Details

sample188.0ms

Algorithm

intervals

Results

72.0ms	35×	body	2560	valid
66.0ms	91×	body	1280	valid
23.0ms	62×	body	640	valid
7.0ms	39×	body	320	valid
3.0ms	62×	body	80	valid
3.0ms	72×	body	80	nan
2.0ms	18×	body	160	valid

simplify39.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 50.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b	(pow (+ 1.0 (/ i n)) n)
11.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite88.0ms

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:

37.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
254.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms	(pow (+ 1.0 (/ i n)) n)
350.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune927.0ms

Filtered

293 candidates to 223 candidates (76.1%)

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: 25.4b

Counts

294 → 6

localize19.0ms

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)))
9.9b	(* (pow i 2) (log 1.0))
17.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite54.0ms

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))
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))

series566.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
217.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
136.0ms	(* (pow i 2) (log 1.0))
189.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify150.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

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

prune707.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	201	11	212
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	202	16	218

Merged error: 13.2b

Counts

218 → 16

localize16.0ms

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))
9.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.9b	(* (pow i 2) (log 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

9.0ms	(* 0.5 (pow i 2))
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)
7.0ms	(* (pow i 2) (log 1.0))

series512.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 0.5 (pow i 2))
209.0ms	(* 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)
135.0ms	(* (pow i 2) (log 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	518	1449
1	2468	1227
2	5001	1223

prune373.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 13.2b

Counts

140 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

9.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.9b	(* (pow i 2) (log 1.0))
9.9b	(* (pow i 2) (log 1.0))
9.9b	(* (pow i 2) (log 1.0))

rewrite35.0ms

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:

12.0ms	(/ (- (+ (* 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))
6.0ms	(* (pow i 2) (log 1.0))
7.0ms	(* (pow i 2) (log 1.0))

series555.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
140.0ms	(* (pow i 2) (log 1.0))
142.0ms	(* (pow i 2) (log 1.0))
141.0ms	(* (pow i 2) (log 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	300	1247
1	1278	1100
2	5002	1083

prune532.0ms

Filtered

144 candidates to 93 candidates (64.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	144	16	160

Merged error: 13.2b

Counts

160 → 16

regimes384.0ms

Accuracy

69.2% (5.5b remaining)

Error of 16.8b against oracle of 11.3b and baseline of 29.2b

bsearch393.0ms

Steps

Iters	Range		Point
10	1.4694898840348096e+269	8.882349655988274e+278	8.738680422589072e+272
7	8.08749080545684e+245	4.769573338120107e+247	2.257527045522283e+246
8	9.842021999831939e+57	5.5185225753047605e+62	1.003540520873365e+58
4	-8.992206990105925e-152	-5.007575919502852e-152	-5.5243256116785745e-152
9	-224735.23723946884	-0.42830885935273133	-0.4700598908891248

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	62
1	74	62

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2898×	body	1280	valid
1.9s	1010×	body	2560	valid
534.0ms	1718×	body	640	valid
160.0ms	922×	body	320	valid
113.0ms	2395×	body	80	valid
92.0ms	2330×	body	80	nan
50.0ms	480×	body	160	valid
29.0ms	8×	body	5120	valid