Details

Time bar (total: 14.2s)

sample88.0ms

Algorithm
intervals
Results
24.0ms130×body160valid
22.0ms250×body80nan
11.0ms126×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
424219
572919
6265819
done500019

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.3b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
30×sqrt-prod
28×difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×associate-/r/ add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square flip3-+ div-exp pow-exp flip-+ associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 130
Calls
4 calls:
5.0ms
(pow (/ t l) 2.0)
14.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(pow (/ t l) 2.0)
102.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
150.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify894.0ms

Counts
142 → 142
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
03223666
16653538
215653367
done50003363

prune438.0ms

Filtered
114 candidates to 142 candidates (-24.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1366142
Fresh000
Picked011
Done000
Total1367143

Merged error: 11.3b

Counts
143 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
15.8b
(cbrt (/ t l))
15.8b
(cbrt (/ t l))
15.8b
(cbrt (/ t l))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
55×times-frac
43×*-un-lft-identity
39×cbrt-prod
37×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×cbrt-div pow1/3 distribute-lft-out-- sqr-pow
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 108
Calls
4 calls:
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
3.0ms
(cbrt (/ t l))
3.0ms
(cbrt (/ t l))
3.0ms
(cbrt (/ t l))

series188.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
13.0ms
(cbrt (/ t l))
17.0ms
(cbrt (/ t l))
13.0ms
(cbrt (/ t l))

simplify1.2s

Counts
120 → 120
Iterations

Useful iterations: 3 (425.0ms)

IterNodesCost
02353122
14162973
28812854
328192821
done50012821

prune363.0ms

Filtered
100 candidates to 120 candidates (-20.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1200120
Fresh055
Picked011
Done011
Total1207127

Merged error: 11.3b

Counts
127 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.9b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
66×sqrt-prod
56×times-frac
42×*-un-lft-identity
30×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
8×pow1
6×rem-sqrt-square distribute-lft-out-- sqr-pow
4×add-exp-log sqrt-pow1 pow1/2 associate-/r/ add-cbrt-cube add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
16.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
38.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
144.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
145.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify864.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
02053718
13903490
28373350
324813350
done50003350

prune619.0ms

Filtered
100 candidates to 122 candidates (-22.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1193122
Fresh044
Picked101
Done112
Total1218129

Merged error: 11.2b

Counts
129 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.9b
(sqrt (asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
39×sqrt-prod
28×times-frac
25×*-un-lft-identity
19×add-cube-cbrt
12×difference-of-squares
8×pow1
6×unpow-prod-down
5×rem-sqrt-square
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
3×sqrt-div distribute-lft-out-- sqr-pow
2×flip3-+ associate-/r/ flip-+
1×div-inv
Counts
4 → 83
Calls
4 calls:
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms
(sqrt (asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
38.0ms
(sqrt (asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
145.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
50.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.4s

Counts
95 → 95
Iterations

Useful iterations: 3 (656.0ms)

IterNodesCost
02652639
15182439
211722328
337952323
done50002323

prune439.0ms

Filtered
78 candidates to 95 candidates (-21.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New94195
Fresh066
Picked011
Done011
Total949103

Merged error: 11.2b

Counts
103 → 9

regimes1.9s

Accuracy

0% (0.3b remaining)

Error of 10.7b against oracle of 10.4b and baseline of 10.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12332
done2332

end0.0ms

sample2.6s

Algorithm
intervals
Results
721.0ms3818×body160valid
691.0ms7935×body80nan
375.0ms4182×body80valid

Profiling

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