Details

analyze328.0ms

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

sample47.0ms

Algorithm

intervals

Results

23.0ms	105×	body	5120	exit
7.0ms	204×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	19×	body	160	valid
0.0ms	4×	body	80	invalid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	6196	12

prune11.0ms

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: 12.4b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- (/ x (exp wj)) wj) (+ wj 1))
5.1b	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
38×	`times-frac`
23×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`associate-/l*`
8×	`distribute-lft-out`
7×	`associate-/r*` `add-cbrt-cube`
6×	`add-exp-log`
5×	`distribute-lft-out--` `add-log-exp`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `flip3--` `sum-log` `flip--`

Counts

3 → 91

Calls

3 calls:

4.0ms	(/ x (exp wj))
11.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
16.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

series30.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ x (exp wj))
10.0ms	(/ (- (/ x (exp wj)) wj) (+ wj 1))
10.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

simplify54.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5860	1345

prune134.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 35

Calls

2 calls:

3.0ms	(+ x (* wj (+ wj (* x -2))))
5.0ms	(* wj (+ wj (* x -2)))

series15.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ x (* wj (+ wj (* x -2))))
8.0ms	(* wj (+ wj (* x -2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4935	405
1	4935	405

prune59.0ms

Filtered

28 candidates to 41 candidates (-46.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	40	7	47

Merged error: 0.3b

Counts

47 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (* (exp wj) (+ wj 1)))
0.0b	(* (exp wj) (+ wj 1))
5.1b	(- (+ wj (/ x (* (exp wj) (+ wj 1)))) (/ wj (+ wj 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`times-frac`
13×	`add-cbrt-cube`
11×	`add-exp-log`
9×	`add-log-exp`
6×	`pow1` `distribute-lft-out` `associate-/l*`
5×	`associate-/r*`
4×	`flip3-+` `associate-r/` `associate-r*` `associate-/r/` `flip-+`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`frac-2neg` `diff-log` `prod-exp` `clear-num` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
7.0ms	(/ x (* (exp wj) (+ wj 1)))
7.0ms	(* (exp wj) (+ wj 1))
14.0ms	(- (+ wj (/ x (* (exp wj) (+ wj 1)))) (/ wj (+ wj 1)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ wj (+ wj 1))
14.0ms	(/ x (* (exp wj) (+ wj 1)))
4.0ms	(* (exp wj) (+ wj 1))
10.0ms	(- (+ wj (/ x (* (exp wj) (+ wj 1)))) (/ wj (+ wj 1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5002	1316

prune139.0ms

Filtered

81 candidates to 110 candidates (-35.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Merged error: 0.3b

Counts

117 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1))))
5.1b	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
5.1b	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
5.1b	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
3×	`+-commutative` `associate-+r-` `div-sub` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 53

Calls

4 calls:

19.0ms	(cbrt (+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1))))
17.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
17.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
17.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1))))
10.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
10.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))
10.0ms	(+ wj (/ (- (/ x (exp wj)) wj) (+ wj 1)))

simplify49.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5151	1084

prune120.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	65	8	73

Merged error: 0.3b

Counts

73 → 8

regimes137.0ms

Accuracy

97% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 2.1b

bsearch35.0ms

Steps

Iters	Range		Point
8	1.8349841215167185e-12	9.674301107779206e-09	4.002066009806822e-09
9	-7.420290712929357e-07	-1.1167978716537103e-11	-4.5385141887408526e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	34
1	48	34

end0.0ms

sample1.5s

Algorithm

intervals

Results

849.0ms	3782×	body	5120	exit
228.0ms	6259×	body	80	valid
90.0ms	482×	body	640	valid
85.0ms	726×	body	320	valid
41.0ms	533×	body	160	valid
4.0ms	81×	body	80	invalid
0.0ms	11×	body	80	overflowed

Details

analyze328.0ms

sample47.0ms

simplify60.0ms

prune11.0ms

localize8.0ms

rewrite34.0ms

series30.0ms

simplify54.0ms

prune134.0ms

localize6.0ms

rewrite9.0ms

series15.0ms

simplify48.0ms

prune59.0ms

localize9.0ms

rewrite35.0ms

series30.0ms

simplify47.0ms

prune139.0ms

localize15.0ms

rewrite71.0ms

series54.0ms

simplify49.0ms

prune120.0ms

regimes137.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample1.5s

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