Details

sample126.0ms

Algorithm

intervals

Results

29.0ms	117×	body	160	valid
28.0ms	225×	body	80	nan
18.0ms	139×	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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(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))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite72.0ms

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:

6.0ms	(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))))
47.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (/ t l) 2.0)
95.0ms	(pow (/ Om Omc) 2.0)
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
446.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify978.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1847
1	740
0	319

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(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))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite66.0ms

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:

7.0ms	(pow (/ t l) 2.0)
5.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
42.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ t l) 2.0)
105.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
403.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify913.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1847
1	740
0	319

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
8.7b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite89.0ms

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)
74.0ms	(/ (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))

series722.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (/ Om Omc) 2.0)
434.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
21.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
145.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify971.0ms

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: 9.5b

localize116.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
7.6b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

178×	`sqrt-prod`
164×	`add-sqr-sqrt`
112×	`times-frac`
78×	`*-un-lft-identity`
54×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`distribute-lft-out--` `sqr-pow`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
6×	`pow1/2` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 180

Calls

4 calls:

49.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
34.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
52.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
59.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

454.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
454.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
412.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
392.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify955.0ms

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
3	1839
2	723
1	361
0	226

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

regimes1.0s

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
0	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	8096×	body	80	nan
816.0ms	3854×	body	160	valid
776.0ms	4146×	body	80	valid