Details

sample125.0ms

Algorithm

intervals

Results

44.0ms	287×	body	80	nan
32.0ms	114×	body	160	valid
20.0ms	142×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
6	2008
5	1100
4	363
3	142
2	61
1	32
0	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (+ (/ t l) (/ t l)) (/ t l))
1.2b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
8.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
100×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
77×	`add-cube-cbrt`
49×	`associate-l`
26×	`associate-r`
21×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
15×	`distribute-rgt-out`
14×	`pow1`
13×	`swap-sqr` `distribute-lft-out`
10×	`div-inv`
6×	`prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `distribute-lft1-in` `pow-prod-down` `frac-add` `distribute-rgt1-in` `associate-r/` `associate-/r/` `-commutative`
1×	`pow2` `asin-acos` `sqrt-pow1` `pow-plus` `pow1/2` `count-2` `sqrt-div` `pow-sqr` `pow-prod-up`

Counts

4 → 183

Calls

4 calls:

14.0ms	(* (/ Om Omc) (/ Om Omc))
56.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
8.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ Om Omc) (/ Om Omc))
52.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
13.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
157.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.0s

Counts

195 → 195

Iterations

Iter	Nodes
done	2002
2	2002
1	971
0	370

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (/ t l) (/ t l)) (/ t l))
1.2b	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
3.5b	(log (exp (* (/ Om Omc) (/ Om Omc))))
8.0b	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
72×	`times-frac`
69×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
36×	`associate-l`
27×	`sqrt-prod`
15×	`distribute-rgt-out`
13×	`associate-r` `distribute-lft-out`
11×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`log-pow` `div-inv` `distribute-lft-out--` `difference-of-squares`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`frac-times` `log-prod` `flip3-+` `associate-*l/` `flip-+`
2×	`rem-sqrt-square` `distribute-lft1-in` `frac-add` `distribute-rgt1-in` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `asin-acos` `exp-prod` `sqrt-pow1` `exp-to-pow` `pow1/2` `count-2` `sqrt-div` `div-exp` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 136

Calls

4 calls:

46.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
4.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
13.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
21.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
50.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
155.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.2s

Counts

148 → 148

Iterations

Iter	Nodes
done	2042
3	2042
2	1700
1	629
0	291

prune737.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
1.2b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))))))
1.5b	(* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))
8.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l))))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
44×	`prod-exp`
34×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
21×	`sqrt-prod`
19×	`*-un-lft-identity` `times-frac` `div-exp`
18×	`cbrt-unprod`
16×	`add-cube-cbrt`
13×	`frac-times`
10×	`pow1`
9×	`cbrt-undiv` `associate-*r/`
7×	`associate-l` `associate-*l/`
6×	`rec-exp` `1-exp` `difference-of-squares`
5×	`flip3-+` `flip-+`
4×	`frac-add` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow-prod-down`
2×	`rem-sqrt-square` `associate-/r/` `div-inv`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `associate-r` `*-commutative`

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))))))
97.0ms	(* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))
13.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l))))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt l)
18.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))))))
67.0ms	(* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l)))
157.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (/ 1 (* (cbrt l) (cbrt l))) (* (+ (/ t (cbrt l)) (/ t (cbrt l))) (/ t l))))))

simplify1.3s

Counts

131 → 131

Iterations

Iter	Nodes
done	2001
2	2001
1	730
0	290

prune767.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.1b

localize62.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
9.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
9.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
9.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`sqrt-prod`
19×	`*-un-lft-identity`
16×	`times-frac` `add-cube-cbrt`
9×	`cbrt-prod`
6×	`difference-of-squares`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

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

series477.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
107.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
104.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
99.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))

simplify1.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
4	2000
3	1940
2	573
1	266
0	143

prune651.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.1b

regimes557.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	3875×	body	160	valid
1.5s	8113×	body	80	nan
833.0ms	4125×	body	80	valid