Details

Time bar (total: 22.8s)

sample114.0ms

Algorithm
intervals
Results
35.0ms128×body160valid
23.0ms215×body80nan
15.0ms128×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
426519
579819
6301619
done500119

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite87.0ms

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:
6.0ms
(pow (/ Om Omc) 2.0)
9.0ms
(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))))))
64.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series731.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (/ Om Omc) 2.0)
85.0ms
(pow (/ t l) 2.0)
29.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
516.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.5s

Counts
118 → 118
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03522388
16932272
214382160
339292150
done50012144

prune611.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ -1 (* l (/ -1 t)))
0.3b
(pow (/ -1 (* l (/ -1 t))) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
34×times-frac
30×sqrt-prod
27×*-un-lft-identity
23×add-exp-log
21×add-cube-cbrt
14×unpow-prod-down
13×add-cbrt-cube
12×difference-of-squares
8×div-exp
6×pow1
4×cbrt-undiv pow-exp prod-exp associate-/r/ add-log-exp sqr-pow
3×pow-unpow div-inv associate-/l* distribute-lft-out--
2×rem-sqrt-square associate-*r/ cbrt-unprod
1×pow-to-exp asin-acos pow-pow frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div clear-num associate-/r* flip-+
Counts
4 → 99
Calls
4 calls:
11.0ms
(/ -1 (* l (/ -1 t)))
13.0ms
(pow (/ -1 (* l (/ -1 t))) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
48.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ -1 (* l (/ -1 t)))
80.0ms
(pow (/ -1 (* l (/ -1 t))) 2.0)
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
391.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

simplify1.5s

Counts
111 → 111
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03002717
16242575
215101934
done50001926

prune506.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
26.9b
(cbrt (pow (/ t l) 2.0))
26.9b
(cbrt (pow (/ t l) 2.0))
26.9b
(cbrt (pow (/ t l) 2.0))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 117
Calls
4 calls:
82.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
8.0ms
(cbrt (pow (/ t l) 2.0))
9.0ms
(cbrt (pow (/ t l) 2.0))
9.0ms
(cbrt (pow (/ t l) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
439.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
346.0ms
(cbrt (pow (/ t l) 2.0))
305.0ms
(cbrt (pow (/ t l) 2.0))
377.0ms
(cbrt (pow (/ t l) 2.0))

simplify1.5s

Counts
129 → 129
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02694003
15163851
210282921
326082705
done50012704

prune803.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

localize41.0ms

Local error

Found 4 expressions with local error:

26.9b
(cbrt (pow (/ t l) 2.0))
26.9b
(cbrt (pow (/ t l) 2.0))
26.9b
(cbrt (pow (/ t l) 2.0))
26.9b
(cbrt (pow (/ t l) 2.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log pow1/3 add-cbrt-cube div-inv add-log-exp sqr-pow
Counts
4 → 100
Calls
4 calls:
8.0ms
(cbrt (pow (/ t l) 2.0))
9.0ms
(cbrt (pow (/ t l) 2.0))
8.0ms
(cbrt (pow (/ t l) 2.0))
8.0ms
(cbrt (pow (/ t l) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
345.0ms
(cbrt (pow (/ t l) 2.0))
359.0ms
(cbrt (pow (/ t l) 2.0))
363.0ms
(cbrt (pow (/ t l) 2.0))
393.0ms
(cbrt (pow (/ t l) 2.0))

simplify1.3s

Counts
112 → 112
Iterations

Useful iterations: 3 (214.0ms)

IterNodesCost
01211964
12351912
24321864
39601852
423971852
done50001852

prune904.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.5b

regimes815.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.3s7919×body80nan
1.1s3788×body160valid
530.0ms4212×body80valid