Details

sample171.0ms

Algorithm

intervals

Results

65.0ms	232×	body	80	nan
33.0ms	124×	body	160	valid
18.0ms	132×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	101	19
4	277	19
5	1561	19
done	5001	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite117.0ms

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:

11.0ms	(pow (/ t l) 2.0)
12.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
85.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow (/ t l) 2.0)
123.0ms	(pow (/ Om Omc) 2.0)
36.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
674.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.0s

Counts

118 → 118

Iterations

Useful iterations: 2 (849.0ms)

Iter	Nodes	Cost
0	352	2388
1	858	2272
2	2372	2160
done	5002	2160

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.1b	(log (exp (pow (/ Om Omc) 2.0)))
7.6b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite222.0ms

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:

14.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
31.0ms	(log (exp (pow (/ Om Omc) 2.0)))
170.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

125.0ms	(pow (/ Om Omc) 2.0)
43.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
133.0ms	(log (exp (pow (/ Om Omc) 2.0)))
700.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: 2 (570.0ms)

Iter	Nodes	Cost
0	282	2216
1	614	1931
2	1678	1809
done	5000	1809

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.8b	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.1b	(log (exp (pow (/ Om Omc) 2.0)))
7.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite396.0ms

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:

2.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
330.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
39.0ms	(log (exp (pow (/ Om Omc) 2.0)))
11.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

42.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
691.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
118.0ms	(log (exp (pow (/ Om Omc) 2.0)))
365.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts

150 → 150

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	307	4241
1	557	3585
2	1717	3454
done	5001	3450

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.2b

localize61.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
30.8b	(cbrt (pow (/ t l) 2.0))
30.8b	(cbrt (pow (/ t l) 2.0))
30.8b	(cbrt (pow (/ t l) 2.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

74.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
9.0ms	(cbrt (pow (/ t l) 2.0))
16.0ms	(cbrt (pow (/ t l) 2.0))
8.0ms	(cbrt (pow (/ t l) 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

656.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
530.0ms	(cbrt (pow (/ t l) 2.0))
534.0ms	(cbrt (pow (/ t l) 2.0))
493.0ms	(cbrt (pow (/ t l) 2.0))

simplify2.9s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	269	4003
1	522	3851
2	1314	2921
3	4372	2705
done	5002	2705

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.2b

regimes2.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	3753×	body	160	valid
1.3s	7884×	body	80	nan
555.0ms	4247×	body	80	valid