Details

Time bar (total: 7.2s)

sample84.0ms

Algorithm
intervals
Results
22.0ms237×body80nan
21.0ms114×body160valid
13.0ms142×body80valid

simplify74.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
0494419
1494419

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.7b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
10.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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:
5.0ms
(pow (/ t l) 2.0)
12.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ t l) 2.0)
95.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
140.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050323363

prune417.0ms

Filtered
114 candidates to 142 candidates (-24.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1357142
Fresh000
Picked011
Done000
Total1358143

Merged error: 11.6b

Counts
143 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 sqrt-div flip-+
2×sqrt-pow1
1×frac-times pow1/2 associate-*r/ pow-prod-down associate-*l/ sqrt-prod
Counts
4 → 53
Calls
4 calls:
23.0ms
(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (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))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
66.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049281160
149281160

prune281.0ms

Filtered
59 candidates to 65 candidates (-10.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New64165
Fresh066
Picked011
Done011
Total64973

Merged error: 11.6b

Counts
73 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
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))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series229.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
49.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049421114
149421114

prune372.0ms

Filtered
60 candidates to 68 candidates (-13.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New67168
Fresh066
Picked011
Done112
Total68977

Merged error: 11.6b

Counts
77 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

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))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
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))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
49.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
67.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049421109
149421109

prune408.0ms

Filtered
60 candidates to 70 candidates (-16.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New70070
Fresh066
Picked011
Done022
Total70979

Merged error: 11.6b

Counts
79 → 9

regimes1.5s

Accuracy

0% (0.2b remaining)

Error of 10.4b against oracle of 10.2b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02857
12857

end0.0ms

sample2.6s

Algorithm
intervals
Results
732.0ms8095×body80nan
692.0ms3786×body160valid
382.0ms4214×body80valid

Profiling

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