Details

Time bar (total: 15.7s)

sample65.0ms

Algorithm
intervals
Results
17.0ms237×body80nan
15.0ms130×body160valid
8.0ms126×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
Calls
4 calls:
9.0ms
(pow (/ t l) 2.0)
6.0ms
(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))))
38.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
60.0ms
(pow (/ Om Omc) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
288.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.2s

Counts
124 → 124
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03192298
15822196
211152088
326522082
done50002076

prune489.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
Calls
4 calls:
6.0ms
(pow (/ t l) 2.0)
9.0ms
(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))))
38.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ t l) 2.0)
62.0ms
(pow (/ Om Omc) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
284.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.4s

Counts
124 → 124
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03192298
15822196
211152088
326522082
done50002076

prune544.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (/ -1 l) (/ -1 t))
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
458×times-frac
247×add-sqr-sqrt
226×*-un-lft-identity
220×add-cube-cbrt
31×div-inv
28×sqrt-prod
19×add-exp-log unpow-prod-down
16×add-cbrt-cube
13×associate-/r* associate-/l*
12×difference-of-squares
9×div-exp
8×cbrt-undiv
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow distribute-lft-out--
2×rem-sqrt-square pow-exp
1×pow-to-exp asin-acos pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/r/ associate-/l/
Counts
4 → 299
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
19.0ms
(/ (/ -1 l) (/ -1 t))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
37.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ Om Omc) 2.0)
9.0ms
(/ (/ -1 l) (/ -1 t))
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
282.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

simplify838.0ms

Counts
311 → 311
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
06606369
115915907
done50005263

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0))))
0.8b
(/ (cbrt -1) (/ (- l) t))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
451×times-frac
261×add-sqr-sqrt
240×*-un-lft-identity
234×add-cube-cbrt
105×cbrt-prod
63×distribute-lft-neg-in distribute-rgt-neg-in
34×associate-/r*
28×sqrt-prod
21×neg-mul-1
19×unpow-prod-down
12×add-exp-log difference-of-squares
10×div-inv
7×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp sqr-pow
3×cbrt-undiv pow-unpow distribute-lft-out--
2×rem-sqrt-square pow-exp
1×pow-to-exp asin-acos pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/r/
Counts
4 → 343
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0))))
20.0ms
(/ (cbrt -1) (/ (- l) t))
38.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ Om Omc) 2.0)
26.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0))))
74.0ms
(/ (cbrt -1) (/ (- l) t))
400.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (* (* (cbrt -1) (cbrt -1)) (/ (cbrt -1) (/ (- l) t))) 2.0) 1.0)))

simplify1.6s

Counts
355 → 355
Iterations

Useful iterations: done (1.6s)

IterNodesCost
06647348
113286899
236076674
done50006360

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

regimes458.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02024
done2024

end0.0ms

sample1.8s

Algorithm
intervals
Results
463.0ms7914×body80nan
446.0ms3840×body160valid
239.0ms4160×body80valid