Details

analyze831.0ms (7.6%)

Algorithm

1×

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

sample223.0ms (2%)

Algorithm

1×

intervals

Results

87.0ms	96×	body	1280	valid
86.0ms	39×	body	2560	valid
18.0ms	46×	body	640	valid
5.0ms	9×	body	640	invalid
4.0ms	18×	body	320	valid
3.0ms	44×	body	80	valid
2.0ms	13×	body	160	valid
2.0ms	1×	body	2560	invalid
2.0ms	2×	body	1280	invalid
2.0ms	5×	body	320	invalid
1.0ms	12×	body	80	invalid
1.0ms	4×	body	160	invalid
0.0ms	9×	body	80	nan

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5281	15

prune6.0ms (0.1%)

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: 48.4b

Counts

2 → 1

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b	(pow (+ 1.0 (/ i n)) n)
13.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite83.0ms (0.8%)

Algorithm

1×	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:

32.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0ms	(pow (+ 1.0 (/ i n)) n)

series182.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
61.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune731.0ms (6.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	285	7	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	286	7	293

Merged error: 23.0b

Counts

293 → 7

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n)))
11.1b	(* (log 1.0) (* (* i i) 0.5))
21.6b	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac`
94×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
32×	`add-exp-log` `add-cbrt-cube`
21×	`pow1`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
9×	`div-inv`
8×	`associate-l`
6×	`cbrt-undiv` `div-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`-commutative` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `clear-num` `log-pow` `flip--`

Counts

4 → 180

Calls

4 calls:

19.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n)))
13.0ms	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n))
7.0ms	(* (log 1.0) (* (* i i) 0.5))
5.0ms	(* (* i i) 0.5)

series57.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n))
20.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) (/ i n)))
13.0ms	(* (log 1.0) (* (* i i) 0.5))
3.0ms	(* (* i i) 0.5)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5027	5909

prune741.0ms (6.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	178	14	192
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	179	20	199

Merged error: 8.6b

Counts

199 → 20

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n)
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n))
10.5b	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i)
11.1b	(* (log 1.0) (* (* i i) 0.5))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
20×	`associate-l`
19×	`times-frac`
13×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `clear-num` `log-pow` `flip--`

Counts

4 → 105

Calls

4 calls:

12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n))
12.0ms	(* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n)
11.0ms	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i)
7.0ms	(* (log 1.0) (* (* i i) 0.5))

series71.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n))
18.0ms	(* (/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i) n)
15.0ms	(/ (- (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) 0.5))) (* (log 1.0) (* (* i i) 0.5))) i)
13.0ms	(* (log 1.0) (* (* i i) 0.5))

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5039	2564

prune397.0ms (3.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	118	19	137

Merged error: 8.6b

Counts

137 → 19

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

11.1b	(* (log 1.0) (- n (* (* i i) 0.5)))
11.3b	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
11.3b	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
11.3b	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`associate-*r/`
18×	`cbrt-div`
12×	`frac-add`
11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
7×	`pow1` `flip3--` `flip--`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
3×	`pow1/3` `associate-r`
2×	`sub-neg`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

6.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
6.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
6.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
6.0ms	(* (log 1.0) (- n (* (* i i) 0.5)))

series182.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
55.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
53.0ms	(cbrt (+ (* i (+ 1.0 (* i 0.5))) (* (log 1.0) (- n (* (* i i) 0.5)))))
18.0ms	(* (log 1.0) (- n (* (* i i) 0.5)))

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5682	2920

prune481.0ms (4.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	87	18	105

Merged error: 8.6b

Counts

105 → 18

regimes295.0ms (2.7%)

Accuracy

Total 6.0b remaining (41.4%)

Threshold costs 0b (0%)

bsearch201.0ms (1.8%)

Steps

Iters	Range		Point
8	203.83346152816426	382937.73952731065	206.5505471855869
10	-32745437244888.45	-2.9518020392315095e-06	-0.1758689209773507

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	111	122
1	111	122

end0.0ms (0%)

sample6.1s (55.3%)

Algorithm

1×

intervals

Results

2.5s	2925×	body	1280	valid
2.1s	953×	body	2560	valid
614.0ms	1522×	body	640	valid
169.0ms	704×	body	320	valid
116.0ms	226×	body	640	invalid
112.0ms	1574×	body	80	valid
88.0ms	110×	body	1280	invalid
56.0ms	180×	body	320	invalid
49.0ms	322×	body	160	valid
36.0ms	402×	body	80	invalid
18.0ms	10×	body	2560	invalid
16.0ms	85×	body	160	invalid
12.0ms	285×	body	80	nan

Details

analyze831.0ms (7.6%)

sample223.0ms (2%)

simplify41.0ms (0.4%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite83.0ms (0.8%)

series182.0ms (1.7%)

simplify81.0ms (0.7%)

prune731.0ms (6.6%)

localize14.0ms (0.1%)

rewrite51.0ms (0.5%)

series57.0ms (0.5%)

simplify53.0ms (0.5%)

prune741.0ms (6.7%)

localize16.0ms (0.1%)

rewrite45.0ms (0.4%)

series71.0ms (0.6%)

simplify33.0ms (0.3%)

prune397.0ms (3.6%)

localize27.0ms (0.2%)

rewrite27.0ms (0.2%)

series182.0ms (1.7%)

simplify33.0ms (0.3%)

prune481.0ms (4.4%)

regimes295.0ms (2.7%)

bsearch201.0ms (1.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.1s (55.3%)

Profiling