Details

sample451.0ms

Algorithm

intervals

Results

62.0ms	495×	body	80	nan
26.0ms	289×	body	80	valid

simplify127.0ms

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

prune9.0ms

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: 32.2b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

7.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
19.9b	(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:

11.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.0s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
405.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
28.0ms	(/ (* l l) Om)
5.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify122.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (22.0ms)

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

prune976.0ms

Filtered

115 candidates to 75 candidates (34.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	13	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Merged error: 20.9b

Counts

116 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
7.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

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))
11.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.3s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* n (pow (/ l Om) 2.0))
1.5s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
402.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune1.3s

Filtered

131 candidates to 86 candidates (34.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Merged error: 19.0b

Counts

144 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- t (* 2.0 (* l (/ l Om))))
0.1b	(* l (/ l Om))
7.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
18.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
20×	`add-sqr-sqrt`
18×	`add-exp-log` `associate-r` `add-cbrt-cube`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `pow-prod-down`
10×	`times-frac`
8×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sub-neg` `associate-*r/`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+`
3×	`flip3--` `flip--`
2×	`sqrt-div` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `pow1/2` `diff-log` `div-exp` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

3.0ms	(- t (* 2.0 (* l (/ l Om))))
6.0ms	(* l (/ l Om))
11.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
8.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

56.0ms	(- t (* 2.0 (* l (/ l Om))))
26.0ms	(* l (/ l Om))
158.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
1.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

simplify123.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	513	740
1	2772	628
2	5001	623

prune600.0ms

Filtered

104 candidates to 65 candidates (37.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	103	14	117

Merged error: 19.0b

Counts

117 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
7.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.9b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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:

8.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
10.0ms	(* (* 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*))))))

series7.3s

Counts

4 → 12

Calls

4 calls:

146.0ms	(* n (pow (/ l Om) 2.0))
1.7s	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
412.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1052	1821
1	5001	1638

prune1.4s

Filtered

141 candidates to 85 candidates (39.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	3	9	12
Picked	0	1	1
Done	1	0	1
Total	139	16	155

Merged error: 15.8b

Counts

155 → 16

regimes1.1s

Accuracy

2.5% (12.5b remaining)

Error of 31.5b against oracle of 19.1b and baseline of 31.9b

bsearch410.0ms

Steps

Iters	Range	Point
8	3.6478999796003252e+174	2.7330236319169843e+178	5.025940990514969e+174
7	2.3341742417101446e-123	4.4741154001161504e-122	2.4794868703323314e-122
9	-4.805612024424144e-303	3.5507366646130136e-307	1.7123231787798296e-308

Iters

Range

Point

3.6478999796003252e+174

2.7330236319169843e+178

5.025940990514969e+174

2.3341742417101446e-123

4.4741154001161504e-122

2.4794868703323314e-122

-4.805612024424144e-303

3.5507366646130136e-307

1.7123231787798296e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	70
1	54	70

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	15120×	body	80	nan
821.0ms	9233×	body	80	valid

Details

sample451.0ms

simplify127.0ms

prune9.0ms

localize29.0ms

rewrite45.0ms

series7.0s

simplify122.0ms

prune976.0ms

localize17.0ms

rewrite44.0ms

series7.3s

simplify40.0ms

prune1.3s

localize16.0ms

rewrite30.0ms

series1.5s

simplify123.0ms

prune600.0ms

localize17.0ms

rewrite48.0ms

series7.3s

simplify45.0ms

prune1.4s

regimes1.1s

bsearch410.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling