Details

sample28.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 10.717773%

Guaranteed chance to sample good point: 1.668034%

Results

46.0ms	432×	body	80	nan
26.0ms	256×	body	80	valid
5.0ms	50×	body	80	invalid

simplify123.0ms

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

prune8.0ms

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

localize21.0ms

Local error

Found 4 expressions with local error:

7.5b	(* n (pow (/ l Om) 2.0))
8.2b	(/ (* l l) Om)
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite39.0ms

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:

8.0ms	(* 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:

45.0ms	(* n (pow (/ l Om) 2.0))
3.0ms	(/ (* l l) Om)
357.0ms	(* (* (* 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*)))))

simplify134.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (26.0ms)

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

prune356.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	108	16	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	16	125

Merged error: 25.0b

Counts

125 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

6.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.5b	(* n (pow (/ l Om) 2.0))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(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:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* (* 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:

127.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
42.0ms	(* n (pow (/ l Om) 2.0))
354.0ms	(* (* (* 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*)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1071	1765
1	5001	1602

prune319.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	131	16	147

Merged error: 23.1b

Counts

147 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.5b	(* n (pow (/ l Om) 2.0))
20.4b	(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:

12.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms	(* n (pow (/ l Om) 2.0))
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:

350.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
128.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
41.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1136	1927
1	5001	1732

prune325.0ms

Filtered

85 candidates to 141 candidates (-65.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	139	18	157

Merged error: 20.1b

Counts

157 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) (/ 2.0 2)))
6.2b	(* (* 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*)))))
6.3b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
20.4b	(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*))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log`
69×	`prod-exp`
34×	`associate-*r/`
31×	`pow1`
27×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-r`
20×	`pow-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down` `cbrt-unprod`
14×	`add-cube-cbrt`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `sub-neg` `times-frac` `div-exp`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`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 → 146

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
12.0ms	(* (* 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*)))))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
11.0ms	(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*))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

48.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
351.0ms	(* (* 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*)))))
129.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(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*))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1308	2694
1	5001	2292

prune292.0ms

Filtered

91 candidates to 158 candidates (-73.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	158	18	176

Merged error: 19.9b

Counts

176 → 18

regimes1.7s

Accuracy

36.1% (7.9b remaining)

Error of 26.5b against oracle of 18.6b and baseline of 31.0b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	115
1	76	115

end0.0ms

sample32.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 10.717773%

Guaranteed chance to sample good point: 1.668034%

Results

1.2s	12354×	body	80	nan
817.0ms	8000×	body	80	valid
129.0ms	1250×	body	80	invalid

Details

sample28.4s

simplify123.0ms

prune8.0ms

localize21.0ms

rewrite39.0ms

series2.3s

simplify134.0ms

prune356.0ms

localize20.0ms

rewrite46.0ms

series2.4s

simplify47.0ms

prune319.0ms

localize20.0ms

rewrite48.0ms

series2.4s

simplify49.0ms

prune325.0ms

localize25.0ms

rewrite54.0ms

series2.4s

simplify54.0ms

prune292.0ms

regimes1.7s

bsearch3.0ms

simplify3.0ms

end0.0ms

sample32.7s

Profiling