Details

Time bar (total: 6.1s)

sample67.0ms

Algorithm
intervals
Results
20.0ms144×body160valid
15.0ms216×body80nan
11.0ms112×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5437110
6500110

prune4.0ms

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: 9.4b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(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))))))
8.9b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×sqrt-div
3×sqrt-prod div-inv
2×pow-to-exp unpow-prod-down associate-/r/ associate-/l/ sqr-pow
1×asin-acos flip3-- frac-2neg flip3-+ pow1/2 clear-num flip-- flip-+
Counts
4 → 16
Calls
4 calls:
2.0ms
(pow (/ Om Omc) 2.0)
2.0ms
(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))))))
5.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ Om Omc) 2.0)
62.0ms
(pow (/ t l) 2.0)
18.0ms
(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)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0334246
1905230
23920230
35001229

prune107.0ms

Filtered
28 candidates to 23 candidates (82.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New26228
Fresh000
Picked011
Done000
Total26329

Merged error: 9.4b

Counts
29 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(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)))))
0.5b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
2×flip3-+ associate-/r/ flip-+ div-inv associate-/l/
1×pow-to-exp unpow-prod-down asin-acos sqrt-undiv flip3-- frac-2neg pow1/2 clear-num flip-- sqr-pow
Counts
4 → 15
Calls
4 calls:
2.0ms
(pow (/ t l) 2.0)
6.0ms
(/ (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))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ t l) 2.0)
348.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
21.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
177.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0278249
1777240
23513240
35001240

prune113.0ms

Filtered
27 candidates to 23 candidates (85.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New26127
Fresh011
Picked011
Done011
Total26430

Merged error: 9.4b

Counts
30 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ 1 l) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))))))
8.9b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0))))))
14.7b
(* (pow t 2.0) (pow (/ 1 l) 2.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
5×sqrt-div sqr-pow
3×pow-to-exp sqrt-prod div-inv
2×unpow-prod-down associate-*r* associate-/r/ associate-/l/
1×asin-acos flip3-- pow-pow frac-2neg flip3-+ pow1/2 associate-*l* pow-prod-down prod-exp clear-num *-commutative flip-- flip-+ inv-pow unswap-sqr
Counts
4 → 21
Calls
4 calls:
2.0ms
(pow (/ 1 l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))))))
6.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0))))))
5.0ms
(* (pow t 2.0) (pow (/ 1 l) 2.0))

series832.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(pow (/ 1 l) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))))))
312.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0))))))
321.0ms
(* (pow t 2.0) (pow (/ 1 l) 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0451346
11229340
25001338

prune150.0ms

Filtered
33 candidates to 27 candidates (81.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New32133
Fresh101
Picked011
Done112
Total34337

Merged error: 9.4b

Counts
37 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))))))
8.9b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
21×sqr-pow
18×div-inv
14×associate-*r* pow-prod-down
12×pow-unpow
10×associate-*l*
7×unswap-sqr
6×swap-sqr
5×pow-to-exp unpow-prod-down sqrt-div *-commutative
3×prod-exp sqrt-prod
2×associate-/r/ pow-sqr pow-prod-up associate-/l/
1×pow2 asin-acos flip3-- frac-2neg flip3-+ pow1/2 clear-num flip-- flip-+
Counts
4 → 41
Calls
4 calls:
2.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))))))

series860.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ Om Omc) 2.0)
322.0ms
(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))))))
454.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0590642
12243596
25002591

prune209.0ms

Filtered
53 candidates to 39 candidates (73.6%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New52153
Fresh000
Picked011
Done022
Total52456

Merged error: 9.4b

Counts
56 → 4

regimes306.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01911
11911

end0.0ms

sample1.8s

Algorithm
intervals
Results
542.0ms7750×body80nan
537.0ms3823×body160valid
296.0ms4177×body80valid