Details

Time bar (total: 55.5s)

sample335.0ms

Algorithm
intervals
Results
192.0ms293×body80nan
34.0ms126×body160valid
19.0ms130×body80valid

simplify9.9s

Counts
1 → 1
Iterations
IterNodes
done5001
62687
5775
4250
3102
251
129
016

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
11.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite147.0ms

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))))
111.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
117.0ms
(pow (/ t l) 2.0)
149.0ms
(pow (/ Om Omc) 2.0)
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
749.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify7.1s

Counts
124 → 124
Iterations
IterNodes
done5003
33895
21461
1730
0319

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize127.0ms

Local error

Found 4 expressions with local error:

11.5b
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
84×cbrt-prod
81×times-frac
58×*-un-lft-identity
40×add-cube-cbrt
36×difference-of-squares
18×unpow-prod-down
12×pow1
9×sqrt-pow1 pow1/3 distribute-lft-out-- sqr-pow
7×cbrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-div div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*r/ associate-*l/ sqrt-prod
Counts
4 → 141
Calls
4 calls:
100.0ms
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
42.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
532.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
39.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series2.7s

Counts
4 → 12
Calls
4 calls:
650.0ms
(sqrt (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
715.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
662.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
694.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify4.9s

Counts
153 → 153
Iterations
IterNodes
done5000
44452
31294
2595
1319
0188

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize169.0ms

Local error

Found 4 expressions with local error:

11.6b
(sqrt (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.6b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
17.6b
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×cbrt-prod
27×times-frac
24×*-un-lft-identity
18×add-cube-cbrt
12×pow1 difference-of-squares
9×sqrt-pow1 pow1/3
6×unpow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×distribute-lft-out-- sqr-pow
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square cbrt-div pow-plus pow1/2 sqrt-prod div-inv
Counts
4 → 86
Calls
4 calls:
20.0ms
(sqrt (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
40.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
309.0ms
(sqrt (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
681.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
250.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
256.0ms
(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify3.3s

Counts
98 → 98
Iterations
IterNodes
done5000
31845
2736
1385
0219

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.9b

localize260.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
112×cbrt-prod
108×times-frac
76×*-un-lft-identity
52×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×distribute-lft-out-- sqr-pow
4×pow1 add-exp-log expm1-log1p-u cbrt-div pow1/3 add-cbrt-cube log1p-expm1-u div-inv add-log-exp
Counts
4 → 156
Calls
4 calls:
52.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
40.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
44.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
40.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series2.6s

Counts
4 → 12
Calls
4 calls:
638.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
654.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
640.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
666.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify4.7s

Counts
168 → 168
Iterations
IterNodes
done5000
44333
31144
2504
1280
0160

prune3.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.9b

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done15
015

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.5s3833×body160valid
1.4s8002×body80nan
1.4s4167×body80valid