Details

Time bar (total: 22.8s)

sample113.0ms

Algorithm
intervals
Results
29.0ms128×body160valid
28.0ms265×body80nan
14.0ms128×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune8.0ms

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 (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite105.0ms

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:
13.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
69.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (/ Om Omc) 2.0)
94.0ms
(pow (/ t l) 2.0)
14.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
450.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03192298
15822196
211152088
326512082
done50012076

prune794.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
3.9b
(log (exp (pow (/ Om Omc) 2.0)))
10.8b
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
37×times-frac
31×add-cube-cbrt
26×unpow-prod-down
22×sqrt-prod
21×log-pow
17×exp-prod
10×pow1
7×add-exp-log
6×distribute-lft-out--
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow log-prod div-inv difference-of-squares
2×rem-sqrt-square pow-exp sqr-pow
1×pow-to-exp asin-acos pow-pow sqrt-pow1 pow1/2 sqrt-div div-exp rem-log-exp
Counts
4 → 107
Calls
4 calls:
15.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
32.0ms
(log (exp (pow (/ Om Omc) 2.0)))
186.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(pow (/ t l) 2.0)
24.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
93.0ms
(log (exp (pow (/ Om Omc) 2.0)))
426.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.6s

Counts
119 → 119
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03012146
15121868
29751755
322611753
done50001743

prune723.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
3.9b
(log (exp (pow (/ Om Omc) 2.0)))
10.8b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
69×*-un-lft-identity
63×add-sqr-sqrt times-frac
48×add-cube-cbrt
25×log-pow
17×exp-prod
14×distribute-lft-out--
13×pow1 unpow-prod-down
9×associate-/l*
7×difference-of-squares
6×add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod
2×sqrt-div div-inv associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num flip-- sqr-pow
Counts
4 → 142
Calls
4 calls:
216.0ms
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
41.0ms
(log (exp (pow (/ Om Omc) 2.0)))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series580.0ms

Counts
4 → 12
Calls
4 calls:
373.0ms
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
14.0ms
(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
68.0ms
(log (exp (pow (/ Om Omc) 2.0)))
124.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.4s

Counts
154 → 154
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02904034
14673385
28893264
319973262
done50003246

prune784.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
0.3b
(/ (/ -1 l) (/ -1 t))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
10.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
852×times-frac
423×add-sqr-sqrt
402×*-un-lft-identity
396×add-cube-cbrt
180×unpow-prod-down
57×div-inv
29×add-exp-log
28×sqrt-prod
16×div-exp add-cbrt-cube
13×associate-/r* associate-/l*
12×difference-of-squares
8×cbrt-undiv
6×pow1
5×pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×pow-to-exp asin-acos pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/l/
Counts
4 → 463
Calls
4 calls:
43.0ms
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
27.0ms
(/ (/ -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))))
73.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(pow (/ (/ -1 l) (/ -1 t)) 2.0)
16.0ms
(/ (/ -1 l) (/ -1 t))
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0))))
460.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0) 1.0)))

simplify1.9s

Counts
475 → 475
Iterations

Useful iterations: done (1.9s)

IterNodesCost
093110656
123819843
done50008904

prune2.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.6b

regimes864.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01720
done1720

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.3s7893×body80nan
969.0ms3856×body160valid
578.0ms4144×body80valid