Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample56.0ms

Algorithm

intervals

Results

12.0ms	188×	body	80	valid
8.0ms	25×	body	1280	valid
7.0ms	256×	pre	80	true
6.0ms	24×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	11×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.0b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite29.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series19.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (41.0ms)

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

prune105.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 15.0b

Counts

72 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
3.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

31.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series46.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune227.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	10	123
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 4.7b

Counts

132 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

25.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
22.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
22.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
41.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify134.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	336	1065
1	979	1017
2	4616	980
3	5001	980

prune293.0ms

Filtered

86 candidates to 117 candidates (-36.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 4.7b

Counts

127 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
3.0b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
131×	`add-sqr-sqrt`
123×	`associate-*r/`
90×	`distribute-lft-out`
83×	`flip3-+` `flip-+`
73×	`add-cube-cbrt`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
47×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
38×	`associate-/r/`
26×	`flip3--` `flip--`
24×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
11×	`sqr-pow`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 327

Calls

4 calls:

25.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
58.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
53.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series146.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
13.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
102.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
21.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify129.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2085	7822
1	5002	7442

prune3.3s

Filtered

212 candidates to 339 candidates (-59.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	342	5	347

Merged error: 4.6b

Counts

347 → 5

regimes110.0ms

Accuracy

76.8% (2.9b remaining)

Error of 5.8b against oracle of 2.9b and baseline of 15.6b

bsearch41.0ms

Steps

Iters	Range		Point
8	7.814088603503307	261803.90864640454	257952.67455795372

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample727.0ms

Algorithm

intervals

Results

189.0ms	5877×	body	80	valid
133.0ms	818×	body	1280	valid
132.0ms	8000×	pre	80	true
90.0ms	713×	body	640	valid
39.0ms	371×	body	320	valid
14.0ms	221×	body	160	valid

Details

analyze4.0ms

sample56.0ms

simplify70.0ms

prune3.0ms

localize8.0ms

rewrite29.0ms

series19.0ms

simplify48.0ms

prune105.0ms

localize12.0ms

rewrite61.0ms

series46.0ms

simplify54.0ms

prune227.0ms

localize16.0ms

rewrite59.0ms

series98.0ms

simplify134.0ms

prune293.0ms

localize31.0ms

rewrite179.0ms

series146.0ms

simplify129.0ms

prune3.3s

regimes110.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample727.0ms

Profiling