Details

Time bar (total: 18.8s)

sample101.0ms

Algorithm
intervals
Results
28.0ms293×body80nan
18.0ms101×body160valid
14.0ms155×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01619
12919
25118
310818
429218
5158518
done500018

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
12.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite132.0ms

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)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
72.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
45.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series759.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(pow (/ Om Omc) 2.0)
14.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
264.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
397.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify907.0ms

Counts
146 → 146
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
02763461
16053355
217703198
done50013196

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.4b

localize38.0ms

Local error

Found 4 expressions with local error:

12.9b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
12.9b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.9b
(sqrt (pow (/ Om Omc) 2.0))
14.9b
(sqrt (pow (/ Om Omc) 2.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 94
Calls
4 calls:
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.0ms
(sqrt (pow (/ Om Omc) 2.0))
10.0ms
(sqrt (pow (/ Om Omc) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
157.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
160.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
325.0ms
(sqrt (pow (/ Om Omc) 2.0))
393.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify856.0ms

Counts
106 → 106
Iterations

Useful iterations: done (851.0ms)

IterNodesCost
01711478
13261364
26521338
317111338
done50011320

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.3b

localize96.0ms

Local error

Found 4 expressions with local error:

12.9b
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
12.9b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.9b
(sqrt (pow (/ Om Omc) 2.0))
14.9b
(sqrt (pow (/ Om Omc) 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×times-frac
10×rem-sqrt-square
6×pow1
4×add-exp-log expm1-log1p-u sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 94
Calls
4 calls:
3.0ms
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
11.0ms
(sqrt (pow (/ Om Omc) 2.0))
10.0ms
(sqrt (pow (/ Om Omc) 2.0))

series947.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (fma 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0) 1.0))
118.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
298.0ms
(sqrt (pow (/ Om Omc) 2.0))
400.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify970.0ms

Counts
106 → 106
Iterations

Useful iterations: done (965.0ms)

IterNodesCost
01891550
13561428
27101368
318581360
done50011312

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.3b

localize55.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
19.4b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
19.4b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
19.4b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-div
2×sqrt-pow1
1×frac-times pow1/2 associate-*r/ pow-prod-down associate-*l/ sqrt-prod
Counts
4 → 55
Calls
4 calls:
75.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series920.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
175.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
194.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
185.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.5s

Counts
67 → 67
Iterations

Useful iterations: 4 (645.0ms)

IterNodesCost
0891495
11661394
23601147
3943916
43867889
done5000889

prune542.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.3b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 10.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02845
13145
done3145

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s7994×body80nan
902.0ms4160×body80valid
899.0ms3840×body160valid