Details

Time bar (total: 13.2s)

sample62.0ms

Algorithm
intervals
Results
16.0ms111×body160valid
15.0ms251×body80nan
9.0ms145×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
424219
573019
6275919
done500119

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
3.0ms
(pow (/ t l) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
29.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
61.0ms
(pow (/ t l) 2.0)
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
322.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify679.0ms

Counts
118 → 118
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
03522388
16972272
217712160
done50012160

prune458.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
43.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series588.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ t l) 2.0)
324.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
18.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify674.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (229.0ms)

IterNodesCost
03384611
16254260
216314140
done50004140

prune615.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.7b
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div sqrt-prod
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 flip-+
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×asin-acos pow1/2
Counts
4 → 54
Calls
4 calls:
0.0ms
(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
3.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
252.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
248.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.4s

Counts
66 → 66
Iterations

Useful iterations: 3 (392.0ms)

IterNodesCost
01531587
13261514
29601375
347471337
done50001337

prune394.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize35.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (pow (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 4))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
6×cbrt-div sqrt-prod
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
3×flip3-+ flip-+
1×sqr-pow
Counts
4 → 60
Calls
4 calls:
5.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 4))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
273.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 4))
246.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
438.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (337.0ms)

IterNodesCost
01181551
12541477
27471361
337801238
done50001238

prune500.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

regimes742.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
12021
done2021

end0.0ms

sample1.7s

Algorithm
intervals
Results
489.0ms8170×body80nan
460.0ms3852×body160valid
252.0ms4148×body80valid