Details

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.956421%

Guaranteed chance to sample good point: 57.924404%

Results

77.0ms	95×	body	1280	valid
76.0ms	37×	body	2560	valid
21.0ms	53×	body	640	valid
4.0ms	52×	body	80	valid
3.0ms	7×	body	640	invalid
3.0ms	13×	body	320	valid
3.0ms	4×	body	1280	invalid
2.0ms	6×	body	320	invalid
1.0ms	16×	body	80	invalid
1.0ms	3×	body	160	invalid
1.0ms	6×	body	160	valid
0.0ms	9×	body	80	nan

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

prune3.0ms

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

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
10.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite80.0ms

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)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
15.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series186.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
60.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune653.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

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: 19.0b

Counts

294 → 6

localize19.0ms

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)))
7.4b	(* (pow i 2) (log 1.0))
17.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite51.0ms

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

series60.0ms

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)))
17.0ms	(* (pow i 2) (log 1.0))
19.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify150.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

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

prune813.0ms

Filtered

157 candidates to 212 candidates (-35.0%)

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: 7.5b

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))
7.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.4b	(* (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:

7.0ms	(* 0.5 (pow i 2))
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))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 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))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.0ms	(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (66.0ms)

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

prune329.0ms

Filtered

79 candidates to 124 candidates (-57.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	124	17	141

Merged error: 7.5b

Counts

141 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

7.4b	(* (pow i 2) (log 1.0))
7.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
7.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
7.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `associate-r` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/3` `prod-exp` `flip--`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

8.0ms	(* (pow i 2) (log 1.0))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
8.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (pow i 2) (log 1.0))
55.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
57.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
55.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	333	1468
1	1220	1365
2	5002	1347

prune670.0ms

Filtered

70 candidates to 85 candidates (-21.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	85	17	102

Merged error: 7.5b

Counts

102 → 17

regimes294.0ms

Accuracy

68.3% (5.7b remaining)

Error of 16.7b against oracle of 11.0b and baseline of 28.9b

bsearch355.0ms

Steps

Iters	Range		Point
9	1.8146240512922834e+250	3.354835105769148e+255	1.3545253801925772e+252
7	8.212337951483374e+131	1.8761634991667e+133	1.7764578067101197e+133
11	0.0003288718850142013	9.840401450849524e+22	0.22710708797976797
9	-16.011709609627676	-1.7988917796407912e-07	-0.0008777616013522305

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	48
1	71	48

end0.0ms

sample8.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.956421%

Guaranteed chance to sample good point: 57.924404%

Results

2.4s	2766×	body	1280	valid
2.1s	988×	body	2560	valid
640.0ms	1573×	body	640	valid
163.0ms	700×	body	320	valid
117.0ms	236×	body	640	invalid
112.0ms	1600×	body	80	valid
89.0ms	108×	body	1280	invalid
55.0ms	173×	body	320	invalid
53.0ms	365×	body	160	valid
37.0ms	395×	body	80	invalid
33.0ms	8×	body	5120	valid
25.0ms	13×	body	2560	invalid
16.0ms	86×	body	160	invalid
8.0ms	167×	body	80	nan

Details

sample3.0s

simplify43.0ms

prune3.0ms

localize8.0ms

rewrite80.0ms

series186.0ms

simplify66.0ms

prune653.0ms

localize19.0ms

rewrite51.0ms

series60.0ms

simplify150.0ms

prune813.0ms

localize16.0ms

rewrite38.0ms

series50.0ms

simplify81.0ms

prune329.0ms

localize21.0ms

rewrite35.0ms

series181.0ms

simplify58.0ms

prune670.0ms

regimes294.0ms

bsearch355.0ms

simplify2.0ms

end0.0ms

sample8.8s

Profiling