Details

analyze3.0ms

Algorithm: search

sample29.0ms

Algorithm

intervals

Results

10.0ms	195×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	27×	body	640	valid
3.0ms	18×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	9×	body	160	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

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: 14.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series19.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune296.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 13.8b

Counts

72 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 137

Calls

4 calls:

28.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series37.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5002	1268

prune214.0ms

Filtered

103 candidates to 149 candidates (-44.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	153	6	159

Merged error: 1.7b

Counts

159 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series65.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	278	606
1	720	576
2	2734	500
3	5001	491

prune164.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 1.7b

Counts

78 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.2b	(exp (log (cbrt (+ (+ alpha beta) 2.0))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
15×	`cbrt-prod`
14×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `distribute-lft-out`
8×	`log-prod` `exp-sum`
6×	`cbrt-div` `add-log-exp`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`log-div` `exp-diff` `log-pow` `difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(exp (log (cbrt (+ (+ alpha beta) 2.0))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ (+ alpha beta) 2.0))
18.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms	(exp (log (cbrt (+ (+ alpha beta) 2.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	320	649
1	780	619
2	2815	535
3	5002	518

prune168.0ms

Filtered

56 candidates to 80 candidates (-42.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 1.7b

Counts

87 → 8

regimes124.0ms

Accuracy

74.9% (3.5b remaining)

Error of 6.6b against oracle of 3.2b and baseline of 16.9b

bsearch48.0ms

Steps

Iters	Range		Point
10	1.9289392656899156	12398370093021546.0	399096.16819610895

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	40
1	51	40

end0.0ms

analyze2.0ms

Algorithm: search

sample712.0ms

Algorithm

intervals

Results

181.0ms	5808×	body	80	valid
141.0ms	859×	body	1280	valid
121.0ms	8000×	pre	80	true
91.0ms	730×	body	640	valid
37.0ms	380×	body	320	valid
14.0ms	223×	body	160	valid

Details

analyze3.0ms

sample29.0ms

simplify66.0ms

prune3.0ms

localize7.0ms

rewrite30.0ms

series19.0ms

simplify37.0ms

prune296.0ms

localize9.0ms

rewrite61.0ms

series37.0ms

simplify56.0ms

prune214.0ms

localize20.0ms

rewrite30.0ms

series65.0ms

simplify68.0ms

prune164.0ms

localize21.0ms

rewrite36.0ms

series64.0ms

simplify72.0ms

prune168.0ms

regimes124.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample712.0ms

Profiling