Details

sample59.0ms

Algorithm

intervals

Results

16.0ms	251×	body	80	nan
15.0ms	123×	body	160	valid
8.0ms	133×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	242	19
5	730	19
6	2759	19
done	5001	19

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

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)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
32.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ Om Omc) 2.0)
64.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify651.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (229.0ms)

Iter	Nodes	Cost
0	352	2388
1	697	2272
2	1771	2160
done	5001	2160

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
4.1b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 101

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(log (exp (pow (/ Om Omc) 2.0)))
70.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
63.0ms	(log (exp (pow (/ Om Omc) 2.0)))
314.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify615.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	334	2216
1	626	1932
2	1623	1815
done	5000	1815

prune436.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
4.1b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `log-pow`
17×	`exp-prod`
7×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `sqrt-prod`
2×	`sqrt-div` `pow-exp` `div-inv` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
65.0ms	(log (exp (pow (/ Om Omc) 2.0)))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify558.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (180.0ms)

Iter	Nodes	Cost
0	290	1313
1	553	1160
2	1528	1079
done	5000	1079

prune450.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.3b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.5b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.5b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 133

Calls

4 calls:

0.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
31.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

33.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
344.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
337.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
344.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.3s

Counts

145 → 145

Iterations

Useful iterations: 3 (488.0ms)

Iter	Nodes	Cost
0	296	5194
1	535	5053
2	1195	4860
3	4041	4799
done	5000	4799

prune783.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.3b

regimes813.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	20	21
done	20	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

493.0ms	7939×	body	80	nan
464.0ms	3848×	body	160	valid
254.0ms	4152×	body	80	valid