Details

Time bar (total: 12.3s)

sample92.0ms

Algorithm
intervals
Results
25.0ms130×body160valid
23.0ms250×body80nan
12.0ms126×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310119
425519
584119
6307319
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

localize15.0ms

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)))))

rewrite45.0ms

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))))))
19.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(pow (/ t l) 2.0)
107.0ms
(/ (- 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))))))
152.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify465.0ms

Counts
142 → 142
Iterations

Useful iterations: done (455.0ms)

IterNodesCost
03223666
16693543
216873375
done50003367

prune455.0ms

Filtered
116 candidates to 142 candidates (-22.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1366142
Fresh000
Picked011
Done000
Total1367143

Merged error: 11.3b

Counts
143 → 7

localize20.0ms

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))

rewrite30.0ms

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:
16.0ms
(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))

series196.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(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))))))
14.0ms
(cbrt (/ t l))
14.0ms
(cbrt (/ t l))
14.0ms
(cbrt (/ t l))

simplify1.1s

Counts
120 → 120
Iterations

Useful iterations: 3 (268.0ms)

IterNodesCost
02353122
14182976
29262857
330302821
done50002821

prune368.0ms

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)))))

rewrite39.0ms

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)))))))
17.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
40.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
151.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
152.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify641.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
02053718
13903490
28633350
324063350
done50003350

prune630.0ms

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

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
14.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series282.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
36.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
151.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
56.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify925.0ms

Counts
95 → 95
Iterations

Useful iterations: 3 (371.0ms)

IterNodesCost
02782639
15402445
212872328
339642323
done50002323

prune462.0ms

Filtered
79 candidates to 95 candidates (-20.3%)
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

sample2.7s

Algorithm
intervals
Results
752.0ms3818×body160valid
713.0ms7935×body80nan
389.0ms4182×body80valid

Profiling

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