Details

Time bar (total: 11.3s)

sample75.0ms

Algorithm
intervals
Results
24.0ms286×body80nan
18.0ms118×body160valid
10.0ms138×body80valid

simplify131.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5437110
6500110

prune4.0ms

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: 12.1b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite66.0ms

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

series614.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ Om Omc) 2.0)
210.0ms
(/ (- 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)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06632579
120422485
250012472

prune482.0ms

Filtered
193 candidates to 126 candidates (34.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1876193
Fresh000
Picked101
Done000
Total1886194

Merged error: 12.0b

Counts
194 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0b
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
2318×sqrt-prod
1682×add-sqr-sqrt
1528×*-un-lft-identity
963×times-frac
742×sqrt-div
576×frac-times
562×associate-/l*
453×add-cube-cbrt
428×difference-of-squares
408×associate-/r*
352×distribute-lft-out
270×associate-*l*
263×swap-sqr
214×unpow-prod-down
139×distribute-lft-out--
107×sqr-pow
102×associate-/l/
94×associate-*r*
52×clear-num
51×flip3-- frac-2neg flip--
50×unswap-sqr
47×rem-sqrt-square
24×associate-*r/ associate-*l/
14×pow1
10×associate-/r/
8×sqrt-pow1
7×flip3-+ flip-+
6×add-exp-log add-cbrt-cube
5×div-inv
4×add-log-exp
3×pow1/2
2×un-div-inv *-commutative
1×cbrt-undiv pow2 sqrt-undiv pow-plus div-exp pow-prod-down pow-sqr pow-prod-up
Counts
4 → 1307
Calls
4 calls:
28.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
235.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series986.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
178.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
177.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
314.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify381.0ms

Algorithm
egg-herbie
Counts
1319 → 1319
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0344235603
1500134875

prune1.9s

Filtered
1319 candidates to 348 candidates (73.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New131721319
Fresh235
Picked011
Done000
Total131961325

Merged error: 12.0b

Counts
1325 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (* (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod
112×add-sqr-sqrt
104×sqrt-div
58×unswap-sqr
38×*-un-lft-identity
37×associate-*l*
30×flip3-+ flip-+
28×frac-times
19×rem-sqrt-square
18×associate-*r*
16×pow1 add-cube-cbrt
14×associate-*l/
11×sqrt-pow1 distribute-lft-out
8×associate-*r/
7×pow1/2 pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
2×*-commutative
Counts
4 → 161
Calls
4 calls:
56.0ms
(sqrt (* (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series843.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(sqrt (* (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
177.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06023558
117063529
250023447

prune825.0ms

Filtered
173 candidates to 105 candidates (39.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1730173
Fresh044
Picked011
Done011
Total1736179

Merged error: 12.0b

Counts
179 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite50.0ms

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))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series919.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
247.0ms
(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

prune407.0ms

Filtered
74 candidates to 60 candidates (18.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New74074
Fresh033
Picked011
Done022
Total74680

Merged error: 12.0b

Counts
80 → 6

regimes656.0ms

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
02123
12123

end0.0ms

sample2.0s

Algorithm
intervals
Results
745.0ms7903×body80nan
547.0ms3839×body160valid
290.0ms4161×body80valid