Details

Time bar (total: 34.4s)

sample131.0ms

Algorithm
intervals
Results
37.0ms275×body80nan
32.0ms121×body160valid
19.0ms135×body80valid

simplify3.6s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite144.0ms

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:
12.0ms
(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))))))
67.0ms
(/ (- 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)))))

series984.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ Om Omc) 2.0)
31.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
346.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
513.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.1s

Counts
142 → 142
Iterations
IterNodes
done5003
21761
1723
0308

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite85.0ms

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:
7.0ms
(pow (/ Om Omc) 2.0)
58.0ms
(/ (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)))))))
6.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series930.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ Om Omc) 2.0)
528.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
30.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
277.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify3.0s

Counts
163 → 163
Iterations
IterNodes
done5000
34912
21549
1692
0329

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.9b

localize95.0ms

Local error

Found 4 expressions with local error:

12.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.1b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b
(sqrt (pow (/ Om Omc) 2.0))
16.9b
(sqrt (pow (/ Om Omc) 2.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×*-un-lft-identity add-cube-cbrt
20×times-frac
10×rem-sqrt-square
6×pow1
4×sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div add-exp-log add-log-exp sqr-pow
2×flip3-+ flip-+ div-inv
Counts
4 → 90
Calls
4 calls:
8.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(sqrt (pow (/ Om Omc) 2.0))
8.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
275.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
348.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
419.0ms
(sqrt (pow (/ Om Omc) 2.0))
375.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify4.8s

Counts
102 → 102
Iterations
IterNodes
done5000
32539
2858
1366
0175

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.9b

localize58.0ms

Local error

Found 4 expressions with local error:

16.9b
(sqrt (pow (/ Om Omc) 2.0))
17.2b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.2b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.2b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×sqrt-prod
15×unpow-prod-down *-un-lft-identity add-cube-cbrt
10×times-frac
9×cbrt-prod
6×cbrt-div
4×pow1 rem-sqrt-square add-cbrt-cube add-exp-log add-log-exp
3×flip3-+ pow1/3 flip-+
2×sqr-pow
1×sqrt-pow1 pow1/2 div-inv
Counts
4 → 69
Calls
4 calls:
16.0ms
(sqrt (pow (/ Om Omc) 2.0))
4.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
431.0ms
(sqrt (pow (/ Om Omc) 2.0))
409.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
419.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
335.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify4.9s

Counts
81 → 81
Iterations
IterNodes
done5000
32875
2895
1374
0177

prune972.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.9b

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s8012×body80nan
977.0ms3756×body160valid
634.0ms4244×body80valid