Details

Time bar (total: 34.2s)

sample9.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 6.829834%

Guaranteed chance to sample good point: 0.157222%

Results
43.0ms446×body80nan
24.0ms256×body80valid
3.0ms31×body80invalid

simplify123.0ms

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: 33.5b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
8.5b
(/ (* l l) Om)
20.8b
(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
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:
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.0ms
(/ (* l l) Om)
9.0ms
(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:
122.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
342.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
3.0ms
(/ (* l l) Om)
1.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify366.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010041621
148961448
250011448

prune301.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10015115
Fresh000
Picked101
Done000
Total10115116

Merged error: 22.2b

Counts
116 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) 2.0))
5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(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:
8.0ms
(* n (pow (/ l Om) 2.0))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(* (* (* 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*)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* n (pow (/ l Om) 2.0))
123.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
344.0ms
(* (* (* 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*)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010711765
150011602

prune307.0ms

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

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1274131
Fresh31114
Picked011
Done000
Total13016146

Merged error: 21.5b

Counts
146 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

13.2b
(cbrt (/ l Om))
13.2b
(cbrt (/ l Om))
13.2b
(cbrt (/ l Om))
20.8b
(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*)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 85
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
11.0ms
(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*)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
12.0ms
(cbrt (/ l Om))
12.0ms
(cbrt (/ l Om))
12.0ms
(cbrt (/ l Om))
1.8s
(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*)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06111155
124871107
250021095

prune292.0ms

Filtered
83 candidates to 97 candidates (-16.9%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh01414
Picked011
Done011
Total9716113

Merged error: 21.5b

Counts
113 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) 2.0))
5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b
(/ (* l l) Om)
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite37.0ms

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:
8.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.0ms
(/ (* l l) Om)
10.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* n (pow (/ l Om) 2.0))
126.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
1.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify104.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09461106
143321032
250021032

prune201.0ms

Filtered
83 candidates to 118 candidates (-42.2%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1108118
Fresh5813
Picked101
Done112
Total11717134

Merged error: 17.4b

Counts
134 → 17

regimes1.6s

Accuracy

6.4% (11.6b remaining)

Error of 31.1b against oracle of 19.4b and baseline of 31.9b

bsearch372.0ms

Steps
ItersRangePoint
6
6.866326184056093e+190
5.2820533939337934e+191
1.2633370902589806e+191
7
1.3593792393874027e-56
5.804875834489461e-55
3.4992493273958607e-56
6
2.5301528446693064e-120
2.7875027563082076e-119
9.727724262613734e-120
9
-4.0800348380048156e-200
-2.53897245513157e-208
-3.625282788406271e-207
9
-5.46797666198994e+170
-5.57095105094058e+163
-1.1332115487758652e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07686
17686

end0.0ms

sample12.5s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 6.829834%

Guaranteed chance to sample good point: 0.157222%

Results
1.3s13484×body80nan
779.0ms8000×body80valid
126.0ms1217×body80invalid

Profiling

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