Details

Time bar (total: 25.2s)

sample136.0ms

Algorithm
intervals
Results
34.0ms124×body160valid
32.0ms232×body80nan
19.0ms132×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
01619
12919
25118
310818
429218
5158518
done500018

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
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))))
7.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite127.0ms

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 (/ t l) 2.0)
13.0ms
(pow (/ Om Omc) 2.0)
2.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
89.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(pow (/ t l) 2.0)
125.0ms
(pow (/ Om Omc) 2.0)
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
572.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: 2 (672.0ms)

IterNodesCost
03192298
17402196
218492088
done50002088

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
3.1b
(log (exp (pow (/ Om Omc) 2.0)))
7.6b
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite226.0ms

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:
11.0ms
(pow (/ Om Omc) 2.0)
4.0ms
(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)))
169.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series754.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(pow (/ Om Omc) 2.0)
23.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
106.0ms
(log (exp (pow (/ Om Omc) 2.0)))
510.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.7s

Counts
119 → 119
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02492146
14961863
211521749
336561749
done50021743

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
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))))
7.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite131.0ms

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 (/ t l) 2.0)
13.0ms
(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))))
95.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series834.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(pow (/ t l) 2.0)
125.0ms
(pow (/ Om Omc) 2.0)
24.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
565.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: 2 (669.0ms)

IterNodesCost
03192298
17402196
218492088
done50002088

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b
(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
0.8b
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
3.1b
(log (exp (pow (/ Om Omc) 2.0)))
7.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite317.0ms

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:
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)))))
267.0ms
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
34.0ms
(log (exp (pow (/ Om Omc) 2.0)))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series828.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
489.0ms
(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
116.0ms
(log (exp (pow (/ Om Omc) 2.0)))
200.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.0s

Counts
154 → 154
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02904034
14793385
212713266
done50003262

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.2b

regimes1.4s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01720
done1720

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.8s3753×body160valid
1.4s7884×body80nan
780.0ms4247×body80valid