Details

analyze784.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample201.0ms

Algorithm

intervals

Results

84.0ms	96×	body	1280	valid
59.0ms	29×	body	2560	valid
24.0ms	65×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	11×	body	640	invalid
5.0ms	7×	body	1280	invalid
2.0ms	7×	body	320	invalid
2.0ms	33×	body	80	valid
1.0ms	8×	body	160	valid
1.0ms	10×	body	80	invalid
1.0ms	4×	body	160	invalid
0.0ms	8×	body	80	nan

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5405	15

prune10.0ms

Filtered

1 candidates to 1 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: 46.7b

Counts

2 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.5b	(pow (+ 1.0 (/ i n)) n)
10.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite81.0ms

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 → 280

Calls

4 calls:

29.0ms	(* 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)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series179.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
32.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
56.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify71.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4974	5887
1	4974	5887

prune591.0ms

Filtered

227 candidates to 292 candidates (-28.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	287	5	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	289	5	294

Merged error: 21.5b

Counts

294 → 5

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))

8.4b

(* (* i i) (* 0.5 (log 1.0)))

14.7b

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
94×	`add-sqr-sqrt`
85×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
29×	`add-exp-log` `add-cbrt-cube`
17×	`pow1`
13×	`associate-/r*`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
4×	`associate-l`
3×	`associate-/l*` `add-log-exp` `unswap-sqr`
2×	`associate-+r-` `associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `associate-*r/` `clear-num` `flip-+`

Counts

3 → 173

Calls

3 calls:

20.0ms

(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))

8.0ms

(* (* i i) (* 0.5 (log 1.0)))

17.0ms

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

series57.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms

(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))

17.0ms

(* (* i i) (* 0.5 (log 1.0)))

19.0ms

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5562	5254

prune523.0ms

Filtered

135 candidates to 182 candidates (-34.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	171	11	182
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	172	15	187

Merged error: 10.7b

Counts

187 → 15

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b

(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n)

0.1b

(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n))

8.0b

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `times-frac` `add-cbrt-cube`
16×	`associate-l`
10×	`pow1`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
2×	`associate-l/` `-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`

Counts

3 → 82

Calls

3 calls:

10.0ms

(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n)

12.0ms

(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n))

9.0ms

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i)

series52.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms

(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n)

20.0ms

(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i) n))

14.0ms

(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) i)

simplify33.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5178	2432

prune306.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	91	15	106

Merged error: 10.7b

Counts

106 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
0.6b	(cbrt i)
1.2b	(* (* (cbrt n) (cbrt n)) (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i))))
4.7b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
7×	`times-frac` `associate-r`
6×	`cbrt-undiv` `cbrt-prod` `div-exp`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/l*`
2×	`pow1/3` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `associate-r/` `associate-l` `clear-num` `associate-/r` `*-commutative` `flip-+`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt i)
1.0ms	(cbrt i)
15.0ms	(* (* (cbrt n) (cbrt n)) (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i))))
13.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt i)
21.0ms	(cbrt i)
46.0ms	(* (* (cbrt n) (cbrt n)) (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i))))
31.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i (* i 0.5)) (- 1 (log 1.0))))) (* (cbrt i) (cbrt i)))

simplify68.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5069	1901

prune175.0ms

Filtered

61 candidates to 90 candidates (-47.5%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	3	9	12
Picked	1	0	1
Done	0	2	2
Total	85	20	105

Merged error: 10.7b

Counts

105 → 20

regimes331.0ms

Accuracy

62.6% (6.5b remaining)

Error of 17.7b against oracle of 11.2b and baseline of 28.6b

bsearch230.0ms

Steps

Iters	Range		Point
5	9.515551006350562e+232	2.085792419784816e+233	2.0505733833233406e+233
10	8.79888905158276e+136	2.744620001756711e+154	1.9138780675951828e+154
6	7.666020809529884e-27	8.815773246004529e-26	8.673643612537732e-26
10	-9.242488964659013e-10	-1.1925246151655632e-22	-9.145040014018987e-10

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	319	137
1	319	137

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2858×	body	1280	valid
2.1s	1007×	body	2560	valid
621.0ms	1575×	body	640	valid
168.0ms	710×	body	320	valid
129.0ms	262×	body	640	invalid
107.0ms	1527×	body	80	valid
85.0ms	109×	body	1280	invalid
47.0ms	154×	body	320	invalid
46.0ms	317×	body	160	valid
41.0ms	458×	body	80	invalid
20.0ms	6×	body	5120	valid
18.0ms	96×	body	160	invalid
15.0ms	8×	body	2560	invalid
14.0ms	314×	body	80	nan

Details

analyze784.0ms

sample201.0ms

simplify52.0ms

prune10.0ms

localize8.0ms

rewrite81.0ms

series179.0ms

simplify71.0ms

prune591.0ms

localize16.0ms

rewrite53.0ms

series57.0ms

simplify63.0ms

prune523.0ms

localize14.0ms

rewrite33.0ms

series52.0ms

simplify33.0ms

prune306.0ms

localize21.0ms

rewrite32.0ms

series118.0ms

simplify68.0ms

prune175.0ms

regimes331.0ms

bsearch230.0ms

simplify4.0ms

end0.0ms

sample6.1s

Profiling