Details

sample87.0ms

Algorithm

intervals

Results

32.0ms	405×	body	80	nan
21.0ms	285×	body	80	valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune4.0ms

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

localize19.0ms

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*)))))

rewrite35.0ms

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:

4.0ms	(/ (* 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*))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* l l) Om)
351.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	662	923
1	2843	908
2	5001	907

prune304.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	47	13	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	13	61

Merged error: 21.8b

Counts

61 → 13

localize18.0ms

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*)))))

rewrite34.0ms

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

series6.5s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* n (pow (/ l Om) 2.0))
360.0ms	(* (* 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*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	664	925
1	2858	910
2	5001	909

prune297.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	48	10	58
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	59	12	71

Merged error: 20.5b

Counts

71 → 12

localize21.0ms

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*))))))

rewrite31.0ms

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)))
6.0ms	(* (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*)))))
11.0ms	(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*))))))

series6.5s

Counts

4 → 12

Calls

4 calls:

174.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
330.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s	(* (* (* 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*)))))
4.6s	(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*))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	694	1108
1	2941	1089
2	5001	1088

prune504.0ms

Filtered

56 candidates to 44 candidates (78.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	56	12	68

Merged error: 19.8b

Counts

68 → 12

localize22.0ms

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*)))))))

rewrite37.0ms

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*))
15.0ms	(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*)))))))

series6.4s

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*))))))
160.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
335.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
4.6s	(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*)))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	749	1229
1	3087	1206
2	5001	1205

prune264.0ms

Filtered

64 candidates to 44 candidates (68.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	61	15	76

Merged error: 19.4b

Counts

76 → 15

regimes659.0ms

Accuracy

36.9% (10.0b remaining)

Error of 27.2b against oracle of 17.2b and baseline of 33.1b

bsearch252.0ms

Steps

Iters	Range		Point
3	3.869605900086527e-303	5.311244769838657e-303	3.959708329446035e-303
7	-1.3722220988249033e-247	-7.7261680944798965e-249	-9.586008970714456e-249
7	-3981383454.147858	-32904787.96497473	-3923563313.012581

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	83
1	67	83

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	14946×	body	80	nan
678.0ms	9184×	body	80	valid