Details

Time bar (total: 7.7s)

sample100.0ms

Algorithm
intervals
Results
27.0ms287×body80nan
21.0ms111×body160valid
13.0ms145×body80valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0494419
1494419

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.2b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite33.0ms

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)
11.0ms
(/ (- 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))))))
11.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
92.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
134.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049863355
149863355

prune413.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1366142
Fresh000
Picked011
Done000
Total1367143

Merged error: 10.2b

Counts
143 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
22×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac
10×add-exp-log
7×pow1
6×pow-unpow
4×pow-exp add-cbrt-cube add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow sqrt-div div-exp div-inv sqr-pow
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 79
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
12.0ms
(pow (/ Om Omc) 2.0)
14.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
46.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
051721118

prune234.0ms

Filtered
69 candidates to 91 candidates (-31.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New90191
Fresh055
Picked011
Done011
Total90898

Merged error: 10.2b

Counts
98 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
126×sqrt-prod
117×add-sqr-sqrt
80×cbrt-div
72×*-un-lft-identity
71×cbrt-prod
60×add-cube-cbrt
50×associate-/r/
40×flip3-+ flip-+
24×frac-times difference-of-squares
12×unpow-prod-down associate-*r/ associate-*l/
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 180
Calls
4 calls:
27.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
64.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
67.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify92.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0499510323
1499510323

prune1.2s

Filtered
161 candidates to 192 candidates (-19.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1920192
Fresh055
Picked011
Done022
Total1928200

Merged error: 10.2b

Counts
200 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(asin (/ (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))))))))
2.0b
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite9.0ms

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:
1.0ms
(asin (/ (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)))))
2.0ms
(cbrt (+ 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:
23.0ms
(asin (/ (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))))))))
63.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
64.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
62.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify36.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050851362

prune251.0ms

Filtered
61 candidates to 66 candidates (-8.2%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New66066
Fresh044
Picked011
Done033
Total66874

Merged error: 10.2b

Counts
74 → 8

regimes1.4s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01819
11819

end0.0ms

sample2.7s

Algorithm
intervals
Results
763.0ms3850×body160valid
755.0ms7934×body80nan
398.0ms4150×body80valid

Profiling

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