Details

Time bar (total: 43.7s)

sample81.0ms

Algorithm
intervals
Results
25.0ms121×body160valid
16.0ms225×body80nan
10.0ms135×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

localize18.0ms

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)))))

rewrite165.0ms

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)
89.0ms
(/ (- 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))))))
61.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
78.0ms
(pow (/ t l) 2.0)
343.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
38.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
550.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts
142 → 142
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03173657
16473534
215073367
346953363
done50003360

prune904.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize20.0ms

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)))))

rewrite229.0ms

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:
26.0ms
(/ (/ -1 l) (/ -1 t))
108.0ms
(/ (- 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))))))
68.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series980.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (/ -1 l) (/ -1 t))
360.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))
40.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
568.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify1.2s

Counts
329 → 329
Iterations

Useful iterations: done (1.2s)

IterNodesCost
06508068
116357589
done50006700

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite608.0ms

Algorithm
rewrite-expression-head
Rules
5211×times-frac
2018×add-sqr-sqrt
1973×*-un-lft-identity
1959×add-cube-cbrt
816×cbrt-prod
432×distribute-lft-neg-in distribute-rgt-neg-in
268×div-inv
211×associate-/r*
144×neg-mul-1
63×add-exp-log
43×div-exp
30×sqrt-prod add-cbrt-cube
28×difference-of-squares
25×cbrt-undiv
15×associate-/l*
14×unpow-prod-down
7×distribute-lft-out-- sqr-pow
6×1-exp prod-exp
5×pow1 associate-/r/
4×add-log-exp
3×cbrt-unprod 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 → 1809
Calls
4 calls:
90.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0))))
129.0ms
(/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1)))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0))))))
66.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
488.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0))))
123.0ms
(/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1)))
77.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0))))))
579.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ (* (cbrt -1) (cbrt -1)) 1) (/ (/ (- l) t) (cbrt -1))) 2.0)))))

simplify2.6s

Counts
1821 → 1821
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0294959961
done500053394

prune16.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)))))

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
181×add-exp-log
115×div-exp
89×add-sqr-sqrt
56×times-frac
44×*-un-lft-identity
34×pow-exp
33×prod-exp
30×add-cube-cbrt sqrt-prod
28×difference-of-squares
15×unpow-prod-down
8×pow1 associate-/l* sqr-pow
7×distribute-lft-out--
6×rec-exp 1-exp add-cbrt-cube
4×associate-/r/ add-log-exp
3×pow-unpow associate-/r*
2×rem-sqrt-square pow-pow flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub pow-prod-down clear-num flip--
Counts
4 → 151
Calls
4 calls:
364.0ms
(pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)
103.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))))
64.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
243.0ms
(pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)
481.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))
81.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0))))))
710.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ (cbrt -1) (sqrt 1)) (- l)) (/ (/ (cbrt -1) (sqrt 1)) (/ (/ 1 t) (cbrt -1)))) 2.0)))))

simplify1.5s

Counts
163 → 163
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03787754
17026974
216825435
done50004425

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

regimes985.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02431
13029
23229
done3229

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s3767×body160valid
1.1s7895×body80nan
597.0ms4233×body80valid