Details

Time bar (total: 20.7s)

analyze7.6s

Algorithm
search
sampling

Space saved by range analysis: 0.292611%

Space saved by search: 10.979023%

Guaranteed chance to sample good point: 1.668034%

sample101.0ms

Algorithm
intervals
Results
38.0ms405×body80nan
29.0ms256×body80valid
3.0ms32×body80invalid

simplify121.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.3b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (* l l) Om)
6.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite41.0ms

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*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (* l l) Om)
136.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
379.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* 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*)))))

simplify126.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010041621
148961448
250021448

prune291.0ms

Filtered
75 candidates to 115 candidates (-53.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh000
Picked101
Done000
Total10511116

Merged error: 22.9b

Counts
116 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) 2.0))
6.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.4b
(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
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))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms
(* (* (* 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*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
45.0ms
(* n (pow (/ l Om) 2.0))
153.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
390.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s
(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
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010711765
150011602

prune298.0ms

Filtered
87 candidates to 131 candidates (-50.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1247131
Fresh4610
Picked101
Done000
Total12913142

Merged error: 22.1b

Counts
142 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) 2.0))
6.3b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.4b
(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
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*))
10.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
45.0ms
(* n (pow (/ l Om) 2.0))
382.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
139.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s
(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
011361922
150011732

prune324.0ms

Filtered
86 candidates to 141 candidates (-64.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New13110141
Fresh4812
Picked101
Done000
Total13618154

Merged error: 17.9b

Counts
154 → 18

localize29.0ms

Local error

Found 4 expressions with local error:

13.8b
(cbrt (/ l Om))
13.8b
(cbrt (/ l Om))
13.8b
(cbrt (/ l Om))
18.4b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×pow1
16×associate-*r/
8×pow-prod-down
6×sqrt-div
5×flip3-- sqrt-pow1 flip--
4×add-exp-log frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 86
Calls
4 calls:
3.0ms
(cbrt (/ l Om))
3.0ms
(cbrt (/ l Om))
3.0ms
(cbrt (/ l Om))
12.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
13.0ms
(cbrt (/ l Om))
13.0ms
(cbrt (/ l Om))
13.0ms
(cbrt (/ l Om))
2.1s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

simplify75.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06291155
125151107
250011095

prune226.0ms

Filtered
83 candidates to 98 candidates (-18.1%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New95398
Fresh51217
Picked011
Done000
Total10016116

Merged error: 17.3b

Counts
116 → 16

regimes1.3s

bsearch3.0ms

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