Details

Time bar (total: 9.4s)

sample77.0ms

Algorithm
intervals
Results
22.0ms124×body160valid
22.0ms251×body80nan
11.0ms132×body80valid

simplify130.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
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: 6.8b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.2b
(pow (/ t l) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.2b
(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×expm1-log1p-u associate-/r/ log1p-expm1-u 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 → 138
Calls
4 calls:
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
4.0ms
(pow (/ t l) 2.0)
15.0ms
(/ (- 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)))))

series740.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms
(pow (/ t l) 2.0)
208.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
450.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06641948
121061846
250011828

prune530.0ms

Filtered
150 candidates to 123 candidates (82.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1464150
Fresh000
Picked011
Done000
Total1465151

Merged error: 6.7b

Counts
151 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.2b
(pow (/ t l) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.2b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite33.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 159
Calls
4 calls:
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms
(pow (/ t l) 2.0)
18.0ms
(/ (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))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms
(pow (/ t l) 2.0)
319.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
190.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06382554
120442381
250012370

prune494.0ms

Filtered
171 candidates to 114 candidates (66.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1710171
Fresh033
Picked011
Done011
Total1715176

Merged error: 6.7b

Counts
176 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
126×sqrt-prod
117×add-sqr-sqrt
80×cbrt-div
72×*-un-lft-identity
71×cbrt-prod
60×add-cube-cbrt
50×associate-/r/
40×flip3-+ flip-+
24×frac-times difference-of-squares
12×unpow-prod-down associate-*r/ associate-*l/
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 188
Calls
4 calls:
31.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
311.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
244.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify113.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
09546303
129456199
250016188

prune899.0ms

Filtered
200 candidates to 171 candidates (85.5%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2000200
Fresh022
Picked011
Done022
Total2005205

Merged error: 6.7b

Counts
205 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.4b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.4b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
66×sqrt-prod
56×times-frac
42×*-un-lft-identity
30×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
8×pow1
6×rem-sqrt-square distribute-lft-out-- sqr-pow
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 118
Calls
4 calls:
12.0ms
(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)))))
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series726.0ms

Counts
4 → 12
Calls
4 calls:
321.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
320.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
44.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
41.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
03982016
19541942
235001934
350011910

prune598.0ms

Filtered
130 candidates to 108 candidates (83.1%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1264130
Fresh011
Picked101
Done033
Total1278135

Merged error: 6.7b

Counts
135 → 8

regimes678.0ms

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
01810
11810

end0.0ms

sample2.3s

Algorithm
intervals
Results
763.0ms8189×body80nan
697.0ms3857×body160valid
387.0ms4143×body80valid

Profiling

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