Details

sample60.0ms

Algorithm

intervals

Results

15.0ms	251×	body	80	nan
13.0ms	111×	body	160	valid
9.0ms	145×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	106	18
4	252	18
5	760	18
6	2815	18
done	5000	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(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))))
8.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite41.0ms

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:

3.0ms	(pow (/ Om Omc) 2.0)
3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
27.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
67.0ms	(pow (/ t l) 2.0)
11.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
266.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify857.0ms

Counts

124 → 124

Iterations

Useful iterations: done (853.0ms)

Iter	Nodes	Cost
0	319	2298
1	586	2196
2	1363	2088
done	5000	2062

prune475.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.4b	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
29×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`sqrt-prod`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `sqr-pow`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 103

Calls

4 calls:

3.0ms	(pow (/ Om Omc) 2.0)
3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
6.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
66.0ms	(pow (/ t l) 2.0)
10.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
306.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.1s

Counts

115 → 115

Iterations

Useful iterations: 3 (717.0ms)

Iter	Nodes	Cost
0	276	2077
1	502	1852
2	1120	1740
3	3587	1720
done	5000	1720

prune451.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b	(asin (fabs (/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
8.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

65×	`sqrt-prod`
60×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`times-frac`
45×	`add-cube-cbrt`
13×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
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×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `sqr-pow`

Counts

4 → 134

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
9.0ms	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.0ms	(asin (fabs (/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series484.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
299.0ms	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
15.0ms	(asin (fabs (/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
109.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.8s

Counts

146 → 146

Iterations

Useful iterations: 3 (763.0ms)

Iter	Nodes	Cost
0	273	3836
1	469	3266
2	1062	3146
3	3484	3124
done	5001	3124

prune537.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
1.7b	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
14.8b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.8b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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:

0.0ms	(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
1.0ms	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series397.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(asin (fabs (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
128.0ms	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
124.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
126.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 4 (884.0ms)

Iter	Nodes	Cost
0	115	1332
1	204	1276
2	423	1129
3	1151	1123
4	4740	1096
done	5000	1096

prune318.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.3b

regimes448.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

474.0ms	8170×	body	80	nan
451.0ms	3852×	body	160	valid
247.0ms	4148×	body	80	valid