Details

Time bar (total: 35.1s)

sample127.0ms

Algorithm
intervals
Results
38.0ms129×body160valid
31.0ms286×body80nan
15.0ms127×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod 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×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp 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 → 134
Calls
4 calls:
7.0ms
(pow (/ Om Omc) 2.0)
110.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
58.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series745.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(pow (/ Om Omc) 2.0)
230.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
25.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
419.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.2s

Counts
146 → 146
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02763461
15123355
210953196
331783184
done50013181

prune908.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
9.4b
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))

rewrite544.0ms

Algorithm
rewrite-expression-head
Rules
1094×times-frac
1007×add-sqr-sqrt
995×sqrt-prod
877×*-un-lft-identity
333×add-cube-cbrt
330×difference-of-squares
206×distribute-lft-out
162×unpow-prod-down
70×sqr-pow
66×distribute-lft-out--
51×associate-/r*
24×associate-/r/
15×div-inv
11×rem-sqrt-square flip3-- flip--
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×associate-/l/
1×frac-2neg flip3-+ sqrt-div clear-num flip-+
Counts
4 → 669
Calls
4 calls:
198.0ms
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
198.0ms
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
15.0ms
(sqrt (pow (/ Om Omc) 2.0))
17.0ms
(sqrt (pow (/ Om Omc) 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
612.0ms
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
904.0ms
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (fma 2.0 (pow (/ t l) 2.0) 1.0) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
432.0ms
(sqrt (pow (/ Om Omc) 2.0))
379.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify2.2s

Counts
681 → 681
Iterations

Useful iterations: done (2.1s)

IterNodesCost
069834752
1126833246
2379131572
done500031353

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (/ (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (sqrt (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
9.4b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))

rewrite563.0ms

Algorithm
rewrite-expression-head
Rules
2948×sqrt-prod
2012×times-frac
1781×add-sqr-sqrt
1368×*-un-lft-identity
692×add-cube-cbrt
540×difference-of-squares
246×unpow-prod-down
230×distribute-lft-out
114×associate-/r*
112×sqr-pow
108×distribute-lft-out--
20×sqrt-div
19×associate-/r/
12×div-inv
9×add-exp-log rem-sqrt-square flip3-- add-cbrt-cube flip--
8×associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×sqrt-undiv associate-/l/
1×frac-2neg flip3-+ clear-num flip-+
Counts
4 → 1133
Calls
4 calls:
249.0ms
(/ (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (/ (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (sqrt (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
16.0ms
(sqrt (pow (/ Om Omc) 2.0))
14.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
714.0ms
(/ (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (/ (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (sqrt (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
160.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
410.0ms
(sqrt (pow (/ Om Omc) 2.0))
415.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify3.1s

Counts
1145 → 1145
Iterations

Useful iterations: 2 (1.8s)

IterNodesCost
089466949
1182360864
2436360244
done500060244

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.1b

localize60.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod
60×unpow-prod-down
52×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
16×rem-sqrt-square
8×sqr-pow
4×pow1 add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u div-inv add-log-exp
Counts
4 → 128
Calls
4 calls:
10.0ms
(sqrt (pow (/ Om Omc) 2.0))
10.0ms
(sqrt (pow (/ Om Omc) 2.0))
17.0ms
(sqrt (pow (/ Om Omc) 2.0))
35.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
457.0ms
(sqrt (pow (/ Om Omc) 2.0))
447.0ms
(sqrt (pow (/ Om Omc) 2.0))
415.0ms
(sqrt (pow (/ Om Omc) 2.0))
453.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify1.7s

Counts
140 → 140
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
01222032
12351920
24541904
39821904
424521904
done50011904

prune2.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.1b

regimes753.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01930
12030
done2030

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.4s8023×body80nan
1.1s4139×body80valid
899.0ms3861×body160valid