Details

sample437.0ms

Algorithm

intervals

Results

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

simplify121.0ms

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

localize28.0ms

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*)))))

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

series2.5s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
131.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1004	1625
1	4884	1448
2	5001	1448

prune1.0s

Filtered

115 candidates to 75 candidates (34.8%)

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: 20.7b

Counts

116 → 14

localize18.0ms

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*)))))

rewrite48.0ms

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

42.0ms	(* n (pow (/ l Om) 2.0))
359.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms	(* (* 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*)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1071	1765
1	5001	1602

prune1.3s

Filtered

131 candidates to 86 candidates (34.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Merged error: 18.8b

Counts

145 → 14

localize12.0ms

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)))

rewrite31.0ms

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))))
7.0ms	(* 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)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- t (* 2.0 (* l (/ l Om))))
3.0ms	(* l (/ l Om))
38.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
180.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (111.0ms)

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

prune609.0ms

Filtered

104 candidates to 65 candidates (37.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	103	15	118

Merged error: 18.8b

Counts

118 → 15

localize18.0ms

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*))))))

rewrite49.0ms

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))
12.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms	(* (* 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:

42.0ms	(* n (pow (/ l Om) 2.0))
356.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
128.0ms	(* (* 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*))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1136	1927
1	5001	1732

prune1.4s

Filtered

141 candidates to 85 candidates (39.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	3	10	13
Picked	0	1	1
Done	1	0	1
Total	139	17	156

Merged error: 15.5b

Counts

156 → 17

regimes1.2s

Accuracy

2.5% (12.6b remaining)

Error of 31.5b against oracle of 18.9b and baseline of 31.9b

bsearch412.0ms

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

sample3.5s

Algorithm

intervals

Results

1.3s	15120×	body	80	nan
797.0ms	9233×	body	80	valid

Details

sample437.0ms

simplify121.0ms

prune9.0ms

localize28.0ms

rewrite46.0ms

series2.5s

simplify124.0ms

prune1.0s

localize18.0ms

rewrite48.0ms

series2.5s

simplify42.0ms

prune1.3s

localize12.0ms

rewrite31.0ms

series232.0ms

simplify120.0ms

prune609.0ms

localize18.0ms

rewrite49.0ms

series2.5s

simplify43.0ms

prune1.4s

regimes1.2s

bsearch412.0ms

simplify2.0ms

end0.0ms

sample3.5s

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