Details

Time bar (total: 26.2s)

sample135.0ms

Algorithm
intervals
Results
51.0ms482×body80nan
27.0ms287×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02128
14928
214928
356928
4281928
done500028

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.2b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.1b
(/ (* l l) Om)
8.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite49.0ms

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:
15.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms
(/ (* l l) Om)
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(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:
139.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.0ms
(/ (* l l) Om)
387.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.4s

Counts
115 → 115
Iterations

Useful iterations: 2 (624.0ms)

IterNodesCost
03393357
19963108
243172739
done50002739

prune317.0ms

Filtered
76 candidates to 115 candidates (-51.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10015115
Fresh000
Picked101
Done000
Total10115116

Merged error: 21.6b

Counts
116 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
6.2b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite54.0ms

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))
14.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms
(* (* (* 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*)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
48.0ms
(* n (pow (/ l Om) 2.0))
143.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
394.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

simplify1.5s

Counts
131 → 131
Iterations

Useful iterations: 2 (753.0ms)

IterNodesCost
03783628
110683351
243263000
done50003000

prune350.0ms

Filtered
89 candidates to 131 candidates (-47.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1247131
Fresh7714
Picked101
Done000
Total13214146

Merged error: 19.2b

Counts
146 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

4.9b
(* n (pow (/ l Om) (/ 2.0 2)))
6.2b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
16.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×pow1 add-sqr-sqrt associate-*r*
24×add-cbrt-cube
22×associate-*r/
20×pow-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 associate--l+ add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
12.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
18.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
12.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
53.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
140.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
393.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
2.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.9s

Counts
148 → 148
Iterations

Useful iterations: 2 (860.0ms)

IterNodesCost
04255240
112424172
248093709
done50003709

prune394.0ms

Filtered
90 candidates to 148 candidates (-64.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1453148
Fresh11213
Picked101
Done000
Total14715162

Merged error: 18.3b

Counts
162 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

4.9b
(* n (pow (/ l Om) (/ 2.0 2)))
5.6b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
8.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
16.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×unpow-prod-down associate-*r/
29×add-exp-log
25×*-un-lft-identity associate-*r*
23×pow1 add-cube-cbrt
21×associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
8×frac-sub cbrt-unprod unswap-sqr
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 pow-exp associate--l+ add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
9.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
12.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
16.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
12.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
53.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
135.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
393.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
2.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify1.6s

Counts
148 → 148
Iterations

Useful iterations: 2 (816.0ms)

IterNodesCost
04394678
112054364
246553593
done50003593

prune376.0ms

Filtered
108 candidates to 148 candidates (-37.0%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1453148
Fresh11314
Picked011
Done000
Total14617163

Merged error: 18.3b

Counts
163 → 17

regimes1.6s

Accuracy

17.2% (7.2b remaining)

Error of 29.3b against oracle of 22.1b and baseline of 30.8b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
043164
159127
done59127

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s15062×body80nan
902.0ms9219×body80valid

Profiling

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