Details

Time bar (total: 16.6s)

sample188.0ms

Algorithm
intervals
Results
45.0ms447×body80nan
27.0ms294×body80valid

simplify116.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.6b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.7b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.5b
(/ (* l l) Om)
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite39.0ms

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

series2.5s

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
493.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
3.0ms
(/ (* l l) Om)
1.9s
(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
250011448

prune282.0ms

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: 24.7b

Counts
116 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b
(* n (pow (/ l Om) 2.0))
6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.7b
(* (* (* 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*)))))

rewrite45.0ms

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

series2.4s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* n (pow (/ l Om) 2.0))
126.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
347.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010711769
150021602

prune296.0ms

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

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b
(* n (pow (/ l Om) 2.0))
6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.7b
(* (* 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*))))))

rewrite46.0ms

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))
10.0ms
(* (* 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*))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* n (pow (/ l Om) 2.0))
128.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
353.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011361922
150011732

prune288.0ms

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

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1374141
Fresh21012
Picked011
Done000
Total13915154

Merged error: 18.7b

Counts
154 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (pow (/ l Om) 2.0) (- U U*))
6.6b
(* n (* (pow (/ l Om) 2.0) (- U U*)))
8.7b
(* (* (* 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*))))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
34×associate-*r/
25×pow1 add-sqr-sqrt
21×associate-*l*
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
14×distribute-rgt-in distribute-lft-in
13×pow-prod-down
12×flip3-- flip--
10×sub-neg times-frac cbrt-unprod
9×associate-*r*
8×frac-sub
6×sqrt-div
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 → 129
Calls
4 calls:
10.0ms
(* (pow (/ l Om) 2.0) (- U U*))
10.0ms
(* 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*)))))
9.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (pow (/ l Om) 2.0) (- U U*))
126.0ms
(* n (* (pow (/ l Om) 2.0) (- U U*)))
356.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* 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*))))))

simplify130.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011041912
148931718
250011718

prune228.0ms

Filtered
91 candidates to 141 candidates (-54.9%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1383141
Fresh21113
Picked101
Done011
Total14115156

Merged error: 18.4b

Counts
156 → 15

regimes1.2s

Accuracy

30.3% (8.7b remaining)

Error of 28.0b against oracle of 19.3b and baseline of 31.8b

bsearch107.0ms

Steps
ItersRangePoint
8
6.620563442974465e-300
1.8132366500734473e-295
6.792569253522237e-300
6
-1.7567292826230496e-210
-1.764478145044159e-211
-9.136797103304265e-211

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04438
14438

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s14732×body80nan
861.0ms9228×body80valid

Profiling

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