Details

Time bar (total: 25.5s)

sample136.0ms

Algorithm
intervals
Results
44.0ms257×body80nan
27.0ms117×body160valid
18.0ms139×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310119
427719
5156119
done500119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(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))))))
1.0b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite204.0ms

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:
6.0ms
(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))))))
94.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
97.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series957.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ t l) 2.0)
26.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
334.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
501.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.5s

Counts
142 → 142
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03173657
17553534
224383369
done50003367

prune874.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.7b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
658×times-frac
647×sqrt-prod
560×add-sqr-sqrt
325×*-un-lft-identity
253×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
19×sqrt-div
14×associate-/r/
9×rem-sqrt-square flip3-+ flip-+
7×pow1 div-inv
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-pow1 pow1/2
1×asin-acos
Counts
4 → 385
Calls
4 calls:
1.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
134.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
20.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
39.0ms
(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
469.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
274.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
304.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify980.0ms

Counts
397 → 397
Iterations

Useful iterations: done (929.0ms)

IterNodesCost
087323423
1159720859
done500119606

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.5b

localize49.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
1008×sqrt-prod
678×times-frac
578×add-sqr-sqrt
338×*-un-lft-identity
266×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
21×sqrt-div
14×associate-/r/
12×rem-sqrt-square
10×flip3-+ flip-+
8×pow1
7×div-inv
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
Counts
4 → 412
Calls
4 calls:
153.0ms
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
800.0ms
(sqrt (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
300.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
320.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
300.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts
424 → 424
Iterations

Useful iterations: done (1.4s)

IterNodesCost
094325200
1125523130
2269922724
done500122723

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.5b

localize50.0ms

Local error

Found 4 expressions with local error:

9.7b
(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
14.0b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite443.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
90×cbrt-prod
81×times-frac
58×*-un-lft-identity
40×add-cube-cbrt
36×difference-of-squares
24×pow1
18×unpow-prod-down
15×cbrt-div sqrt-pow1
12×pow1/3
9×pow-prod-up distribute-lft-out-- sqr-pow
7×sqrt-div
6×pow-plus associate-/r/
5×frac-times pow-prod-down associate-*l/
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-*r/ pow-sqr flip-+ div-inv
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 148
Calls
4 calls:
321.0ms
(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
37.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
37.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
37.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
496.0ms
(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
510.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
518.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
496.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.6s

Counts
160 → 160
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02265516
14215249
29364735
330044687
done50014672

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.5b

regimes639.0ms

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.6b and baseline of 10.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s8004×body80nan
973.0ms3760×body160valid
615.0ms4240×body80valid