Details

Time bar (total: 26.6s)

sample116.0ms

Algorithm
intervals
Results
31.0ms225×body80nan
29.0ms121×body160valid
16.0ms135×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
12919
24919
310019
426519
579819
6301619
done500119

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize25.0ms

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)))))

rewrite191.0ms

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:
9.0ms
(pow (/ t l) 2.0)
97.0ms
(/ (- 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))))))
78.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series996.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(pow (/ t l) 2.0)
343.0ms
(/ (- 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))))))
544.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.2s

Counts
142 → 142
Iterations

Useful iterations: done (3.2s)

IterNodesCost
03173657
16473534
215073367
346953363
done50003360

prune782.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize41.0ms

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)))))

rewrite196.0ms

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:
22.0ms
(/ (/ -1 l) (/ -1 t))
87.0ms
(/ (- 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))))))
49.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series839.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (/ -1 l) (/ -1 t))
380.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
27.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
415.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify1.1s

Counts
329 → 329
Iterations

Useful iterations: done (1.1s)

IterNodesCost
06508068
116357589
done50006700

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
99×add-exp-log
87×times-frac
70×div-exp
57×*-un-lft-identity
43×add-cube-cbrt
39×1-exp
30×sqrt-prod
28×prod-exp difference-of-squares
27×add-cbrt-cube
21×associate-/l*
14×unpow-prod-down
12×cbrt-undiv
10×rec-exp
7×distribute-lft-out-- sqr-pow
5×pow1 associate-/r/ div-inv
4×associate-/r* cbrt-unprod 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 associate-*r/ flip--
Counts
4 → 182
Calls
4 calls:
83.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0))))
18.0ms
(/ (/ 1 1) (* 1 (/ l t)))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0))))))
48.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0)))))

series888.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0))))
15.0ms
(/ (/ 1 1) (* 1 (/ l t)))
32.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0))))))
488.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ 1 1) (* 1 (/ l t))) 2.0)))))

simplify2.8s

Counts
194 → 194
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
03755394
17314089
215663797
344333399
done50003399

prune772.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize49.0ms

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)))

rewrite185.0ms

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))))))
83.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
48.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
40.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
44.0ms
(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))))))
448.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0))))
560.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))
485.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* (pow (* (/ 1 l) t) 2.0) 2.0) 1.0)))

simplify1.5s

Counts
145 → 145
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02975688
15395561
210814866
326324799
done50004784

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

regimes386.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02025
12521
done2521

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s3767×body160valid
1.0s7895×body80nan
512.0ms4233×body80valid