Details

Time bar (total: 18.3s)

analyze2.4s

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

sample88.0ms

Algorithm
intervals
Results
28.0ms112×body160valid
18.0ms157×body80nan
17.0ms144×body80valid

simplify136.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (124.0ms)

IterNodesCost
0473329
1473329

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.0b

Counts
2 → 1

localize255.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite83.0ms

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:
10.0ms
(pow (/ t l) 2.0)
29.0ms
(/ (- 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))))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (/ t l) 2.0)
176.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
301.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify191.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (122.0ms)

IterNodesCost
049515132
149515132

prune918.0ms

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: 10.9b

Counts
143 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.5b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite61.0ms

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:
5.0ms
(pow (/ t l) 2.0)
32.0ms
(/ (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))))))
7.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(pow (/ t l) 2.0)
267.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
23.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify161.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049726432
149726432

prune899.0ms

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1630163
Fresh077
Picked011
Done000
Total1638171

Merged error: 10.9b

Counts
171 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.1b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
66×sqrt-prod
56×times-frac
42×*-un-lft-identity
30×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
8×pow1
6×rem-sqrt-square distribute-lft-out-- sqr-pow
4×add-exp-log sqrt-pow1 pow1/2 associate-/r/ add-cbrt-cube add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
2.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
42.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
233.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
257.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
052155174

prune1.2s

Filtered
100 candidates to 122 candidates (-22.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1175122
Fresh246
Picked101
Done011
Total12010130

Merged error: 10.9b

Counts
130 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt
93×sqrt-prod
84×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
8×pow1
7×rem-sqrt-square
6×associate-/r/
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 139
Calls
4 calls:
3.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
25.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series888.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
265.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
279.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
275.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify126.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
052156639

prune2.1s

Filtered
124 candidates to 151 candidates (-21.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1483151
Fresh178
Picked101
Done011
Total15011161

Merged error: 10.9b

Counts
161 → 11

regimes3.9s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03031
13031

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s3879×body160valid
687.0ms4682×body80nan
600.0ms4121×body80valid

Profiling

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