Details

analyze2.5s

Algorithm: search

sample90.0ms

Algorithm

intervals

Results

33.0ms	360×	body	80	nan
27.0ms	256×	body	80	valid
4.0ms	39×	body	80	invalid

simplify115.0ms

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

prune5.0ms

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: 30.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
8.0b	(/ (* l l) Om)
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
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*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* n (pow (/ l Om) 2.0))
3.0ms	(/ (* l l) Om)
359.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1026	1598
1	4937	1447
2	5001	1447

prune318.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	13	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	13	125

Merged error: 19.6b

Counts

125 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b	(* n (pow (/ l Om) 2.0))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.2b	(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:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms	(* n (pow (/ l Om) 2.0))
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*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
42.0ms	(* n (pow (/ l Om) 2.0))
359.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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	1071	1765
1	5001	1602

prune312.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	130	14	144

Merged error: 17.5b

Counts

144 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
16.2b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `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 → 129

Calls

4 calls:

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

series2.4s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
43.0ms	(* n (pow (/ l Om) 2.0))
350.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1136	1922
1	5001	1732

prune308.0ms

Filtered

85 candidates to 141 candidates (-65.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	132	9	141
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	138	17	155

Merged error: 14.0b

Counts

155 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

6.6b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
16.2b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
16.2b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
16.2b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

64×	`associate-*r/`
55×	`pow1`
32×	`pow-prod-down`
20×	`flip3--` `flip--`
18×	`sqrt-div`
16×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `frac-sub` `add-cbrt-cube`
15×	`sqrt-pow1`
8×	`sub-neg` `prod-exp` `associate--l+` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`pow1/2` `sqrt-prod`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 104

Calls

4 calls:

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*))))))
11.0ms	(sqrt (* (* 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*))))))

series6.1s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	797	2521
1	3400	2344
2	5001	2344

prune437.0ms

Filtered

75 candidates to 116 candidates (-54.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	116	17	133

Merged error: 14.0b

Counts

133 → 17

regimes1.1s

Accuracy

26.2% (10.1b remaining)

Error of 28.5b against oracle of 18.4b and baseline of 32.1b

bsearch11.9s

Steps

Iters	Range	Point
8	6.703181257223616e-180	3.7488696509832866e-176	6.796930102604649e-180
9	6.139677607077306e-226	2.772139004479524e-220	2.7397237309823033e-220
10	-3.5719822293001854e-308	4.7882246416144595e-296	-2.2306880959054e-310

Iters

Range

Point

6.703181257223616e-180

3.7488696509832866e-176

6.796930102604649e-180

6.139677607077306e-226

2.772139004479524e-220

2.7397237309823033e-220

-3.5719822293001854e-308

4.7882246416144595e-296

-2.2306880959054e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	88
1	61	88

end0.0ms

analyze2.3s

Algorithm: search

sample2.8s

Algorithm

intervals

Results

1.2s	12671×	body	80	nan
751.0ms	8000×	body	80	valid
111.0ms	1156×	body	80	invalid

Details

analyze2.5s

sample90.0ms

simplify115.0ms

prune5.0ms

localize19.0ms

rewrite40.0ms

series2.3s

simplify125.0ms

prune318.0ms

localize19.0ms

rewrite47.0ms

series2.4s

simplify41.0ms

prune312.0ms

localize19.0ms

rewrite48.0ms

series2.4s

simplify44.0ms

prune308.0ms

localize28.0ms

rewrite49.0ms

series6.1s

simplify98.0ms

prune437.0ms

regimes1.1s

bsearch11.9s

simplify2.0ms

end0.0ms

analyze2.3s

sample2.8s

Profiling