Details

Time bar (total: 21.4s)

sample155.0ms

Algorithm
intervals
Results
40.0ms281×body80nan
31.0ms143×body80valid
31.0ms113×body160valid

simplify1.1s

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize49.0ms

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)))))

rewrite74.0ms

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:
8.0ms
(pow (/ t l) 2.0)
10.0ms
(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))))))
50.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(pow (/ t l) 2.0)
114.0ms
(pow (/ Om Omc) 2.0)
42.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
608.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.1s

Counts
118 → 118
Iterations
IterNodes
done5000
22371
1858
0352

prune935.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize35.0ms

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))))

rewrite104.0ms

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:
5.0ms
(pow (/ Om Omc) 2.0)
89.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series911.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(pow (/ Om Omc) 2.0)
495.0ms
(/ (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)))))))
293.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.1s

Counts
163 → 163
Iterations
IterNodes
done5001
22240
1703
0329

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize78.0ms

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)))

rewrite20.0ms

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:
0.0ms
(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))))))))
9.0ms
(sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
5.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
5.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
48.0ms
(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))))))))
370.0ms
(sqrt (cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
393.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
353.0ms
(cbrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

simplify642.0ms

Counts
66 → 66
Iterations
IterNodes
done5001
21143
1334
0155

prune933.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.2b

localize62.0ms

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)))))

rewrite133.0ms

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:
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)))))))
51.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
76.0ms
(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:
75.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
83.0ms
(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)))))
512.0ms
(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

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.2b

regimes2.0s

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
done20
120
018

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.6s4196×body80valid
1.2s8214×body80nan
1.0s3804×body160valid