Details

Time bar (total: 38.1s)

sample439.0ms

Algorithm
intervals
Results
49.0ms495×body80nan
28.0ms289×body80valid

simplify121.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune9.0ms

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: 32.2b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b
(/ (* l l) Om)
19.9b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

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:
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms
(/ (* l l) Om)
13.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.0s

Counts
4 → 12
Calls
4 calls:
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
413.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms
(/ (* l l) Om)
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify122.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09371544
147641385
250011385

prune755.0ms

Filtered
115 candidates to 75 candidates (65.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10213115
Fresh000
Picked101
Done000
Total10313116

Merged error: 20.9b

Counts
116 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
7.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.9b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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))
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(* (* 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*)))))

series9.2s

Counts
4 → 12
Calls
4 calls:
135.0ms
(* n (pow (/ l Om) 2.0))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
409.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09871668
150011508

prune777.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1265131
Fresh4812
Picked101
Done000
Total13113144

Merged error: 19.0b

Counts
144 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- t (* 2.0 (* l (/ l Om))))
0.1b
(* l (/ l Om))
7.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
18.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
20×add-sqr-sqrt
18×add-exp-log associate-*r* add-cbrt-cube
15×*-un-lft-identity
13×add-cube-cbrt pow-prod-down
10×times-frac
8×prod-exp cbrt-unprod
6×add-log-exp
5×sub-neg associate-*r/
4×distribute-rgt-in distribute-lft-in sqrt-pow1 associate-*l* associate--l+
3×flip3-- flip--
2×sqrt-div *-commutative unswap-sqr
1×cbrt-undiv pow1/2 diff-log div-exp sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
3.0ms
(- t (* 2.0 (* l (/ l Om))))
7.0ms
(* l (/ l Om))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
11.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
47.0ms
(- t (* 2.0 (* l (/ l Om))))
23.0ms
(* l (/ l Om))
132.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0))
1.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) 0)))

simplify120.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
0513740
12772628
25001623

prune541.0ms

Filtered
104 candidates to 65 candidates (62.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New995104
Fresh4812
Picked011
Done000
Total10314117

Merged error: 19.0b

Counts
117 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
7.2b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.9b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite51.0ms

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

series9.2s

Counts
4 → 12
Calls
4 calls:
146.0ms
(* n (pow (/ l Om) 2.0))
1.8s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
423.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify42.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010521826
150011638

prune710.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1356141
Fresh3912
Picked011
Done101
Total13916155

Merged error: 15.8b

Counts
155 → 16

regimes1.3s

Accuracy

2.5% (12.5b remaining)

Error of 31.5b against oracle of 19.1b and baseline of 31.9b

bsearch412.0ms

Steps
ItersRangePoint
8
3.6478999796003252e+174
2.7330236319169843e+178
5.025940990514969e+174
7
2.3341742417101446e-123
4.4741154001161504e-122
2.4794868703323314e-122
9
-4.805612024424144e-303
3.5507366646130136e-307
1.7123231787798296e-308

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05470
15470

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.4s15120×body80nan
877.0ms9233×body80valid

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