Details

sample347.0ms

Algorithm

intervals

Results

35.0ms	480×	body	80	nan
21.0ms	296×	body	80	valid

simplify135.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune6.0ms

Filtered

1 candidates to 0 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: 36.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b	(* n (pow (/ l Om) 2.0))
7.3b	(/ (* l l) Om)
11.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
12×	`associate-l`
10×	`flip3--` `flip--`
8×	`*-commutative` `frac-sub`
6×	`sqrt-div` `sqrt-prod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate--l+`
2×	`associate-r` `div-inv` `associate-/l*`
1×	`unpow-prod-down` `frac-2neg` `pow1/2` `clear-num` `sqr-pow`

Counts

4 → 40

Calls

4 calls:

3.0ms	(* n (pow (/ l Om) 2.0))
4.0ms	(/ (* l l) Om)
9.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.0s

Counts

4 → 12

Calls

4 calls:

141.0ms	(* n (pow (/ l Om) 2.0))
18.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	606	849
1	2576	844
2	5003	844

prune276.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	39	13	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	13	53

Merged error: 22.3b

Counts

53 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b	(* n (pow (/ l Om) 2.0))
11.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-*r/`
16×	`associate-l`
11×	`flip3--` `flip--`
9×	`*-commutative`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `sqrt-prod`
4×	`associate-r` `associate--l+`
2×	`unpow-prod-down` `div-inv` `sqr-pow`
1×	`pow1/2`

Counts

4 → 46

Calls

4 calls:

5.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(* n (pow (/ l Om) 2.0))
9.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
142.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	644	930
1	2742	925
2	5003	925

prune301.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	46	12	58
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	56	15	71

Merged error: 19.7b

Counts

71 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b	(* n (pow (/ l Om) 2.0))
7.0b	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.0b	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-*r/`
18×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
11×	`flip3--` `flip--`
10×	`sub-neg`
9×	`*-commutative`
8×	`associate-l` `associate--l+` `frac-sub`
6×	`sqrt-div` `sqrt-prod`
2×	`unpow-prod-down` `div-inv` `sqr-pow`
1×	`pow1/2`

Counts

4 → 54

Calls

4 calls:

5.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(* n (pow (/ l Om) 2.0))
9.0ms	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.0ms	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.6s

Counts

4 → 12

Calls

4 calls:

350.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
142.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.8s	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	712	1035
1	3107	1030
2	5002	1030

prune300.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	64	17	81

Merged error: 19.1b

Counts

81 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (pow (/ l Om) (/ 2.0 2)))
6.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
7.0b	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
20.0b	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
18×	`distribute-rgt-in` `distribute-lft-in`
11×	`flip3--` `flip--`
10×	`sub-neg` `associate-r`
8×	`associate--l+` `*-commutative` `frac-sub`
6×	`sqrt-div` `associate-l` `sqrt-prod`
2×	`unpow-prod-down` `div-inv` `sqr-pow`
1×	`pow1/2`

Counts

4 → 52

Calls

4 calls:

3.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
6.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.0ms	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
13.0ms	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

series7.6s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
325.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s	(* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
5.8s	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

simplify84.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	741	1244
1	3203	1235
2	5001	1235

prune264.0ms

Filtered

64 candidates to 44 candidates (68.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	7	9	16
Picked	0	1	1
Done	0	0	0
Total	65	16	81

Merged error: 19.1b

Counts

81 → 16

regimes598.0ms

Accuracy

28.2% (10.4b remaining)

Error of 27.1b against oracle of 16.7b and baseline of 31.2b

bsearch223.0ms

Steps

Iters	Range		Point
6	4.0579098542429e-270	5.896477154731374e-269	5.089393355706581e-270
8	-4.115389571217162e+103	-9.760952735897169e+98	-1.0253190992107003e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	53
1	54	53

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	14660×	body	80	nan
661.0ms	9167×	body	80	valid