Details

sample332.0ms

Algorithm

intervals

Results

30.0ms	405×	body	80	nan
23.0ms	285×	body	80	valid

simplify123.0ms

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

prune5.0ms

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: 36.1b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.0b	(/ (* l l) Om)
8.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
23.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite32.0ms

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--l+`
2×	`associate-r` `div-inv` `associate-/l*`
1×	`unpow-prod-down` `frac-2neg` `pow1/2` `clear-num` `sqr-pow`

Counts

4 → 48

Calls

4 calls:

3.0ms	(/ (* l l) Om)
6.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* l l) Om)
353.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	642	928
1	2727	923
2	5002	923

prune307.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	46	14	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	14	61

Merged error: 21.9b

Counts

61 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

4.3b	(* n (pow (/ l Om) 2.0))
8.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
23.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite31.0ms

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:

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

series6.2s

Counts

4 → 12

Calls

4 calls:

133.0ms	(* n (pow (/ l Om) 2.0))
355.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (14.0ms)

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

prune291.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	46	12	58
Fresh	13	0	13
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 20.7b

Counts

72 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) (/ 2.0 2)))
7.0b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
8.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
23.1b	(sqrt (* (* (* 2.0 n) U) (- (- 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

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

Counts

4 → 44

Calls

4 calls:

3.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
5.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.4s

Counts

4 → 12

Calls

4 calls:

151.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
316.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	673	1114
1	2819	1105
2	5001	1093

prune309.0ms

Filtered

56 candidates to 45 candidates (80.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	55	13	68

Merged error: 19.6b

Counts

68 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

4.7b	(* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
6.2b	(* n (pow (/ l Om) (/ 2.0 2)))
7.0b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
23.1b	(sqrt (* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

rewrite30.0ms

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:

10.0ms	(* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
3.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
5.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.0ms	(sqrt (* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

series6.3s

Counts

4 → 12

Calls

4 calls:

1.3s	(* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
158.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
326.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
4.5s	(sqrt (* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	728	1235
1	2965	1226
2	5002	1202

prune259.0ms

Filtered

64 candidates to 44 candidates (68.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	62	15	77

Merged error: 19.1b

Counts

77 → 15

regimes641.0ms

Accuracy

31.8% (10.3b remaining)

Error of 27.4b against oracle of 17.0b and baseline of 32.2b

bsearch106.0ms

Steps

Iters	Range		Point
8	-1.043383083232938e-307	9.244453159373683e-306	1.112803335181648e-307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	40
1	43	40

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	14946×	body	80	nan
696.0ms	9184×	body	80	valid