Details

analyze811.0ms

Algorithm: search

sample219.0ms

Algorithm

intervals

Results

79.0ms	93×	body	1280	valid
79.0ms	36×	body	2560	valid
19.0ms	45×	body	640	valid
6.0ms	12×	body	640	invalid
5.0ms	20×	body	320	valid
4.0ms	1×	body	5120	valid
3.0ms	48×	body	80	valid
3.0ms	13×	body	160	valid
2.0ms	7×	body	320	invalid
2.0ms	1×	body	2560	invalid
2.0ms	2×	body	1280	invalid
2.0ms	18×	body	80	invalid
1.0ms	3×	body	160	invalid
1.0ms	10×	body	80	nan

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: 48.9b

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)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
12.9b	(/ (- (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:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
19.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series194.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
37.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
65.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune616.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	7	294

Merged error: 24.6b

Counts

294 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)))
13.8b	(* (pow i 2) (log 1.0))
21.8b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 200

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
19.0ms	(* 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))

series63.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
23.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
17.0ms	(* (pow i 2) (log 1.0))
20.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify152.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune860.0ms

Filtered

157 candidates to 212 candidates (-35.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	197	15	212
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	198	21	219

Merged error: 11.5b

Counts

219 → 21

localize20.0ms

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))
13.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.8b	(* (pow i 2) (log 1.0))

rewrite44.0ms

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)
12.0ms	(* 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))

series73.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
25.0ms	(* 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)
13.0ms	(* (pow i 2) (log 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (64.0ms)

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

prune426.0ms

Filtered

87 candidates to 129 candidates (-48.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	130	20	150

Merged error: 11.5b

Counts

150 → 20

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
0.1b	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

13.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
15.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

series33.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
16.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

simplify43.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	252	736
1	1188	612
2	5001	612

prune83.0ms

Filtered

30 candidates to 46 candidates (-53.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	2	17	19
Picked	0	1	1
Done	0	0	0
Total	45	21	66

Merged error: 11.5b

Counts

66 → 21

regimes496.0ms

Accuracy

68.3% (5.7b remaining)

Error of 16.8b against oracle of 11.1b and baseline of 29.0b

bsearch1.0s

Steps

Iters	Range		Point
10	6.0766470363712426e+289	1.329734336036192e+303	4.058977410036035e+302
8	2.3488019233100838e+257	1.1247681309305912e+261	1.3189758437011078e+260
10	6942117362.412387	3.2154390793082164e+22	7030377895.169148
9	-12.636229124631068	-4.985885037694516e-09	-1.8032163663211869

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	51
1	79	51

end0.0ms

analyze804.0ms

Algorithm: search

sample6.0s

Algorithm

intervals

Results

2.4s	2785×	body	1280	valid
2.1s	991×	body	2560	valid
624.0ms	1540×	body	640	valid
155.0ms	676×	body	320	valid
115.0ms	233×	body	640	invalid
115.0ms	1664×	body	80	valid
84.0ms	102×	body	1280	invalid
60.0ms	189×	body	320	invalid
52.0ms	339×	body	160	valid
39.0ms	414×	body	80	invalid
22.0ms	12×	body	2560	invalid
21.0ms	5×	body	5120	valid
17.0ms	92×	body	160	invalid
15.0ms	318×	body	80	nan

Details

analyze811.0ms

sample219.0ms

simplify44.0ms

prune3.0ms

localize9.0ms

rewrite85.0ms

series194.0ms

simplify63.0ms

prune616.0ms

localize21.0ms

rewrite55.0ms

series63.0ms

simplify152.0ms

prune860.0ms

localize20.0ms

rewrite44.0ms

series73.0ms

simplify83.0ms

prune426.0ms

localize13.0ms

rewrite29.0ms

series33.0ms

simplify43.0ms

prune83.0ms

regimes496.0ms

bsearch1.0s

simplify2.0ms

end0.0ms

analyze804.0ms

sample6.0s

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