Details

sample123.0ms

Algorithm

intervals

Results

45.0ms	466×	body	80	nan
28.0ms	298×	body	80	valid

simplify118.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 35.8b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.4b	(/ (* l l) Om)
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite42.0ms

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:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
14.0ms	(* (* (* 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*)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
397.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.1s	(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 (24.0ms)

Iter	Nodes	Cost
0	1004	1621
1	4896	1448
2	5001	1448

prune271.0ms

Filtered

115 candidates to 75 candidates (34.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	12	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Merged error: 24.7b

Counts

116 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2.0))
6.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

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:

8.0ms	(* n (pow (/ l Om) 2.0))
10.0ms	(* (* 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*))))
11.0ms	(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:

42.0ms	(* n (pow (/ l Om) 2.0))
127.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
356.0ms	(* (* (* 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*)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1071	1769
1	5001	1602

prune292.0ms

Filtered

131 candidates to 86 candidates (34.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	130	13	143

Merged error: 23.2b

Counts

143 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2.0))
6.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.0b	(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:

9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms	(* (* 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:

51.0ms	(* n (pow (/ l Om) 2.0))
129.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1136	1922
1	5001	1732

prune308.0ms

Filtered

141 candidates to 85 candidates (39.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	138	16	154

Merged error: 18.6b

Counts

154 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

6.8b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.0b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
20.0b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

12.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*))))))
10.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series4.6s

Counts

4 → 12

Calls

4 calls:

360.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
363.0ms	(* (* 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*))))))
2.0s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify102.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	797	2882
1	3400	2580
2	5001	2580

prune338.0ms

Filtered

140 candidates to 78 candidates (44.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	140	16	156

Merged error: 18.6b

Counts

156 → 16

regimes1.1s

Accuracy

16.1% (11.1b remaining)

Error of 30.0b against oracle of 18.9b and baseline of 32.1b

bsearch57.0ms

Steps

Iters	Range		Point
8	2.8497356224289583e-280	7.675570892708335e-276	2.9133035110208574e-280

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	24
1	38	24

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	14900×	body	80	nan
837.0ms	9180×	body	80	valid

Details

sample123.0ms

simplify118.0ms

prune5.0ms

localize19.0ms

rewrite42.0ms

series2.6s

simplify123.0ms

prune271.0ms

localize20.0ms

rewrite46.0ms

series2.5s

simplify43.0ms

prune292.0ms

localize19.0ms

rewrite48.0ms

series2.5s

simplify51.0ms

prune308.0ms

localize26.0ms

rewrite51.0ms

series4.6s

simplify102.0ms

prune338.0ms

regimes1.1s

bsearch57.0ms

simplify1.0ms

end0.0ms

sample3.6s

Profiling