Details

sample205.0ms

Algorithm

intervals

Results

99.0ms	106×	body	1280	valid
49.0ms	23×	body	2560	valid
24.0ms	55×	body	640	valid
6.0ms	69×	body	80	nan
6.0ms	79×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 47.8b

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)))
0.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)
9.2b	(/ (- (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))

series1.3s

Counts

4 → 12

Calls

4 calls:

397.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
274.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
230.0ms	(pow (+ 1.0 (/ i n)) n)
363.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify70.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune726.0ms

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: 19.7b

Counts

294 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) 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)))
11.6b	(* (pow i 2) (log 1.0))
16.1b	(/ (- (+ (* 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`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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))

series600.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
220.0ms	(* 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	(* (pow i 2) (log 1.0))
201.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify152.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	929	3604
1	4818	3341
2	5001	3341

prune712.0ms

Filtered

198 candidates to 150 candidates (75.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	188	16	204

Merged error: 10.2b

Counts

204 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.3b	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
11.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b	(* (pow i 2) (log 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-l` `add-log-exp`
8×	`prod-exp`
7×	`associate-r`
6×	`log-prod` `cbrt-unprod`
4×	`unpow-prod-down` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `sum-log` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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))

series559.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
216.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
147.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
149.0ms	(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	547	1517
1	2619	1294
2	5001	1290

prune321.0ms

Filtered

110 candidates to 72 candidates (65.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	110	16	126

Merged error: 10.2b

Counts

126 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
2.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
9.3b	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
11.6b	(* (pow i 2) (log 1.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
121×	`times-frac`
74×	`*-un-lft-identity`
61×	`add-exp-log`
59×	`add-cube-cbrt`
50×	`cbrt-prod`
45×	`associate-l`
37×	`unswap-sqr`
34×	`unpow-prod-down`
26×	`associate-r`
23×	`div-exp` `prod-exp`
17×	`add-cbrt-cube`
11×	`unpow2` `sqr-pow`
7×	`pow1` `pow-to-exp` `pow-exp`
6×	`rec-exp` `log-prod` `1-exp` `associate-/r*`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `div-inv` `associate-/l*`
2×	`*-commutative` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `flip--`

Counts

4 → 215

Calls

4 calls:

1.0ms	(cbrt i)
13.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
29.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
6.0ms	(* (pow i 2) (log 1.0))

series686.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt i)
175.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
180.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
151.0ms	(* (pow i 2) (log 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1015	4620
1	5001	4203

prune772.0ms

Filtered

227 candidates to 156 candidates (68.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	222	5	227
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	227	16	243

Merged error: 10.2b

Counts

243 → 16

regimes567.0ms

Accuracy

71.2% (5.1b remaining)

Error of 16.0b against oracle of 10.9b and baseline of 28.6b

bsearch264.0ms

Steps

Iters	Range		Point
9	2.2826621327002547e-07	1.1080729073972495	0.0004011259599316577
9	-0.029522190497440527	-4.410039720853989e-10	-0.028332219067036327

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	42
1	62	42

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	3021×	body	1280	valid
2.1s	965×	body	2560	valid
741.0ms	1746×	body	640	valid
216.0ms	890×	body	320	valid
175.0ms	2422×	body	80	valid
95.0ms	2172×	body	80	nan
72.0ms	462×	body	160	valid
15.0ms	4×	body	5120	valid

Details

sample205.0ms

simplify45.0ms

prune2.0ms

localize9.0ms

rewrite88.0ms

series1.3s

simplify70.0ms

prune726.0ms

localize20.0ms

rewrite55.0ms

series600.0ms

simplify152.0ms

prune712.0ms

localize30.0ms

rewrite39.0ms

series559.0ms

simplify81.0ms

prune321.0ms

localize22.0ms

rewrite65.0ms

series686.0ms

simplify63.0ms

prune772.0ms

regimes567.0ms

bsearch264.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling