Details

sample179.0ms

Algorithm

intervals

Results

74.0ms	36×	body	2560	valid
58.0ms	79×	body	1280	valid
19.0ms	58×	body	640	valid
6.0ms	35×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	59×	body	80	nan
2.0ms	19×	body	160	valid

simplify47.0ms

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

prune3.0ms

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: 47.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.6b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite87.0ms

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:

34.0ms	(* 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:

367.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
243.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms	(pow (+ 1.0 (/ i n)) n)
352.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify61.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune697.0ms

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: 23.7b

Counts

294 → 6

localize22.0ms

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)))
11.1b	(* (pow i 2) (log 1.0))
19.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite53.0ms

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))
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))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series584.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
217.0ms	(* 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	(* (pow i 2) (log 1.0))
196.0ms	(/ (- (+ (* 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

212 → 212

Iterations

Useful iterations: 1 (27.0ms)

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

prune707.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	200	12	212
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	201	17	218

Merged error: 12.1b

Counts

218 → 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))
10.6b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite43.0ms

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))

series525.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 0.5 (pow i 2))
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))
142.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
140.0ms	(* (pow i 2) (log 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (65.0ms)

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

prune329.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	125	16	141

Merged error: 12.1b

Counts

141 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
0.0b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
0.8b	(log (exp (* 0.5 (pow i 2))))
11.1b	(* (pow i 2) (log 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

11.0ms	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
2.0ms	(log (exp (* 0.5 (pow i 2))))
6.0ms	(* (pow i 2) (log 1.0))

series536.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
215.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
32.0ms	(log (exp (* 0.5 (pow i 2))))
143.0ms	(* (pow i 2) (log 1.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	468	1575
1	2147	1296
2	5001	1278

prune310.0ms

Filtered

111 candidates to 77 candidates (69.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	111	16	127

Merged error: 12.1b

Counts

127 → 16

regimes220.0ms

Accuracy

61.4% (7.2b remaining)

Error of 17.9b against oracle of 10.7b and baseline of 29.4b

bsearch256.0ms

Steps

Iters	Range		Point
11	5.359589792685655e-35	0.011261476250181132	0.011056763714875576
9	-19839.740086288697	-1.810013627382575e-05	-0.24222034813966126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	49
1	72	49

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2874×	body	1280	valid
1.8s	964×	body	2560	valid
569.0ms	1772×	body	640	valid
158.0ms	880×	body	320	valid
118.0ms	2442×	body	80	valid
78.0ms	2178×	body	80	nan
44.0ms	407×	body	160	valid
11.0ms	3×	body	5120	valid