Details

Time bar (total: 19.9s)

sample127.0ms

Algorithm
intervals
Results
38.0ms100×body160valid
30.0ms265×body80nan
15.0ms156×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310119
427719
5156119
done500119

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite177.0ms

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 (/ Om Omc) 2.0)
84.0ms
(/ (- 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))))))
75.0ms
(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:
89.0ms
(pow (/ Om Omc) 2.0)
340.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
36.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
569.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts
142 → 142
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03083657
17333542
223983369
done50003367

prune831.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
0.3b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
11.5b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

rewrite132.0ms

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:
7.0ms
(pow (/ Om Omc) 2.0)
97.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
19.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series963.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (/ Om Omc) 2.0)
572.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
23.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
262.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify1.4s

Counts
163 → 163
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03254597
17004260
222224132
done50004128

prune927.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
11.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))

rewrite231.0ms

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 (/ Om Omc) 2.0)
109.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
107.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
91.0ms
(pow (/ Om Omc) 2.0)
397.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
618.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03083657
17333548
223913371
done50003369

prune830.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))))
11.4b
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
11.5b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
11.5b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
8×add-sqr-sqrt sqrt-pow1
7×sqrt-div sqrt-prod
6×add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square pow1/2
2×flip3-+ flip-+
1×pow2 frac-times asin-acos pow-plus associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
Counts
4 → 57
Calls
4 calls:
1.0ms
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))))
99.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
25.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
19.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series976.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))))
483.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
235.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
228.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify1.9s

Counts
69 → 69
Iterations

Useful iterations: 3 (702.0ms)

IterNodesCost
01271777
12851259
29221124
347301086
done50001086

prune399.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.9b

regimes700.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
11819
done1819

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s3836×body160valid
1.0s8034×body80nan
611.0ms4164×body80valid