Details

Time bar (total: 9.6s)

sample63.0ms

Algorithm
intervals
Results
16.0ms273×body80nan
13.0ms118×body160valid
12.0ms138×body80valid

simplify125.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (- 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))))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite77.0ms

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:
4.0ms
(pow (/ t l) 2.0)
36.0ms
(/ (- 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))))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
214.0ms
(/ (- 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))))))
325.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06481882
120471787
250011774

prune714.0ms

Filtered
142 candidates to 114 candidates (80.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.4b
(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)))))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
99×sqrt-prod
73×times-frac
58×*-un-lft-identity
44×add-cube-cbrt
28×difference-of-squares
14×pow1 unpow-prod-down
11×sqrt-div associate-/l*
8×sqrt-pow1
7×distribute-lft-out-- sqr-pow
6×add-exp-log associate-/r* add-cbrt-cube
4×add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
2×associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-times sqrt-undiv flip3-- frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up flip-- div-inv
Counts
4 → 149
Calls
4 calls:
41.0ms
(/ (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))))
39.0ms
(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)))))))

series980.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
173.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
174.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
317.0ms
(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)))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04142581
111822452
250012410

prune623.0ms

Filtered
161 candidates to 104 candidates (64.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.4b

localize19.0ms

Local error

Found 4 expressions with local error:

10.4b
(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))))))
15.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite68.0ms

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 add-cbrt-cube add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 180
Calls
4 calls:
50.0ms
(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))))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(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:
327.0ms
(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))))))
240.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
244.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
244.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify99.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
09466224
129076123
250016115

prune994.0ms

Filtered
192 candidates to 160 candidates (83.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.4b

localize22.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.8b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite63.0ms

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 sqrt-pow1 pow1/2 associate-/r/ add-cbrt-cube add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 110
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)))))))
30.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series737.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
49.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
321.0ms
(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)))))

simplify96.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
03881928
19201854
233121846
350011822

prune612.0ms

Filtered
122 candidates to 100 candidates (82.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.4b

regimes864.0ms

Accuracy

0% (0.1b remaining)

Error of 10.9b against oracle of 10.8b and baseline of 10.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02123
12123

end0.0ms

sample1.6s

Algorithm
intervals
Results
450.0ms7813×body80nan
424.0ms3742×body160valid
251.0ms4258×body80valid