Details

Time bar (total: 15.1s)

sample54.0ms

Algorithm
intervals
Results
13.0ms232×body80nan
13.0ms116×body160valid
8.0ms140×body80valid

simplify2.0s

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: 12.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite81.0ms

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:
4.0ms
(pow (/ Om Omc) 2.0)
41.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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)))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ Om Omc) 2.0)
226.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
334.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.6s

Counts
142 → 142
Iterations

Useful iterations: 3 (764.0ms)

IterNodesCost
03083657
16363542
214993367
348273355
done50003355

prune568.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.0b

localize21.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log sqrt-pow1 pow1/2 sqrt-div add-cbrt-cube add-log-exp sqr-pow
2×flip3-+ flip-+ div-inv
Counts
4 → 90
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
7.0ms
(sqrt (pow (/ Om Omc) 2.0))

series898.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
263.0ms
(sqrt (pow (/ Om Omc) 2.0))
271.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify913.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
01751610
13681486
28641454
327391454
done50001454

prune589.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize24.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log sqrt-pow1 pow1/2 sqrt-div add-cbrt-cube add-log-exp sqr-pow
2×flip3-+ flip-+ div-inv
Counts
4 → 90
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
7.0ms
(sqrt (pow (/ Om Omc) 2.0))

series893.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
264.0ms
(sqrt (pow (/ Om Omc) 2.0))
265.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify1.1s

Counts
102 → 102
Iterations

Useful iterations: 2 (284.0ms)

IterNodesCost
01751610
13681486
28641454
327391454
done50001454

prune637.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.1b
(sqrt (pow (/ Om Omc) 2.0))
16.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
30×add-sqr-sqrt unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
8×rem-sqrt-square
6×cbrt-prod
4×pow1 add-exp-log cbrt-div add-cbrt-cube add-log-exp sqr-pow
2×sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+ div-inv
Counts
4 → 86
Calls
4 calls:
6.0ms
(sqrt (pow (/ Om Omc) 2.0))
6.0ms
(sqrt (pow (/ Om Omc) 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))))

series1.0s

Counts
4 → 12
Calls
4 calls:
271.0ms
(sqrt (pow (/ Om Omc) 2.0))
268.0ms
(sqrt (pow (/ Om Omc) 2.0))
242.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
247.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: 3 (340.0ms)

IterNodesCost
01761616
13731530
28831472
330271462
done50001462

prune653.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 12.0b

regimes679.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 10.0b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample1.6s

Algorithm
intervals
Results
453.0ms8094×body80nan
441.0ms3849×body160valid
239.0ms4151×body80valid