Details

Time bar (total: 7.8s)

sample94.0ms

Algorithm
intervals
Results
24.0ms125×body160valid
23.0ms241×body80nan
17.0ms131×body80valid

simplify129.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune5.0ms

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: 8.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(/ (- 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))))))
7.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite38.0ms

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)
15.0ms
(/ (- 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))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ t l) 2.0)
97.0ms
(/ (- 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))))))
138.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06621889
120991789
250021774

prune444.0ms

Filtered
142 candidates to 114 candidates (19.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New13210142
Fresh000
Picked101
Done000
Total13310143

Merged error: 8.5b

Counts
143 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.3b
(/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))
0.6b
(asin (sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))))
7.6b
(sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
384×times-frac
335×add-sqr-sqrt
202×*-un-lft-identity
158×add-cube-cbrt
95×sqrt-prod
84×difference-of-squares
55×unpow-prod-down
30×associate-/r*
22×sqr-pow
21×distribute-lft-out--
18×add-exp-log
16×associate-/r/
10×div-inv
9×add-cbrt-cube
8×pow1 div-exp
7×flip3-- flip--
5×rem-sqrt-square
4×add-log-exp
3×cbrt-undiv pow-unpow sqrt-pow1 associate-/l*
2×rec-exp pow-flip 1-exp pow-exp inv-pow
1×pow-to-exp asin-acos pow-pow frac-2neg pow1/2 sqrt-div clear-num
Counts
4 → 292
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
15.0ms
(/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))
1.0ms
(asin (sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))))
22.0ms
(sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0)))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
110.0ms
(/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))
14.0ms
(asin (sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0))))))
143.0ms
(sqrt (/ 1 (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- 1.0 (pow (/ Om Omc) 2.0)))))

simplify137.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011375563
149875218
250015218

prune863.0ms

Filtered
304 candidates to 191 candidates (37.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3040304
Fresh099
Picked011
Done000
Total30410314

Merged error: 8.5b

Counts
314 → 10

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)))))
0.6b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

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:
4.0ms
(pow (/ t l) 2.0)
14.0ms
(/ (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))))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
134.0ms
(/ (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))))

simplify69.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06932519
123312342
250012330

prune422.0ms

Filtered
163 candidates to 107 candidates (34.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1603163
Fresh448
Picked101
Done011
Total1658173

Merged error: 8.5b

Counts
173 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-prod
104×add-sqr-sqrt
78×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
10×pow1 rem-sqrt-square sqrt-div
9×sqrt-pow1
6×distribute-lft-out-- sqr-pow
5×pow1/2
4×add-exp-log flip3-+ associate-/r/ add-cbrt-cube flip-+ add-log-exp
3×pow-flip
2×div-inv
1×inv-pow
Counts
4 → 140
Calls
4 calls:
8.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (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))))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
130.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
49.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06052292
116512239
250012188

prune490.0ms

Filtered
152 candidates to 101 candidates (33.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1511152
Fresh156
Picked011
Done011
Total1528160

Merged error: 8.5b

Counts
160 → 8

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02211
12211

end0.0ms

sample2.5s

Algorithm
intervals
Results
762.0ms7939×body80nan
726.0ms3781×body160valid
402.0ms4219×body80valid

Profiling

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