Details

Time bar (total: 24.2s)

sample142.0ms

Algorithm
intervals
Results
59.0ms121×body160valid
32.0ms225×body80nan
16.0ms135×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310019
426519
579819
6301619
done500119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize24.0ms

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)))))

rewrite220.0ms

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:
7.0ms
(pow (/ t l) 2.0)
112.0ms
(/ (- 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))))))
94.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series956.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(pow (/ t l) 2.0)
346.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
489.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.4s

Counts
142 → 142
Iterations

Useful iterations: done (3.4s)

IterNodesCost
03173657
16473534
215073367
346953363
done50003360

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ -1 l) (/ -1 t))
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
284×add-sqr-sqrt
239×*-un-lft-identity
225×add-cube-cbrt
31×div-inv
30×sqrt-prod
28×difference-of-squares
21×associate-/l*
18×add-exp-log add-cbrt-cube
16×associate-/r*
14×unpow-prod-down
9×cbrt-undiv div-exp
7×distribute-lft-out-- sqr-pow
5×pow1 associate-/r/
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg flip3-+ clear-num flip-+
1×asin-acos flip3-- sqrt-pow1 pow1/2 sqrt-div div-sub flip--
Counts
4 → 317
Calls
4 calls:
33.0ms
(/ (/ -1 l) (/ -1 t))
123.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
54.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (/ -1 l) (/ -1 t))
374.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
38.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
539.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify1.3s

Counts
329 → 329
Iterations

Useful iterations: done (1.3s)

IterNodesCost
06508068
116357589
done50006700

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))
0.6b
(/ -1 (/ (- l) t))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0)))))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
278×times-frac
203×add-sqr-sqrt
158×*-un-lft-identity
144×add-cube-cbrt
37×associate-/r*
36×distribute-lft-neg-in distribute-rgt-neg-in
30×sqrt-prod
28×difference-of-squares
14×unpow-prod-down
12×neg-mul-1
11×add-exp-log add-cbrt-cube associate-/l*
7×div-inv distribute-lft-out-- sqr-pow
5×pow1 associate-/r/
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg flip3-+ clear-num flip-+ associate-/l/
1×asin-acos flip3-- sqrt-pow1 pow1/2 sqrt-div div-sub flip--
Counts
4 → 256
Calls
4 calls:
86.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))
29.0ms
(/ -1 (/ (- l) t))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))))
88.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0)))))

series857.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))
18.0ms
(/ -1 (/ (- l) t))
35.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0))))))
498.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (/ (- l) t)) 2.0)))))

simplify2.4s

Counts
268 → 268
Iterations

Useful iterations: done (2.4s)

IterNodesCost
05286103
111315795
233285339
done50015319

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
1.5b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
15.6b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
92×cbrt-prod
82×times-frac
59×*-un-lft-identity
41×add-cube-cbrt
36×difference-of-squares
33×sqrt-prod
18×unpow-prod-down
9×distribute-lft-out-- sqr-pow
6×associate-/r/
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×sqrt-pow1
1×asin-acos pow1/2 sqrt-div
Counts
4 → 133
Calls
4 calls:
1.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
108.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
45.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
47.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
57.0ms
(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))))
638.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
511.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
506.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

simplify1.7s

Counts
145 → 145
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02975688
15395561
210814866
326324799
done50004784

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

regimes4.0ms