Details

Time bar (total: 32.6s)

sample415.0ms

Algorithm
intervals
Results
64.0ms508×body80nan
27.0ms297×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune6.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.3b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.5b
(/ (* l l) Om)
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite57.0ms

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)
22.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* 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*)))))

series6.2s

Counts
4 → 12
Calls
4 calls:
350.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s
(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 (23.0ms)

IterNodesCost
09371548
147521385
250021385

prune436.0ms

Filtered
115 candidates to 75 candidates (65.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10114115
Fresh000
Picked101
Done000
Total10214116

Merged error: 21.9b

Counts
116 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) 2.0))
6.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms

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

series6.4s

Counts
4 → 12
Calls
4 calls:
141.0ms
(* n (pow (/ l Om) 2.0))
350.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09871668
150011508

prune471.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1256131
Fresh4913
Picked101
Done000
Total13015145

Merged error: 19.9b

Counts
145 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) 2.0))
5.8b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.5b
(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))
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*))
11.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.4s

Counts
4 → 12
Calls
4 calls:
142.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
350.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.7s
(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
141 → 141
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010521821
150011638

prune457.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1365141
Fresh31114
Picked011
Done000
Total13917156

Merged error: 17.1b

Counts
156 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.5b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
18.5b
(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
36×associate-*r/
34×pow1
32×add-exp-log
18×pow-prod-down prod-exp
14×add-cbrt-cube
12×flip3-- sqrt-div flip--
10×add-sqr-sqrt *-un-lft-identity sqrt-pow1 associate-*r*
8×frac-sub
6×add-cube-cbrt cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in pow-exp add-log-exp
2×pow-to-exp pow1/2 div-exp associate-*l* sqrt-prod *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
11.0ms
(* (* 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 (/ 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*))))))

series9.9s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
358.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
06571464
129741388
250021388

prune495.0ms

Filtered
108 candidates to 72 candidates (66.7%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1071108
Fresh01515
Picked011
Done011
Total10718125

Merged error: 17.1b

Counts
125 → 18

regimes694.0ms

bsearch7.0ms

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