Details

Time bar (total: 39.1s)

sample68.0ms

Algorithm
intervals
Results
19.0ms121×body160valid
18.0ms262×body80nan
9.0ms135×body80valid

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5437110
6500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.9b

Counts
2 → 1

localize14.0ms

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))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
142×add-sqr-sqrt
139×*-un-lft-identity
102×times-frac
48×difference-of-squares
46×sqrt-prod
43×add-cube-cbrt
37×unpow-prod-down
36×distribute-lft-out
18×sqrt-div associate-*l*
16×associate-/l*
13×sqr-pow
12×distribute-lft-out--
10×associate-/r*
9×add-exp-log
6×pow1 add-cbrt-cube
4×associate-/r/ associate-/l/ add-log-exp
3×pow-unpow div-inv
2×rem-sqrt-square flip3-- frac-2neg flip3-+ div-exp pow-exp clear-num flip-- flip-+
1×cbrt-undiv pow-to-exp asin-acos pow-pow sqrt-pow1 pow1/2 div-sub
Counts
4 → 181
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
23.0ms
(/ (- 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))))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
323.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06782581
120802485
250012472

prune505.0ms

Filtered
193 candidates to 126 candidates (65.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1858193
Fresh000
Picked101
Done000
Total1868194

Merged error: 10.8b

Counts
194 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.5b
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
1363×add-sqr-sqrt
1195×*-un-lft-identity
1097×times-frac
1001×unpow-prod-down
684×difference-of-squares
672×associate-*l*
498×sqrt-prod
457×sqr-pow
336×distribute-lft-out
280×associate-*r*
219×add-cube-cbrt
155×pow-unpow
152×difference-cubes
76×distribute-lft-out--
57×unswap-sqr
56×*-commutative
54×associate-/l*
50×sqrt-div
36×associate-/r*
16×associate-/r/
12×add-exp-log flip3-+ flip-+
9×add-cbrt-cube
8×frac-times
6×pow1
4×associate-*r/ associate-*l/ associate-/l/ add-log-exp
3×rem-sqrt-square div-exp div-inv
2×cbrt-undiv flip3-- frac-2neg pow-exp clear-num flip--
1×pow-to-exp asin-acos pow-pow sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod
Counts
4 → 1152
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
86.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
120.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ t l) 2.0)
726.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
41.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
906.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify389.0ms

Algorithm
egg-herbie
Counts
1164 → 1164
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0302837066
1500135997

prune3.7s

Filtered
1164 candidates to 588 candidates (50.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New116221164
Fresh257
Picked011
Done000
Total116481172

Merged error: 10.8b

Counts
1172 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.5b
(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
5522×sqrt-prod
4904×add-sqr-sqrt
3432×unpow-prod-down
3061×associate-/l*
3050×*-un-lft-identity
2769×sqrt-div
2455×frac-times
2376×difference-of-squares
1650×associate-*l*
1584×sqr-pow
1432×associate-/r*
1412×times-frac
838×associate-*r*
745×add-cube-cbrt
624×distribute-lft-out
528×difference-cubes pow-unpow
264×distribute-lft-out--
258×unswap-sqr
204×associate-/l/
103×clear-num
102×flip3-- frac-2neg flip--
75×*-commutative
59×associate-*l/
45×associate-*r/
38×rem-sqrt-square
10×associate-/r/
9×pow1 flip3-+ flip-+
4×add-exp-log sqrt-pow1 add-cbrt-cube add-log-exp
3×pow1/2
2×un-div-inv div-inv
1×asin-acos pow-prod-down
Counts
4 → 3599
Calls
4 calls:
1.0ms
(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.9s
(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
48.0ms
(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
942.0ms
(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
194.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
191.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.8s

Algorithm
egg-herbie
Counts
3611 → 3611
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
08741187749

prune21.3s

Filtered
3611 candidates to 2236 candidates (61.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New360923611
Fresh246
Picked011
Done011
Total361183619

Merged error: 10.8b

Counts
3619 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

9.7b
(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))))
15.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt distribute-lft-out
6×cbrt-div
5×pow1 sqrt-prod
4×add-exp-log flip3-+ associate-*l* add-cbrt-cube flip-+ add-log-exp
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series951.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
254.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
255.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
256.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify81.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0186687
1606647
22633635
35003632

prune505.0ms

Filtered
74 candidates to 60 candidates (81.1%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New74074
Fresh055
Picked011
Done022
Total74882

Merged error: 10.8b

Counts
82 → 8

regimes896.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03021
13021

end0.0ms

sample1.9s

Algorithm
intervals
Results
583.0ms8034×body80nan
543.0ms3815×body160valid
303.0ms4185×body80valid