Details

sample176.0ms

Algorithm

intervals

Results

64.0ms	88×	body	1280	valid
63.0ms	31×	body	2560	valid
16.0ms	52×	body	640	valid
5.0ms	1×	body	5120	valid
4.0ms	30×	body	320	valid
4.0ms	86×	body	80	valid
3.0ms	80×	body	80	nan
2.0ms	17×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	139	15
4	338	15
5	986	15
6	4059	15
done	5000	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.2b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite814.0ms

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:

328.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
155.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(pow (+ 1.0 (/ i n)) n)
295.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

369.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
244.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms	(pow (+ 1.0 (/ i n)) n)
350.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.6s

Counts

293 → 293

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	437	6469
1	1183	6125
2	3764	5875
done	5001	5867

prune814.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.2b

localize16.0ms

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)))
9.4b	(* (pow i 2) (log 1.0))
18.6b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

19.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
261.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
14.0ms	(* (pow i 2) (log 1.0))
261.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series586.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
213.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
140.0ms	(* (pow i 2) (log 1.0))
192.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.2s

Counts

198 → 198

Iterations

Useful iterations: 2 (504.0ms)

Iter	Nodes	Cost
0	338	6829
1	902	6613
2	3386	6123
done	5000	6123

prune687.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.4b

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)
9.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.4b	(* (pow i 2) (log 1.0))

rewrite805.0ms

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:

244.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
285.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
258.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))

series636.0ms

Counts

4 → 12

Calls

4 calls:

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))
205.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
132.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
146.0ms	(* (pow i 2) (log 1.0))

simplify921.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	218	3765
1	532	3686
2	1891	3143
done	5001	3143

prune580.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.4b

localize24.0ms

Local error

Found 4 expressions with local error:

9.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.4b	(* (pow i 2) (log 1.0))
9.4b	(* (pow i 2) (log 1.0))
9.4b	(* (pow i 2) (log 1.0))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
21×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r` `log-pow` `-commutative` `cbrt-unprod` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 132

Calls

4 calls:

258.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))
13.0ms	(* (pow i 2) (log 1.0))
14.0ms	(* (pow i 2) (log 1.0))

series560.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms	(* (pow i 2) (log 1.0))
143.0ms	(* (pow i 2) (log 1.0))
138.0ms	(* (pow i 2) (log 1.0))

simplify727.0ms

Counts

144 → 144

Iterations

Useful iterations: done (723.0ms)

Iter	Nodes	Cost
0	136	2322
1	300	2231
2	1031	1984
done	5001	1774

prune624.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.4b

regimes154.0ms

Accuracy

48.6% (12.8b remaining)

Error of 21.0b against oracle of 8.2b and baseline of 33.1b

bsearch221.0ms

Steps

Iters	Range		Point
10	1.4247645541724984e-187	3.537376337853017e-175	3.089742171439268e-181
6	5.2254629500859e-285	6.442889750848156e-284	5.321174585513156e-285
7	-344.8786496099632	-2.176521556311946	-2.3466525277232653

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	103
1	56	103
done	56	103

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	1043×	body	2560	valid
1.8s	2494×	body	1280	valid
448.0ms	1569×	body	640	valid
136.0ms	3021×	body	80	valid
132.0ms	793×	body	320	valid
73.0ms	2273×	body	80	nan
47.0ms	470×	body	160	valid
21.0ms	5×	body	5120	valid