Details

analyze2.5s

Algorithm: search

sample95.0ms

Algorithm

intervals

Results

39.0ms	390×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	41×	body	80	invalid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 36.3b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ (* l l) Om)
7.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite45.0ms

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:

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

series2.5s

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* l l) Om)
131.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
371.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1004	1621
1	4896	1448
2	5002	1448

prune306.0ms

Filtered

75 candidates to 115 candidates (-53.3%)

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: 26.3b

Counts

116 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) 2.0))
7.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite47.0ms

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 (/ 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*)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* n (pow (/ l Om) 2.0))
130.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
364.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1071	1769
1	5001	1602

prune301.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 24.4b

Counts

145 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
7.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.9b	(* (* (* 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*))))
21.6b	(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*)))))

rewrite55.0ms

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:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.0ms	(* (* (* 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*))))
10.0ms	(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*)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

50.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
133.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
370.0ms	(* (* (* 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*))))
2.0s	(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*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1243	2487
1	5001	2141

prune368.0ms

Filtered

91 candidates to 148 candidates (-62.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	148	12	160

Merged error: 24.4b

Counts

160 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))
32.2b	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
32.2b	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
32.2b	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

184×	`associate-*r/`
114×	`cbrt-div`
84×	`flip3--` `flip--`
56×	`frac-times`
54×	`sqrt-div`
52×	`frac-sub`
28×	`associate-*l/`
14×	`pow1`
6×	`pow-prod-down`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 100

Calls

4 calls:

26.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))
13.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
13.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
15.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))

series2.4s

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) (cbrt ( (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))
127.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
126.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
131.0ms	(cbrt (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))

simplify135.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1432	6389
1	4204	6262
2	5001	6262

prune546.0ms

Filtered

73 candidates to 112 candidates (-53.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 24.4b

Counts

124 → 12

regimes1.3s

Accuracy

38.9% (5.9b remaining)

Error of 27.0b against oracle of 21.1b and baseline of 30.8b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	131
1	68	131

end0.0ms

analyze2.3s

Algorithm: search

sample2.8s

Algorithm

intervals

Results

1.2s	12711×	body	80	nan
743.0ms	8000×	body	80	valid
120.0ms	1218×	body	80	invalid

Details

analyze2.5s

sample95.0ms

simplify117.0ms

prune6.0ms

localize19.0ms

rewrite45.0ms

series2.5s

simplify128.0ms

prune306.0ms

localize20.0ms

rewrite47.0ms

series2.5s

simplify43.0ms

prune301.0ms

localize23.0ms

rewrite55.0ms

series2.5s

simplify51.0ms

prune368.0ms

localize27.0ms

rewrite78.0ms

series2.4s

simplify135.0ms

prune546.0ms

regimes1.3s

bsearch1.0ms

simplify3.0ms

end0.0ms

analyze2.3s

sample2.8s

Profiling