Details

sample420.0ms

Algorithm

intervals

Results

55.0ms	450×	body	80	nan
28.0ms	301×	body	80	valid

simplify127.0ms

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: 32.6b

Counts

2 → 1

localize21.0ms

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*)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

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*))))
5.0ms	(/ (* l l) Om)
12.0ms	(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:

345.0ms	(* (* 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*))))
22.0ms	(/ (* l l) Om)
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1548
1	4752	1385
2	5002	1385

prune426.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	101	14	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	14	116

Merged error: 22.7b

Counts

116 → 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*)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 119

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* 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:

140.0ms	(* n (pow (/ l Om) 2.0))
349.0ms	(* (* 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*)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune437.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 21.3b

Counts

145 → 12

localize20.0ms

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*)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
12.0ms	(* (* (* 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*))))
10.0ms	(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:

343.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
155.0ms	(* 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*)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5001	2030

prune476.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	146	14	160

Merged error: 21.2b

Counts

160 → 14

localize31.0ms

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*)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 244

Calls

4 calls:

25.0ms	(* (* (* (* 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))
13.0ms	(* (* (* 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*))))
11.0ms	(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*)))))

series9.0s

Counts

4 → 12

Calls

4 calls:

503.0ms	(* (* (* (* 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*))))
6.5s	(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*)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1611	3706
1	5001	3431

prune735.0ms

Filtered

256 candidates to 94 candidates (36.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	257	13	270

Merged error: 20.7b

Counts

270 → 13

regimes682.0ms

Accuracy

25.8% (7.1b remaining)

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

bsearch6.0ms

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
860.0ms	9229×	body	80	valid

Details

sample420.0ms

simplify127.0ms

prune5.0ms

localize21.0ms

rewrite46.0ms

series6.2s

simplify123.0ms

prune426.0ms

localize17.0ms

rewrite49.0ms

series6.3s

simplify41.0ms

prune437.0ms

localize20.0ms

rewrite58.0ms

series6.4s

simplify48.0ms

prune476.0ms

localize31.0ms

rewrite84.0ms

series9.0s

simplify64.0ms

prune735.0ms

regimes682.0ms

bsearch6.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling