Details

Time bar (total: 8.0s)

sample69.0ms

Algorithm
intervals
Results
22.0ms251×body80nan
16.0ms111×body160valid
10.0ms145×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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:
3.0ms
(pow (/ Om Omc) 2.0)
4.0ms
(pow (/ t l) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
28.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow (/ Om Omc) 2.0)
64.0ms
(pow (/ t l) 2.0)
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06951235
120431164
250021152

prune453.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 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)))))))
8.5b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite57.0ms

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 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
43.0ms
(/ (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)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
314.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
178.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06232507
119872333
250012323

prune601.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.7b
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div sqrt-prod
5×pow1
4×add-exp-log add-cbrt-cube 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 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
3.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series878.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
364.0ms
(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
240.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
240.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify115.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0323853
1999781
24332770
35002769

prune392.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

localize26.0ms

Local error

Found 4 expressions with local error:

14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite7.0ms

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:
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series951.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
232.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0144652
1451604
21974588
35001588

prune443.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 9.3b

regimes589.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample2.0s

Algorithm
intervals
Results
612.0ms8170×body80nan
583.0ms3852×body160valid
308.0ms4148×body80valid