Details

Time bar (total: 21.1s)

sample147.0ms

Algorithm
intervals
Results
49.0ms143×body80valid
30.0ms281×body80nan
26.0ms113×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done5001
51551
4277
3101
249
129
016

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite62.0ms

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:
13.0ms
(pow (/ t l) 2.0)
5.0ms
(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))))))
38.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(pow (/ t l) 2.0)
110.0ms
(pow (/ Om Omc) 2.0)
22.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
536.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.2s

Counts
118 → 118
Iterations
IterNodes
done5000
22371
1858
0352

prune940.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite99.0ms

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 associate-/r* add-cbrt-cube sqrt-div
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×pow-to-exp cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 151
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
70.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series858.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(pow (/ Om Omc) 2.0)
479.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
36.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
272.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.2s

Counts
163 → 163
Iterations
IterNodes
done5001
22240
1703
0329

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))) (sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))))
2.9b
(sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
17.9b
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
17.9b
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div sqrt-prod
5×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×flip3-+ pow1/3 flip-+
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×asin-acos pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))) (sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))))
7.0ms
(sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
8.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
3.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
70.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))) (sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))))
358.0ms
(sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
342.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
392.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

simplify707.0ms

Counts
66 → 66
Iterations
IterNodes
done5001
21143
1334
0155

prune817.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.2b

localize66.0ms

Local error

Found 4 expressions with local error:

8.2b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.2b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite107.0ms

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×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log associate-/r/ add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
2.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
41.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
53.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
86.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
486.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
539.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts
122 → 122
Iterations
IterNodes
done5000
33616
21001
1390
0205

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.2b

regimes2.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s3804×body160valid
1.3s8214×body80nan
588.0ms4196×body80valid