Details

Time bar (total: 9.7s)

sample80.0ms

Algorithm
intervals
Results
24.0ms274×body80nan
23.0ms134×body160valid
11.0ms122×body80valid

simplify123.0ms

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: 11.2b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(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))))))
10.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 114
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
5.0ms
(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))))))
16.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ Om Omc) 2.0)
64.0ms
(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))))))
310.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
07091289
120871218
250011206

prune448.0ms

Filtered
126 candidates to 100 candidates (79.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1206126
Fresh000
Picked011
Done000
Total1207127

Merged error: 11.2b

Counts
127 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.1b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.7b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.7b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 141
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
17.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
36.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
338.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
346.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
338.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
05442927
112752835
244882820
350012820

prune787.0ms

Filtered
153 candidates to 134 candidates (87.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1521153
Fresh145
Picked101
Done011
Total1546160

Merged error: 11.2b

Counts
160 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.1b
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.5b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.7b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
133×add-sqr-sqrt
118×cbrt-prod
103×times-frac
72×sqrt-prod
70×*-un-lft-identity
52×add-cube-cbrt
36×difference-of-squares
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square cbrt-div
4×add-exp-log expm1-log1p-u associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow1/3 div-inv
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 155
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
17.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series945.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
330.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
335.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
07653402
119013293
250013278

prune902.0ms

Filtered
167 candidates to 151 candidates (90.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1670167
Fresh044
Picked011
Done011
Total1676173

Merged error: 11.2b

Counts
173 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.7b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.2b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite32.0ms

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:
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)))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series716.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(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)))))))
314.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
319.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
03982016
19541942
235001934
350021910

prune598.0ms

Filtered
130 candidates to 108 candidates (83.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1264130
Fresh123
Picked101
Done022
Total1288136

Merged error: 11.1b

Counts
136 → 8

regimes672.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample2.3s

Algorithm
intervals
Results
734.0ms7937×body80nan
700.0ms3809×body160valid
381.0ms4191×body80valid