Details

Time bar (total: 15.0s)

sample62.0ms

Algorithm
intervals
Results
19.0ms251×body80nan
13.0ms111×body160valid
9.0ms145×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
424219
572919
6267019
done500019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize14.0ms

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)))))

rewrite42.0ms

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:
3.0ms
(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))))))
28.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ Om Omc) 2.0)
64.0ms
(pow (/ t l) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
320.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts
118 → 118
Iterations

Useful iterations: 3 (680.0ms)

IterNodesCost
03522388
16972272
214962160
343702150
done50002150

prune472.0ms

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))))

rewrite55.0ms

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)
42.0ms
(/ (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))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ t l) 2.0)
320.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts
163 → 163
Iterations

Useful iterations: 3 (729.0ms)

IterNodesCost
03384611
16254260
214034140
346714132
done50004132

prune607.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize20.0ms

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)))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(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))))))))
242.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
247.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
247.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.4s

Counts
66 → 66
Iterations

Useful iterations: 3 (437.0ms)

IterNodesCost
01531587
13261514
29341375
344931337
done50001337

prune400.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize224.0ms

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))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series983.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 4))
238.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
238.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (325.0ms)

IterNodesCost
01181551
12541477
27081361
334371238
done50001238

prune497.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

regimes733.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
12021
done2021

end0.0ms

sample1.6s

Algorithm
intervals
Results
477.0ms8170×body80nan
451.0ms3852×body160valid
251.0ms4148×body80valid