765
1	548	3686
2	2533	3149
done	5000	3149

prune339.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.2b

regimes207.0ms

Accuracy

46.1% (12.2b remaining)

Error of 23.6b against oracle of 11.4b and baseline of 34.0b

bsearch568.0ms

Steps

Iters	Range		Point
7	1.8763976102611505e-155	6.193957419652655e-154	6.2539521969327255e-155
6	1.428658578821738e-291	1.1241352939529096e-290	1.4472641457797862e-291
8	-542359391.39979	-925426.909356872	-934893.9033682138
5	-2.350670412092924e+26	-9.509086209243448e+25	-1.0912719332224593e+26
7	-9.598097109554337e+63	-7.474441928331378e+61	-3.317476088456595e+63
6	-4.85405993564138e+85	-5.838951595693273e+84	-4.0369911640829986e+85
7	-2.854726066546375e+174	-4.469800189377323e+172	-1.0029723224091834e+174

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	211
1	78	211
done	78	211

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	954×	body	2560	valid
1.7s	2510×	body	1280	valid
472.0ms	1657×	body	640	valid
144.0ms	866×	body	320	valid
132.0ms	3029×	body	80	valid
71.0ms	2286×	body	80	nan
43.0ms	423×	body	160	valid
21.0ms	6×	body	5120	valid