Details

Time bar (total: 24.6s)

sample117.0ms

Algorithm
intervals
Results
26.0ms130×body160valid
24.0ms231×body80nan
24.0ms126×body80valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5001
62725
5723
4243
397
249
129
016

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×unpow-prod-down add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×add-cbrt-cube pow-exp 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 → 106
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
21.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
59.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (/ t l) 2.0)
117.0ms
(pow (/ Om Omc) 2.0)
37.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
512.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts
118 → 118
Iterations
IterNodes
done5000
21850
1846
0352

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.6b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
22×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac
10×add-exp-log
7×pow1
6×pow-unpow
4×add-cbrt-cube pow-exp add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow sqrt-div div-exp div-inv sqr-pow
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 79
Calls
4 calls:
6.0ms
(pow (/ t l) 2.0)
6.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (/ t l) 2.0)
111.0ms
(pow (/ Om Omc) 2.0)
21.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
303.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.9s

Counts
91 → 91
Iterations
IterNodes
done5001
21678
1697
0266

prune810.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.4b

localize106.0ms

Local error

Found 4 expressions with local error:

9.7b
(sqrt (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 66
Calls
4 calls:
11.0ms
(sqrt (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
348.0ms
(sqrt (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
290.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
386.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
343.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.9s

Counts
78 → 78
Iterations
IterNodes
done5000
31575
2495
1211
0106

prune977.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.4b

localize91.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0)))))
14.0b
(cbrt (/ t l))
14.0b
(cbrt (/ t l))
14.0b
(cbrt (/ t l))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 81
Calls
4 calls:
7.0ms
(sqrt (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0)))))
4.0ms
(cbrt (/ t l))
4.0ms
(cbrt (/ t l))
4.0ms
(cbrt (/ t l))

series478.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(sqrt (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0)))))
80.0ms
(cbrt (/ t l))
65.0ms
(cbrt (/ t l))
90.0ms
(cbrt (/ t l))

simplify2.2s

Counts
93 → 93
Iterations
IterNodes
done5001
32843
2657
1253
0133

prune1.0s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 9.4b

regimes1.6s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done18
118
016

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s3863×body160valid
980.0ms8068×body80nan
562.0ms4137×body80valid