Details

sample223.0ms

Algorithm

intervals

Results

85.0ms	34×	body	2560	valid
85.0ms	100×	body	1280	valid
21.0ms	46×	body	640	valid
8.0ms	32×	body	320	valid
6.0ms	78×	body	80	valid
3.0ms	72×	body	80	nan
2.0ms	14×	body	160	valid

simplify41.0ms

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: 45.5b

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)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite90.0ms

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:

378.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
266.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
221.0ms	(pow (+ 1.0 (/ i n)) n)
363.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune711.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	285	8	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	286	8	294

Merged error: 22.2b

Counts

294 → 8

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)))
11.4b	(* (pow i 2) (log 1.0))
20.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite59.0ms

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:

9.0ms	(* 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))

series590.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* 0.5 (pow i 2))
219.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
143.0ms	(* (pow i 2) (log 1.0))
197.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify143.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

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

prune714.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	199	13	212
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	200	20	220

Merged error: 9.8b

Counts

220 → 20

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))
10.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b	(* (pow i 2) (log 1.0))

rewrite39.0ms

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:

6.0ms	(* 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)
6.0ms	(* (pow i 2) (log 1.0))

series537.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
228.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
141.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
143.0ms	(* (pow i 2) (log 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (63.0ms)

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

prune338.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	124	20	144

Merged error: 9.8b

Counts

144 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
3.3b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
4.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
11.4b	(* (pow i 2) (log 1.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

183×	`times-frac`
119×	`add-sqr-sqrt`
115×	`add-exp-log`
104×	`add-cube-cbrt` `*-un-lft-identity`
94×	`cbrt-prod`
51×	`associate-/r*`
48×	`unpow-prod-down` `div-exp`
45×	`associate-l`
39×	`prod-exp` `add-cbrt-cube`
22×	`cbrt-undiv`
19×	`cbrt-unprod`
10×	`pow1` `unpow2` `unswap-sqr` `sqr-pow`
8×	`pow-to-exp` `pow-exp`
6×	`log-prod`
5×	`associate-r` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/l/`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`flip3--` `div-sub` `associate-/r/` `log-pow` `flip--`

Counts

4 → 286

Calls

4 calls:

25.0ms	(/ (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
20.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
6.0ms	(* (pow i 2) (log 1.0))

series722.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
163.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
215.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
146.0ms	(* (pow i 2) (log 1.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1581	7202
1	5001	6617

prune1.4s

Filtered

298 candidates to 217 candidates (72.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	289	9	298
Fresh	7	11	18
Picked	1	0	1
Done	0	1	1
Total	297	21	318

Merged error: 9.8b

Counts

318 → 21

regimes333.0ms

Accuracy

68.4% (5.6b remaining)

Error of 16.2b against oracle of 10.6b and baseline of 28.2b

bsearch363.0ms

Steps

Iters	Range		Point
10	6.919042886685739e+222	7.712408044380854e+236	4.093179789596458e+236
8	1.3894494120209264	61499.48832568556	2.7753171010379005
10	-895.7341520863147	-1.971746604603823e-16	-0.42610022092471767

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	53
1	65	53

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	2937×	body	1280	valid
2.2s	1012×	body	2560	valid
746.0ms	1841×	body	640	valid
221.0ms	876×	body	320	valid
179.0ms	2433×	body	80	valid
102.0ms	2271×	body	80	nan
72.0ms	448×	body	160	valid
30.0ms	8×	body	5120	valid

Details

sample223.0ms

simplify41.0ms

prune2.0ms

localize9.0ms

rewrite90.0ms

series1.2s

simplify66.0ms

prune711.0ms

localize16.0ms

rewrite59.0ms

series590.0ms

simplify143.0ms

prune714.0ms

localize21.0ms

rewrite39.0ms

series537.0ms

simplify77.0ms

prune338.0ms

localize29.0ms

rewrite86.0ms

series722.0ms

simplify95.0ms

prune1.4s

regimes333.0ms

bsearch363.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling