Details

sample147.0ms

Algorithm

intervals

Results

37.0ms	265×	body	80	nan
37.0ms	128×	body	160	valid
17.0ms	128×	body	80	valid

simplify3.1s

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	265	19
5	798	19
6	3016	19
done	5001	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite89.0ms

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:

7.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow (/ Om Omc) 2.0)
98.0ms	(pow (/ t l) 2.0)
38.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
479.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.2s

Counts

118 → 118

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	352	2388
1	693	2272
2	1438	2160
3	3929	2150
done	5001	2144

prune590.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.9b	(log (exp (pow (/ Om Omc) 2.0)))
10.8b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite139.0ms

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:

6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
20.0ms	(log (exp (pow (/ Om Omc) 2.0)))
108.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(pow (/ t l) 2.0)
24.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
94.0ms	(log (exp (pow (/ Om Omc) 2.0)))
501.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.9s

Counts

113 → 113

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	334	2216
1	623	1932
2	1303	1815
3	3555	1809
done	5000	1799

prune618.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.9b	(log (exp (pow (/ Om Omc) 2.0)))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
69×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `times-frac`
48×	`add-cube-cbrt`
25×	`log-pow`
17×	`exp-prod`
14×	`distribute-lft-out--`
13×	`pow1` `unpow-prod-down`
9×	`associate-/l*`
7×	`difference-of-squares`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod`
2×	`flip3-+` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `flip--` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

202.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
23.0ms	(log (exp (pow (/ Om Omc) 2.0)))
17.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

416.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
35.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
107.0ms	(log (exp (pow (/ Om Omc) 2.0)))
261.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.7s

Counts

150 → 150

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	307	4241
1	547	3585
2	1206	3452
3	3440	3450
done	5000	3443

prune728.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ -1 l) (/ -1 t))
0.7b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
3.9b	(log (exp (pow (/ Om Omc) 2.0)))
10.8b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

449×	`times-frac`
228×	`add-sqr-sqrt` `*-un-lft-identity`
219×	`add-cube-cbrt`
31×	`div-inv`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
16×	`add-exp-log` `add-cbrt-cube`
13×	`unpow-prod-down` `associate-/r` `associate-/l`
9×	`pow1`
8×	`cbrt-undiv` `div-exp`
6×	`distribute-lft-out--`
4×	`add-log-exp`
3×	`log-prod` `associate-/r/` `difference-of-squares`
2×	`rem-sqrt-square`
1×	`asin-acos` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `rem-log-exp` `clear-num` `flip-+` `associate-/l/` `sqr-pow`

Counts

4 → 288

Calls

4 calls:

17.0ms	(/ (/ -1 l) (/ -1 t))
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
19.0ms	(log (exp (pow (/ Om Omc) 2.0)))
130.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (/ -1 l) (/ -1 t))
29.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
76.0ms	(log (exp (pow (/ Om Omc) 2.0)))
430.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify1.1s

Counts

300 → 300

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	669	6247
1	1616	5603
done	5000	4968

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.6b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	7893×	body	80	nan
842.0ms	3856×	body	160	valid
506.0ms	4144×	body	80	valid