Details

sample364.0ms

Algorithm

intervals

Results

53.0ms	450×	body	80	nan
27.0ms	301×	body	80	valid

simplify133.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	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: 32.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.8b	(/ (* l l) Om)
22.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0ms	(/ (* l l) Om)
15.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

350.0ms	(* (* 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*))))
23.0ms	(/ (* l l) Om)
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011

prune522.0ms

Filtered

153 candidates to 92 candidates (60.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	139	14	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	14	154

Merged error: 22.7b

Counts

154 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b	(* n (pow (/ l Om) 2.0))
5.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

142.0ms	(* n (pow (/ l Om) 2.0))
342.0ms	(* (* 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*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1229	2461
1	5001	2136

prune517.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	171	12	183

Merged error: 21.3b

Counts

183 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.7b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
22.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 174

Calls

4 calls:

17.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
156.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1355	3511
1	5002	2841

prune565.0ms

Filtered

186 candidates to 108 candidates (58.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	184	14	198

Merged error: 21.2b

Counts

198 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.9b	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
6.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
22.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

509×	`add-exp-log`
387×	`prod-exp`
180×	`pow-exp`
85×	`div-exp`
65×	`pow-to-exp`
39×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`add-cube-cbrt` `associate-r`
34×	`unpow-prod-down`
32×	`add-cbrt-cube`
30×	`rec-exp` `1-exp` `prod-diff`
25×	`pow1`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
19×	`cbrt-unprod`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`associate-l` `*-commutative`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 282

Calls

4 calls:

31.0ms	(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
14.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series9.2s

Counts

4 → 12

Calls

4 calls:

508.0ms	(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
157.0ms	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
6.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify264.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1854	4897
1	5001	4417

prune614.0ms

Filtered

294 candidates to 108 candidates (36.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	295	13	308

Merged error: 20.7b

Counts

308 → 13

regimes704.0ms

Accuracy

25.8% (7.1b remaining)

Error of 28.9b against oracle of 21.8b and baseline of 31.4b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	82
1	76	82

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	14843×	body	80	nan
843.0ms	9229×	body	80	valid

Details

sample364.0ms

simplify133.0ms

prune5.0ms

localize20.0ms

rewrite60.0ms

series6.2s

simplify51.0ms

prune522.0ms

localize17.0ms

rewrite52.0ms

series6.3s

simplify50.0ms

prune517.0ms

localize19.0ms

rewrite64.0ms

series6.4s

simplify60.0ms

prune565.0ms

localize29.0ms

rewrite92.0ms

series9.2s

simplify264.0ms

prune614.0ms

regimes704.0ms

bsearch4.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling