Details

analyze501.0ms

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
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

sample53.0ms

Algorithm

intervals

Results

29.0ms	126×	body	5120	exit
7.0ms	198×	body	80	valid
3.0ms	17×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	17×	body	160	valid
0.0ms	6×	body	80	invalid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5002	8

prune19.0ms

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: 13.6b

Counts

2 → 2

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
4.4b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
100×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
10×	`associate-/r/` `add-cbrt-cube`
8×	`add-exp-log` `add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

3 → 143

Calls

3 calls:

5.0ms	(/ x (+ wj 1))
14.0ms	(/ (/ x (+ wj 1)) (exp wj))
55.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series31.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ x (+ wj 1))
11.0ms	(/ (/ x (+ wj 1)) (exp wj))
14.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify87.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	656	1364
1	2971	1315
2	5001	1313

prune248.0ms

Filtered

112 candidates to 152 candidates (-35.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	148	6	154

Merged error: 0.2b

Counts

154 → 6

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate-r` `associate--l+` `sum-log` `*-commutative` `flip--`

Counts

2 → 32

Calls

2 calls:

17.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
9.0ms	(* 2 (* wj x))

series20.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
7.0ms	(* 2 (* wj x))

simplify146.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	162	194
1	645	176
2	3837	174
3	5001	174

prune58.0ms

Filtered

22 candidates to 38 candidates (-72.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Merged error: 0.2b

Counts

44 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ wj 1))
0.0b	(* x (/ (/ 1 (+ wj 1)) (exp wj)))
0.0b	(/ (/ 1 (+ wj 1)) (exp wj))
4.4b	(- (+ (* x (/ (/ 1 (+ wj 1)) (exp wj))) wj) (/ wj (+ wj 1)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
161×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
58×	`associate-r`
25×	`distribute-lft-out`
24×	`add-exp-log`
21×	`associate-/l*`
20×	`add-cbrt-cube`
16×	`associate-/r/`
14×	`div-exp`
10×	`div-inv`
9×	`flip3-+` `flip-+` `add-log-exp`
7×	`pow1` `cbrt-undiv` `associate-/r*`
5×	`prod-exp`
4×	`unswap-sqr`
3×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `associate-r/` `pow-prod-down` `associate--l+` `sum-log` `-commutative` `flip--` `associate-/l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 231

Calls

4 calls:

5.0ms	(/ 1 (+ wj 1))
31.0ms	(* x (/ (/ 1 (+ wj 1)) (exp wj)))
9.0ms	(/ (/ 1 (+ wj 1)) (exp wj))
19.0ms	(- (+ (* x (/ (/ 1 (+ wj 1)) (exp wj))) wj) (/ wj (+ wj 1)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (+ wj 1))
11.0ms	(* x (/ (/ 1 (+ wj 1)) (exp wj)))
6.0ms	(/ (/ 1 (+ wj 1)) (exp wj))
14.0ms	(- (+ (* x (/ (/ 1 (+ wj 1)) (exp wj))) wj) (/ wj (+ wj 1)))

simplify106.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	889	2050
1	4887	1750
2	5002	1738

prune261.0ms

Filtered

141 candidates to 243 candidates (-72.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	243	7	250

Merged error: 0.2b

Counts

250 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (exp wj)))
0.0b	(* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj))))
0.0b	(/ x (+ wj 1))
4.4b	(- (+ (* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
222×	`add-sqr-sqrt`
183×	`*-un-lft-identity`
127×	`add-cube-cbrt`
112×	`associate-r`
95×	`sqrt-prod`
49×	`add-exp-log`
29×	`add-cbrt-cube`
25×	`unswap-sqr`
22×	`associate-l` `distribute-lft-out`
21×	`div-exp`
14×	`associate-/r/`
12×	`prod-exp`
11×	`cbrt-undiv`
10×	`associate-/r*` `div-inv`
9×	`add-log-exp`
8×	`pow1` `flip3-+` `flip-+`
6×	`pow-flip` `cbrt-unprod` `associate-/l*`
4×	`rec-exp` `sqrt-pow1` `1-exp`
3×	`exp-prod`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `associate--l+` `sum-log` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 289

Calls

4 calls:

5.0ms	(/ 1 (sqrt (exp wj)))
61.0ms	(* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj))))
5.0ms	(/ x (+ wj 1))
30.0ms	(- (+ (* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1 (sqrt (exp wj)))
10.0ms	(* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj))))
5.0ms	(/ x (+ wj 1))
10.0ms	(- (+ (* (/ 1 (sqrt (exp wj))) (/ (/ x (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

simplify62.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1304	3381
1	5002	3107

prune350.0ms

Filtered

160 candidates to 301 candidates (-88.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	301	7	308

Merged error: 0.2b

Counts

308 → 7

regimes203.0ms

Accuracy

98.5% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 2.3b

bsearch74.0ms

Steps

Iters	Range		Point
9	6.683655599552235e-14	3.502940561661229e-06	6.482060277710291e-09
7	-9.676145318014125e-08	-5.90692885902093e-10	-3.7212948846946436e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	27
1	40	27

end0.0ms

analyze386.0ms

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
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

sample1.9s

Algorithm

intervals

Results

1.1s	3850×	body	5120	exit
291.0ms	6249×	body	80	valid
109.0ms	758×	body	320	valid
101.0ms	469×	body	640	valid
48.0ms	524×	body	160	valid
4.0ms	79×	body	80	invalid
0.0ms	11×	body	80	overflowed

Details

analyze501.0ms

sample53.0ms

simplify48.0ms

prune19.0ms

localize19.0ms

rewrite81.0ms

series31.0ms

simplify87.0ms

prune248.0ms

localize13.0ms

rewrite27.0ms

series20.0ms

simplify146.0ms

prune58.0ms

localize10.0ms

rewrite76.0ms

series33.0ms

simplify106.0ms

prune261.0ms

localize12.0ms

rewrite117.0ms

series36.0ms

simplify62.0ms

prune350.0ms

regimes203.0ms

bsearch74.0ms

simplify1.0ms

end0.0ms

analyze386.0ms

sample1.9s

Profiling