Details

sample158.0ms

Algorithm

intervals

Results

63.0ms	281×	body	80	nan
29.0ms	113×	body	160	valid
18.0ms	143×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1583
4	292
3	108
2	51
1	29
0	16

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize27.0ms

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))))
12.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`unpow-prod-down` `add-cube-cbrt`
28×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-exp` `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:

5.0ms	(pow (/ t l) 2.0)
5.0ms	(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))))
40.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (/ t l) 2.0)
95.0ms	(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))))
387.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify868.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1847
1	740
0	319

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
12.4b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-div` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 155

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
101.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
3.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series684.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(pow (/ Om Omc) 2.0)
416.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
20.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
147.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify928.0ms

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	1739
1	619
0	312

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
2.9b	(sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
17.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
17.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`asin-acos` `pow1/2`

Counts

4 → 56

Calls

4 calls:

1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
2.0ms	(sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series679.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
212.0ms	(sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
216.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
210.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify693.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	1475
2	499
1	199
0	111

prune646.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.2b

localize33.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
8.2b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
12.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
12.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
62×	`sqrt-prod`
56×	`times-frac`
42×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`pow1`
6×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div` `div-inv`

Counts

4 → 114

Calls

4 calls:

1.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
31.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
48.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series961.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
65.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
411.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
429.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify738.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
3	1473
2	561
1	272
0	165

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.2b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
0	17

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.6s	8214×	body	80	nan
1.5s	3804×	body	160	valid
542.0ms	4196×	body	80	valid