Details

sample222.0ms

Algorithm

intervals

Results

93.0ms	42×	body	2560	valid
70.0ms	84×	body	1280	valid
23.0ms	52×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	74×	body	80	valid
4.0ms	1×	body	5120	valid
3.0ms	68×	body	80	nan
3.0ms	20×	body	160	valid

simplify43.0ms

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: 49.0b

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)))
2.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.9b	(pow (+ 1.0 (/ i n)) n)
13.6b	(/ (- (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:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
18.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

612.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
255.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms	(pow (+ 1.0 (/ i n)) n)
359.0ms	(/ (- (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	5001	3166

prune693.0ms

Filtered

293 candidates to 223 candidates (76.1%)

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: 23.4b

Counts

294 → 7

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)))
12.6b	(* (pow i 2) (log 1.0))
22.8b	(/ (- (+ (* 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:

5.0ms	(* 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))
13.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series545.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
202.0ms	(* 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))
182.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify148.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

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

prune669.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	203	9	212
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	204	15	219

Merged error: 9.6b

Counts

219 → 15

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))
11.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.6b	(* (pow i 2) (log 1.0))

rewrite46.0ms

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)
15.0ms	(* 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))

series663.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
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) n))
130.0ms	(/ (- (+ (* 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))

simplify78.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (60.0ms)

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

prune356.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	128	16	144

Merged error: 9.6b

Counts

144 → 16

localize29.0ms

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)))
4.0b	(* (/ (- (+ (* 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)))
6.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
12.6b	(* (pow i 2) (log 1.0))

rewrite84.0ms

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:

26.0ms	(/ (* (/ (- (+ (* 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))

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)))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
150.0ms	(* (/ (- (+ (* 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)))
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))
143.0ms	(* (pow i 2) (log 1.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1581	7202
1	5001	6617

prune1.2s

Filtered

298 candidates to 217 candidates (72.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	291	7	298
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	293	21	314

Merged error: 9.6b

Counts

314 → 21

regimes388.0ms

Accuracy

63.8% (6.4b remaining)

Error of 17.2b against oracle of 10.8b and baseline of 28.5b

bsearch310.0ms

Steps

Iters	Range		Point
11	1.9315743976412544e+84	1.6920189061781302e+106	1.9550342657861426e+84
9	-3034678.682172776	-0.006911778759371886	-1.3028949140103387

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

2.5s	2908×	body	1280	valid
2.1s	1022×	body	2560	valid
709.0ms	1757×	body	640	valid
223.0ms	901×	body	320	valid
176.0ms	2370×	body	80	valid
103.0ms	2196×	body	80	nan
71.0ms	448×	body	160	valid
44.0ms	11×	body	5120	valid

Details

sample222.0ms

simplify43.0ms

prune2.0ms

localize9.0ms

rewrite88.0ms

series1.4s

simplify63.0ms

prune693.0ms

localize16.0ms

rewrite55.0ms

series545.0ms

simplify148.0ms

prune669.0ms

localize16.0ms

rewrite46.0ms

series663.0ms

simplify78.0ms

prune356.0ms

localize29.0ms

rewrite84.0ms

series689.0ms

simplify89.0ms

prune1.2s

regimes388.0ms

bsearch310.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling