Details

Time bar (total: 12.5s)

sample89.0ms

Algorithm
intervals
Results
21.0ms126×body160valid
20.0ms232×body80nan
11.0ms130×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 8.2b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.6b
(/ (- 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))))))
6.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite39.0ms

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)
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))))))
16.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(pow (/ t l) 2.0)
94.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
137.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06621889
120991789
250021774

prune1.6s

Filtered
142 candidates to 114 candidates (19.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1339142
Fresh000
Picked101
Done000
Total1349143

Merged error: 8.1b

Counts
143 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 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))))))
7.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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)
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))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
133.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms
(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))))

simplify70.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06932519
123312342
250012330

prune1.5s

Filtered
163 candidates to 107 candidates (34.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1621163
Fresh178
Picked011
Done000
Total1639172

Merged error: 8.1b

Counts
172 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.4b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 133
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
16.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
145.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
148.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
146.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify124.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
05322819
112312727
242882718
350012695

prune1.9s

Filtered
145 candidates to 125 candidates (13.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh077
Picked011
Done011
Total1459154

Merged error: 8.1b

Counts
154 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

11.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.7b
(sqrt (pow (/ Om Omc) 2.0))
18.7b
(sqrt (pow (/ Om Omc) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
30×add-sqr-sqrt unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
8×rem-sqrt-square
6×cbrt-prod
4×pow1 add-exp-log cbrt-div add-cbrt-cube add-log-exp sqr-pow
2×sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+ div-inv
Counts
4 → 86
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(sqrt (pow (/ Om Omc) 2.0))
5.0ms
(sqrt (pow (/ Om Omc) 2.0))

series222.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
64.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms
(sqrt (pow (/ Om Omc) 2.0))
48.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0453810
11241778
25001762

prune1.5s

Filtered
98 candidates to 88 candidates (10.2%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New98098
Fresh066
Picked011
Done022
Total989107

Merged error: 8.1b

Counts
107 → 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
01911
11911

end0.0ms

sample2.5s

Algorithm
intervals
Results
701.0ms8069×body80nan
645.0ms3795×body160valid
372.0ms4205×body80valid

Profiling

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