Details

sample208.0ms

Algorithm

intervals

Results

94.0ms	38×	body	2560	valid
57.0ms	66×	body	1280	valid
18.0ms	47×	body	640	valid
8.0ms	34×	body	320	valid
6.0ms	100×	body	80	valid
3.0ms	77×	body	80	nan
1.0ms	8×	body	160	valid

simplify3.6s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

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:

574.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
259.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
33.0ms	(pow (+ 1.0 (/ i n)) n)
523.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

483.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
312.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
329.0ms	(pow (+ 1.0 (/ i n)) n)
509.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.1s

Counts

293 → 293

Iterations

Useful iterations: done (2.1s)

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

prune826.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite724.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

347.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
183.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms	(pow (+ 1.0 (/ i n)) n)
170.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

266.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
218.0ms	(pow (+ 1.0 (/ i n)) n)
379.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify966.0ms

Counts

122 → 122

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	244	2124
1	635	2020
2	1971	1796
done	5000	1788

prune260.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0)))
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0))) (/ i n))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`distribute-lft-out`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`div-inv`
5×	`add-log-exp`
4×	`pow1` `unpow-prod-down` `distribute-rgt-neg-out` `associate-/l*`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3-+` `div-sub` `unsub-neg` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `sum-log` `associate-/r/` `sqr-pow`

Counts

3 → 120

Calls

3 calls:

28.0ms	(+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0)))
20.0ms	(pow (+ 1.0 (/ i n)) n)
87.0ms	(/ (+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0))) (/ i n))

series867.0ms

Counts

3 → 9

Calls

3 calls:

270.0ms	(+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0)))
216.0ms	(pow (+ 1.0 (/ i n)) n)
380.0ms	(/ (+ (* 100.0 (pow (+ 1.0 (/ i n)) n)) (* 100.0 (- 1.0))) (/ i n))

simplify1.2s

Counts

129 → 129

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	273	3420
1	656	2891
2	2244	2740
done	5000	2720

prune350.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
0.0b	(/ 100.0 (/ i (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)

rewrite980.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
38×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
26×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`add-cbrt-cube`
10×	`associate-*l/`
9×	`associate-/r*` `associate-/r/`
7×	`pow1` `associate-l`
6×	`unpow-prod-down` `flip3--` `flip--` `add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp` `div-inv`
3×	`pow-unpow` `associate-r` `associate-/l*` `sqr-pow`
2×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

533.0ms	(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
237.0ms	(/ 100.0 (/ i (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
182.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
23.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
397.0ms	(/ 100.0 (/ i (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
255.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
216.0ms	(pow (+ 1.0 (/ i n)) n)

simplify1.2s

Counts

126 → 126

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	249	2477
1	560	2343
2	1833	2153
done	5001	2132

prune301.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.3b

regimes132.0ms

Accuracy

58.7% (10.2b remaining)

Error of 18.5b against oracle of 8.3b and baseline of 33.0b

bsearch166.0ms

Steps

Iters	Range		Point
6	110.15968793260775	701.025784686831	116.77955258703142
9	-79465067.8176491	-0.35018159126246495	-0.4112290909641322

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	58
1	42	58
done	42	58

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.9s	988×	body	2560	valid
1.9s	2507×	body	1280	valid
496.0ms	1564×	body	640	valid
162.0ms	891×	body	320	valid
137.0ms	3043×	body	80	valid
78.0ms	2285×	body	80	nan
47.0ms	433×	body	160	valid
28.0ms	8×	body	5120	valid