Details

sample204.0ms

Algorithm

intervals

Results

82.0ms	104×	body	1280	valid
66.0ms	30×	body	2560	valid
22.0ms	51×	body	640	valid
7.0ms	29×	body	320	valid
6.0ms	69×	body	80	valid
3.0ms	64×	body	80	nan
3.0ms	19×	body	160	valid

simplify40.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 47.2b

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)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.0b	(pow (+ 1.0 (/ i n)) n)
9.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite91.0ms

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)
20.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series186.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms	(pow (+ 1.0 (/ i n)) n)
58.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune582.0ms

Filtered

293 candidates to 223 candidates (23.9%)

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: 21.6b

Counts

294 → 7

localize18.0ms

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)))
9.6b	(* (pow i 2) (log 1.0))
16.3b	(/ (- (+ (* 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))

series61.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
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)))
13.0ms	(* (pow i 2) (log 1.0))
24.0ms	(/ (- (+ (* 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

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

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

prune813.0ms

Filtered

212 candidates to 157 candidates (25.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	202	10	212
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	202	17	219

Merged error: 11.2b

Counts

219 → 17

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))
9.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.6b	(* (pow i 2) (log 1.0))

rewrite38.0ms

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))

series53.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
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))

simplify75.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (61.0ms)

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

prune317.0ms

Filtered

124 candidates to 79 candidates (36.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	124	17	141

Merged error: 11.2b

Counts

141 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* (/ (- (+ (* 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)))
2.2b	(* (/ (- (+ (* 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)))
5.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
9.6b	(* (pow i 2) (log 1.0))

rewrite81.0ms

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:

28.0ms	(/ (* (/ (- (+ (* 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)))
19.0ms	(* (/ (- (+ (* 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))

series102.0ms

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)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
38.0ms	(* (/ (- (+ (* 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)))
31.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
13.0ms	(* (pow i 2) (log 1.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1629	7295
1	5001	6715

prune1.1s

Filtered

298 candidates to 217 candidates (27.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	289	9	298
Fresh	3	11	14
Picked	1	0	1
Done	1	1	2
Total	294	21	315

Merged error: 11.2b

Counts

315 → 21

regimes358.0ms

Accuracy

69.3% (5.5b remaining)

Error of 16.8b against oracle of 11.4b and baseline of 29.2b

bsearch132.0ms

Steps

Iters	Range		Point
5	0.0002914685688501568	0.0007800520059423635	0.0004574629412369032
10	-36275.906995244724	-8.19926643695862e-11	-0.001693417487092329

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	37
1	58	37

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.4s	2857×	body	1280	valid
2.1s	1014×	body	2560	valid
726.0ms	1788×	body	640	valid
213.0ms	886×	body	320	valid
174.0ms	2395×	body	80	valid
99.0ms	2337×	body	80	nan
74.0ms	488×	body	160	valid
23.0ms	6×	body	5120	valid

Details

sample204.0ms

simplify40.0ms

prune3.0ms

localize8.0ms

rewrite91.0ms

series186.0ms

simplify60.0ms

prune582.0ms

localize18.0ms

rewrite54.0ms

series61.0ms

simplify144.0ms

prune813.0ms

localize16.0ms

rewrite38.0ms

series53.0ms

simplify75.0ms

prune317.0ms

localize24.0ms

rewrite81.0ms

series102.0ms

simplify93.0ms

prune1.1s

regimes358.0ms

bsearch132.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling