Details

Time bar (total: 30.0s)

sample107.0ms

Algorithm
intervals
Results
35.0ms225×body80nan
23.0ms121×body160valid
12.0ms135×body80valid

simplify6.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
13919
215519
3125119
done500019

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize31.0ms

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))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite180.0ms

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×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 130
Calls
4 calls:
10.0ms
(pow (/ t l) 2.0)
94.0ms
(/ (- 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))))))
63.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series898.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(pow (/ t l) 2.0)
304.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
480.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.8s

Counts
142 → 142
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03173657
120883529
done50003363

prune902.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (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)))))))
10.3b
(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))))))
10.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
658×times-frac
647×sqrt-prod
560×add-sqr-sqrt
325×*-un-lft-identity
253×add-cube-cbrt
144×difference-of-squares
72×unpow-prod-down
36×distribute-lft-out-- sqr-pow
19×sqrt-div
14×associate-/r/
9×rem-sqrt-square flip3-+ flip-+
7×pow1 div-inv
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-pow1 pow1/2
1×asin-acos
Counts
4 → 385
Calls
4 calls:
1.0ms
(asin (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)))))))
116.0ms
(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))))))
12.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
40.0ms
(asin (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)))))))
459.0ms
(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))))))
268.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
262.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.1s

Counts
397 → 397
Iterations

Useful iterations: done (2.1s)

IterNodesCost
087323423
1251720856
done500019606

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize59.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
466×sqrt-prod
405×times-frac
235×add-sqr-sqrt
203×*-un-lft-identity
197×add-cube-cbrt
83×cbrt-prod
23×sqrt-div
20×associate-/r/
17×rem-sqrt-square
13×flip3-+ flip-+
10×div-inv
7×pow1 sqrt-pow1
6×cbrt-div
4×add-exp-log pow1/3 add-cbrt-cube add-log-exp
3×pow1/2
2×pow-flip pow-div
Counts
4 → 291
Calls
4 calls:
93.0ms
(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
394.0ms
(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
292.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
337.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
440.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.9s

Counts
303 → 303
Iterations

Useful iterations: done (1.9s)

IterNodesCost
062313894
1196412334
done500011909

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

localize82.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
444.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
385.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
391.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
431.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify861.0ms

Counts
64 → 64
Iterations

Useful iterations: done (858.0ms)

IterNodesCost
0601256
12801196
done50011084

prune722.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.6b

regimes980.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s7895×body80nan
1.2s4233×body80valid
965.0ms3767×body160valid