Details

analyze813.0ms

Algorithm: search

sample211.0ms

Algorithm

intervals

Results

85.0ms	93×	body	1280	valid
63.0ms	28×	body	2560	valid
26.0ms	51×	body	640	valid
5.0ms	22×	body	320	valid
5.0ms	10×	body	640	invalid
4.0ms	5×	body	1280	invalid
3.0ms	51×	body	80	valid
3.0ms	9×	body	320	invalid
2.0ms	11×	body	160	valid
2.0ms	16×	body	80	invalid
1.0ms	14×	body	80	nan
0.0ms	2×	body	160	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 49.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite85.0ms

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:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series186.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
63.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify68.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune610.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Merged error: 22.0b

Counts

294 → 6

localize16.0ms

Local error

Found 3 expressions with local error:

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)))

11.6b

(* (pow i 2) (log 1.0))

18.5b

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 173

Calls

3 calls:

20.0ms

(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))

6.0ms

(* (pow i 2) (log 1.0))

14.0ms

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

series52.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms

(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))

12.0ms

(* (pow i 2) (log 1.0))

19.0ms

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

simplify144.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	837	3435
1	4430	3190
2	5001	3190

prune736.0ms

Filtered

139 candidates to 182 candidates (-30.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	169	13	182
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	170	18	188

Merged error: 11.8b

Counts

188 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
11.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b	(* (pow i 2) (log 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `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-*l/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

11.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
11.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms	(* (pow i 2) (log 1.0))

series70.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
21.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
15.0ms	(* (pow i 2) (log 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	529	1979
1	2435	1684
2	5001	1679

prune386.0ms

Filtered

87 candidates to 129 candidates (-48.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	129	18	147

Merged error: 11.8b

Counts

147 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow i 2) (log 1.0))
11.7b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
11.7b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
11.7b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `associate-r` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/3` `prod-exp` `flip--`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (pow i 2) (log 1.0))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
8.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (pow i 2) (log 1.0))
54.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
56.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
57.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	333	1468
1	1220	1365
2	5002	1347

prune641.0ms

Filtered

70 candidates to 85 candidates (-21.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	84	19	103

Merged error: 11.8b

Counts

103 → 19

regimes324.0ms

Accuracy

66.4% (6.0b remaining)

Error of 17.2b against oracle of 11.2b and baseline of 29.1b

bsearch486.0ms

Steps

Iters	Range		Point
9	5.167741364999036	1199660385.8498375	5.276434081631708
10	-61666.43003918486	-5.3552240917868306e-11	-0.02651864135401642

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	22
1	45	22

end0.0ms

analyze851.0ms

Algorithm: search

sample6.1s

Algorithm

intervals

Results

2.4s	2817×	body	1280	valid
2.1s	970×	body	2560	valid
597.0ms	1513×	body	640	valid
173.0ms	721×	body	320	valid
127.0ms	257×	body	640	invalid
114.0ms	1610×	body	80	valid
86.0ms	107×	body	1280	invalid
53.0ms	359×	body	160	valid
45.0ms	144×	body	320	invalid
42.0ms	443×	body	80	invalid
41.0ms	10×	body	5120	valid
31.0ms	16×	body	2560	invalid
14.0ms	302×	body	80	nan
13.0ms	68×	body	160	invalid

Details

analyze813.0ms

sample211.0ms

simplify44.0ms

prune3.0ms

localize9.0ms

rewrite85.0ms

series186.0ms

simplify68.0ms

prune610.0ms

localize16.0ms

rewrite49.0ms

series52.0ms

simplify144.0ms

prune736.0ms

localize17.0ms

rewrite43.0ms

series70.0ms

simplify84.0ms

prune386.0ms

localize21.0ms

rewrite34.0ms

series180.0ms

simplify55.0ms

prune641.0ms

regimes324.0ms

bsearch486.0ms

simplify2.0ms

end0.0ms

analyze851.0ms

sample6.1s

Profiling