Details

sample201.0ms

Algorithm

intervals

Results

80.0ms	95×	body	1280	valid
72.0ms	32×	body	2560	valid
20.0ms	53×	body	640	valid
6.0ms	29×	body	320	valid
6.0ms	76×	body	80	valid
2.0ms	14×	body	160	valid
2.0ms	59×	body	80	nan

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: 48.5b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b	(pow (+ 1.0 (/ i n)) n)
10.9b	(/ (- (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:

33.0ms	(* 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)
21.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
207.0ms	(pow (+ 1.0 (/ i n)) n)
353.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune678.0ms

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: 21.7b

Counts

294 → 8

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)))

11.4b

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

18.7b

(/ (- (+ (* 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`
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:

24.0ms

(* 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))

15.0ms

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

series541.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms

(* 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

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

193.0ms

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

simplify140.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (23.0ms)

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

prune609.0ms

Filtered

182 candidates to 139 candidates (76.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	173	9	182
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	174	16	190

Merged error: 10.1b

Counts

190 → 16

localize16.0ms

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))
10.8b	(/ (- (+ (* 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))

rewrite48.0ms

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))

series689.0ms

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)))) i) n)
212.0ms	(* 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)
138.0ms	(* (pow i 2) (log 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

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

prune358.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	129	16	145

Merged error: 10.1b

Counts

145 → 16

localize17.0ms

Local error

Found 4 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) (/ 1 n)))
0.2b	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
10.8b	(/ (- (+ (* 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))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
428×	`add-sqr-sqrt`
399×	`*-un-lft-identity`
397×	`add-cube-cbrt`
178×	`associate-r`
65×	`add-exp-log`
57×	`div-inv`
38×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
12×	`prod-exp`
11×	`associate-l` `unswap-sqr`
7×	`pow1`
6×	`log-prod` `cbrt-unprod`
4×	`unpow-prod-down` `rec-exp` `1-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `associate-*r/` `pow-prod-down` `pow-exp` `log-pow` `flip--`

Counts

4 → 492

Calls

4 calls:

49.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
20.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 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))

series685.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
196.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
136.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
145.0ms	(* (pow i 2) (log 1.0))

simplify142.0ms

Algorithm

egg-herbie

Counts

504 → 504

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2117	11874
1	5001	11169

prune1.7s

Filtered

504 candidates to 332 candidates (65.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	503	1	504
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	503	17	520

Merged error: 10.1b

Counts

520 → 17

regimes235.0ms

Accuracy

68.2% (5.6b remaining)

Error of 16.5b against oracle of 10.9b and baseline of 28.5b

bsearch440.0ms

Steps

Iters	Range		Point
7	6.357249456966329e+263	7.886040974040914e+265	4.800169434160537e+265
11	6.351942861320177e+181	1.2468499372895855e+219	2.0295563910853525e+200
9	8.850304217014897e-16	2.8262556577633816e-09	2.787102960201877e-09
7	-5.155753157609302	-0.026333846149416525	-0.11584826690144925

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	46
1	64	46

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	2970×	body	1280	valid
2.2s	990×	body	2560	valid
715.0ms	1747×	body	640	valid
226.0ms	909×	body	320	valid
173.0ms	2412×	body	80	valid
99.0ms	2237×	body	80	nan
69.0ms	434×	body	160	valid
34.0ms	8×	body	5120	valid

Details

sample201.0ms

simplify41.0ms

prune2.0ms

localize8.0ms

rewrite90.0ms

series1.2s

simplify64.0ms

prune678.0ms

localize16.0ms

rewrite54.0ms

series541.0ms

simplify140.0ms

prune609.0ms

localize16.0ms

rewrite48.0ms

series689.0ms

simplify80.0ms

prune358.0ms

localize17.0ms

rewrite127.0ms

series685.0ms

simplify142.0ms

prune1.7s

regimes235.0ms

bsearch440.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling