Details

Time bar (total: 46.7s)

sample188.0ms

Algorithm
intervals
Results
84.0ms293×body80nan
37.0ms126×body160valid
18.0ms130×body80valid

simplify4.9s

Counts
1 → 1
Iterations
IterNodes
done5001
62659
5720
4243
397
249
129
016

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize65.0ms

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))))))
11.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite166.0ms

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×pow-exp add-cbrt-cube 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)
58.0ms
(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))))))
85.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series981.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(pow (/ t l) 2.0)
154.0ms
(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))))))
663.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.6s

Counts
118 → 118
Iterations
IterNodes
done5002
21848
1846
0352

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ Om Omc) (/ Om Omc))
0.5b
(/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))
0.7b
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0))))
11.1b
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0)))

rewrite847.0ms

Algorithm
rewrite-expression-head
Rules
227×add-exp-log
142×div-exp
124×times-frac
88×add-sqr-sqrt
70×add-cube-cbrt *-un-lft-identity
68×unpow-prod-down
65×pow-exp
52×prod-exp
34×add-cbrt-cube
29×associate-/l*
20×pow-to-exp
18×sqrt-prod
15×rec-exp 1-exp
13×cbrt-undiv swap-sqr associate-*r* associate-*l*
12×pow1
8×cbrt-unprod div-inv sqr-pow
5×associate-/r/
4×add-log-exp unswap-sqr
3×difference-of-squares
2×frac-times rem-sqrt-square associate-*r/ associate-*l/
1×pow2 asin-acos frac-2neg sqrt-pow1 flip3-+ pow-plus pow1/2 sqrt-div pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 242
Calls
4 calls:
55.0ms
(* (/ Om Omc) (/ Om Omc))
577.0ms
(/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0))))
170.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0)))

series3.2s

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (/ Om Omc) (/ Om Omc))
862.0ms
(/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))
116.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0))))
2.1s
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ (* 2.0 (/ (pow (/ 1 (pow -1 2.0)) 1.0) (* (/ l t) (/ l t)))) 1.0)))

simplify4.3s

Counts
254 → 254
Iterations
IterNodes
done5004
23509
11213
0487

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.9b

localize156.0ms

Local error

Found 4 expressions with local error:

11.5b
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
90×cbrt-prod
81×times-frac
58×*-un-lft-identity
40×add-cube-cbrt
36×difference-of-squares
18×unpow-prod-down
12×pow1
9×sqrt-pow1 pow1/3 distribute-lft-out-- sqr-pow
7×cbrt-div
6×associate-/r/
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*r/ associate-*l/ sqrt-prod
Counts
4 → 139
Calls
4 calls:
114.0ms
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
46.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
50.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
46.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series2.9s

Counts
4 → 12
Calls
4 calls:
720.0ms
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
720.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
717.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
726.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.3s

Counts
151 → 151
Iterations
IterNodes
done5000
32027
2759
1375
0202

prune2.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.9b

localize212.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.0b
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite196.0ms

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:
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)))))))
94.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
87.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
96.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
105.0ms
(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
703.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
661.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify4.4s

Counts
122 → 122
Iterations
IterNodes
done5004
32199
2806
1391
0205

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.9b

regimes2.3s

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done18
118
016

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.5s3833×body160valid
1.4s8002×body80nan
1.3s4167×body80valid