Details

Time bar (total: 28.4s)

sample113.0ms

Algorithm
intervals
Results
40.0ms120×body160valid
21.0ms233×body80nan
14.0ms136×body80valid

simplify1.8s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite169.0ms

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×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 130
Calls
4 calls:
10.0ms
(pow (/ t l) 2.0)
98.0ms
(/ (- 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))))))
49.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series932.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow (/ t l) 2.0)
307.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
20.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
515.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.4s

Counts
142 → 142
Iterations
IterNodes
done5000
22435
1755
0317

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
713×times-frac
674×sqrt-prod
641×add-sqr-sqrt
364×*-un-lft-identity
278×add-cube-cbrt
172×difference-of-squares
86×unpow-prod-down
43×distribute-lft-out-- sqr-pow
21×sqrt-div
16×associate-/r/
10×flip3-+ flip-+
9×rem-sqrt-square
8×div-inv associate-/l*
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
4×add-log-exp
3×sqrt-pow1 pow1/2
2×associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp flip--
Counts
4 → 456
Calls
4 calls:
92.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
103.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
450.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
509.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
220.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
290.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.1s

Counts
468 → 468
Iterations
IterNodes
done5001
11617
0873

prune3.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.7b

localize128.0ms

Local error

Found 4 expressions with local error:

9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
9.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
260.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
345.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
393.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
356.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.1s

Counts
66 → 66
Iterations
IterNodes
done5001
33901
2658
1195
086

prune880.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.7b

localize114.0ms

Local error

Found 4 expressions with local error:

9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
242.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
259.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
317.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
233.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts
72 → 72
Iterations
IterNodes
done5000
32388
2455
1141
060

prune744.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 10.7b

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done18
118
016

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.9s8095×body80nan
920.0ms3806×body160valid
543.0ms4194×body80valid