Details

sample178.0ms

Algorithm

intervals

Results

58.0ms	129×	body	160	valid
54.0ms	267×	body	80	nan
27.0ms	127×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	3283
5	883
4	308
3	120
2	57
1	30
0	16

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

26.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ Om Omc) (/ Om Omc))
32.0ms	(* (/ t l) (/ t l))
16.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
162.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify957.0ms

Counts

191 → 191

Iterations

Iter	Nodes
2	2851
1	951
0	334

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.6b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0b	(log (exp (* (/ Om Omc) (/ Om Omc))))
7.0b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`times-frac`
56×	`*-un-lft-identity`
44×	`add-cube-cbrt`
27×	`sqrt-prod`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
6×	`log-pow` `distribute-lft-out--` `difference-of-squares`
5×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`log-prod`
2×	`rem-sqrt-square` `associate-/r/`
1×	`pow2` `frac-times` `asin-acos` `exp-prod` `sqrt-pow1` `flip3-+` `pow-plus` `exp-to-pow` `pow1/2` `sqrt-div` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 132

Calls

4 calls:

13.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
3.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
12.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ t l) (/ t l))
18.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
44.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
168.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify2.9s

Counts

144 → 144

Iterations

Iter	Nodes
3	5977
2	1749
1	626
0	257

prune853.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0b	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
4.0b	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
7.0b	(sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`sqrt-prod`
34×	`add-sqr-sqrt`
31×	`times-frac`
22×	`log-pow` `add-cube-cbrt`
21×	`pow1`
15×	`distribute-lft-out--`
12×	`log-prod` `distribute-lft-out`
7×	`sqrt-pow1`
6×	`add-exp-log` `add-log-exp` `difference-of-squares`
4×	`add-cbrt-cube` `insert-posit16`
3×	`pow1/2`
2×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `rem-log-exp` `associate-/r/`
1×	`asin-acos` `flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

2.0ms	(asin (sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.0ms	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
8.0ms	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
83.0ms	(sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(asin (sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
102.0ms	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
74.0ms	(log (sqrt (exp (* (/ Om Omc) (/ Om Omc)))))
227.0ms	(sqrt (/ (- 1 (+ (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))) (log (sqrt (exp (* (/ Om Omc) (/ Om Omc))))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify6.5s

Counts

110 → 110

Iterations

Iter	Nodes
4	8090
3	1742
2	601
1	308
0	175

prune503.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))
0.6b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.1b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 161

Calls

4 calls:

19.0ms	(* (/ Om Omc) (/ Om Omc))
12.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ Om Omc) (/ Om Omc))
38.0ms	(* (/ t l) (/ t l))
16.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
92.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify933.0ms

Counts

173 → 173

Iterations

Iter	Nodes
2	2766
1	838
0	268

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.9b

regimes528.0ms

Accuracy

98.4% (0.1b remaining)

Error of 5.4b against oracle of 5.3b and baseline of 10.2b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	25

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	8206×	body	80	nan
1.4s	3807×	body	160	valid
918.0ms	4193×	body	80	valid