Details

Time bar (total: 9.5s)

analyze1.5s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
18.7%76.4%4.9%9
18.7%76.4%4.9%10
21.8%72.5%5.7%11
21.8%69.8%8.4%12
32.7%46.6%20.7%13
32.7%46.6%20.7%14

sample70.0ms

Algorithm
intervals
Results
24.0ms118×body160valid
14.0ms138×body80valid
14.0ms133×body80nan

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0487219
1487219

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 9.8b

Counts
2 → 1

localize19.0ms

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))))
0.8b
(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)))))

rewrite38.0ms

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 (/ Om Omc) 2.0)
13.0ms
(/ (- 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))))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
99.0ms
(/ (- 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))))))
146.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
049503354
149503354

prune436.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1348142
Fresh000
Picked101
Done000
Total1358143

Merged error: 9.7b

Counts
143 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
15.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series217.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
138.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
49.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify95.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049424128
149424128

prune420.0ms

Filtered
107 candidates to 163 candidates (-52.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1603163
Fresh257
Picked011
Done000
Total1629171

Merged error: 9.7b

Counts
171 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
3.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (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))))

series234.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
67.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
51.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049521254
149521254

prune310.0ms

Filtered
64 candidates to 84 candidates (-31.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New83184
Fresh167
Picked011
Done011
Total84993

Merged error: 9.7b

Counts
93 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(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))))))))
2.4b
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite10.0ms

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))))

series226.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(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))))))))
68.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
67.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify37.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
049741362
149741362

prune259.0ms

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

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New66066
Fresh066
Picked011
Done022
Total66975

Merged error: 9.7b

Counts
75 → 9

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01920
11920

end0.0ms

analyze1.5s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
18.7%76.4%4.9%9
18.7%76.4%4.9%10
21.8%72.5%5.7%11
21.8%69.8%8.4%12
32.7%46.6%20.7%13
32.7%46.6%20.7%14

sample2.0s

Algorithm
intervals
Results
762.0ms3826×body160valid
471.0ms4703×body80nan
403.0ms4174×body80valid

Profiling

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