Details

Time bar (total: 16.6s)

sample114.0ms

Algorithm
intervals
Results
37.0ms408×body80nan
29.0ms289×body80valid

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.4b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (* l l) Om)
9.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.7b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.3b
(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
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:
5.0ms
(/ (* l l) Om)
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (* l l) Om)
130.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
361.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.2s
(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
115 → 115
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010041621
148961448
250021448

prune305.0ms

Filtered
115 candidates to 75 candidates (34.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10114115
Fresh000
Picked101
Done000
Total10214116

Merged error: 25.9b

Counts
116 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

5.5b
(* n (pow (/ l Om) 2.0))
6.7b
(/ (* l l) Om)
9.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
26×add-sqr-sqrt
22×associate-*r*
19×pow1
18×*-un-lft-identity associate-*r/
16×add-cube-cbrt add-cbrt-cube
15×unpow-prod-down
14×prod-exp
13×times-frac
9×pow-prod-down
6×flip3-- sqrt-div flip--
5×sqrt-pow1 cbrt-unprod
4×div-exp associate-*l* pow-exp frac-sub add-log-exp unswap-sqr
3×associate-/r*
2×cbrt-undiv distribute-rgt-in pow-to-exp sub-neg distribute-lft-in *-commutative div-inv sqr-pow
1×frac-2neg pow1/2 clear-num sqrt-prod associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
9.0ms
(* n (pow (/ l Om) 2.0))
5.0ms
(/ (* l l) Om)
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*))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
129.0ms
(* (* 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*))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09461106
143321032
250011032

prune320.0ms

Filtered
118 candidates to 83 candidates (29.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1099118
Fresh5813
Picked101
Done000
Total11517132

Merged error: 19.2b

Counts
132 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
6.7b
(/ (* l l) Om)
9.0b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
21.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
66×prod-exp
34×associate-*r/
31×pow1
30×add-cbrt-cube
18×distribute-rgt-in distribute-lft-in pow-exp
17×pow-prod-down
15×cbrt-unprod
11×flip3-- div-exp flip--
10×sub-neg
9×add-sqr-sqrt pow-to-exp *-un-lft-identity
8×associate--l+ frac-sub
7×add-cube-cbrt
6×sqrt-div associate-*r*
5×sqrt-pow1
4×add-log-exp
3×times-frac associate-/r*
2×cbrt-undiv associate-*l* *-commutative
1×frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 130
Calls
4 calls:
13.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0ms
(/ (* l l) Om)
17.0ms
(* (* (* 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 l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
361.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
3.0ms
(/ (* l l) Om)
132.0ms
(* (* (* 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 l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011742498
150012085

prune348.0ms

Filtered
142 candidates to 73 candidates (48.6%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1366142
Fresh31316
Picked101
Done000
Total14019159

Merged error: 19.0b

Counts
159 → 19

localize27.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) (/ 2.0 2)))
5.3b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
9.0b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
21.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite58.0ms

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:
9.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
13.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
19.0ms
(* (* (* 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 (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
50.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
367.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
130.0ms
(* (* (* 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 (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013143209
150012742

prune289.0ms

Filtered
158 candidates to 92 candidates (41.8%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1553158
Fresh21618
Picked101
Done000
Total15819177

Merged error: 18.5b

Counts
177 → 19

regimes1.1s

Accuracy

30.1% (9.6b remaining)

Error of 27.7b against oracle of 18.1b and baseline of 31.9b

bsearch57.0ms

Steps
ItersRangePoint
8
-3.5120113242835606e-307
2.434920098879601e-307
1.69153011341487e-310

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05952
15952

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.3s14655×body80nan
835.0ms9177×body80valid

Profiling

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