Details

sample142.0ms

Algorithm

intervals

Results

55.0ms	124×	body	160	valid
38.0ms	236×	body	80	nan
21.0ms	132×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	3345
5	901
4	307
3	122
2	59
1	32
0	16

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
9.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
81×	`times-frac`
77×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
26×	`sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
11×	`distribute-lft-out`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`associate-/r*` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `asin-acos` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `sqrt-div` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 163

Calls

4 calls:

17.0ms	(* (/ Om Omc) (/ Om Omc))
41.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
34.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (/ Om Omc) (/ Om Omc))
84.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))
15.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
165.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

simplify910.0ms

Counts

175 → 175

Iterations

Iter	Nodes
2	2093
1	710
0	267

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
9.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
21×	`sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `asin-acos` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `sqrt-div` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 152

Calls

4 calls:

20.0ms	(* (/ Om Omc) (/ Om Omc))
119.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
108.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ Om Omc) (/ Om Omc))
106.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
21.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
198.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

simplify785.0ms

Counts

164 → 164

Iterations

Iter	Nodes
2	2111
1	709
0	267

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1)))
0.7b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
9.2b	(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
85×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
65×	`add-cube-cbrt` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
8×	`associate-/l*`
6×	`associate-/r*` `sqrt-div`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 173

Calls

4 calls:

26.0ms	(* (/ Om Omc) (/ Om Omc))
71.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1)))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
72.0ms	(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

series349.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ Om Omc) (/ Om Omc))
166.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1)))
19.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))))
116.0ms	(sqrt (+ (* (* (/ t l) (/ t l)) 2) 1))

simplify2.9s

Counts

185 → 185

Iterations

Iter	Nodes
3	6062
2	1847
1	673
0	281

prune2.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ l t) (/ l t))
0.4b	(/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))
0.7b	(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))))
9.0b	(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

707×	`times-frac`
669×	`*-un-lft-identity`
533×	`add-sqr-sqrt`
227×	`add-cube-cbrt`
157×	`sqrt-prod`
149×	`distribute-lft-out`
144×	`difference-of-squares`
38×	`associate-/r*`
36×	`distribute-lft-out--`
21×	`add-cbrt-cube` `add-exp-log`
20×	`associate-/r/`
15×	`div-inv`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
9×	`flip3--` `flip--`
7×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square`
2×	`associate-/l/`
1×	`pow2` `frac-times` `asin-acos` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 460

Calls

4 calls:

19.0ms	(* (/ l t) (/ l t))
49.0ms	(/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))
1.0ms	(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))))
28.0ms	(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc)))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ l t) (/ l t))
100.0ms	(/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))
12.0ms	(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc))))))
196.0ms	(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (/ 2 (* (/ l t) (/ l t)))) (- 1 (/ Om Omc)))))

simplify2.0s

Counts

472 → 472

Iterations

Iter	Nodes
2	4329
1	1390
0	601

prune6.4s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes645.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.2b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	30
1	30
0	25

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	7937×	body	80	nan
1.6s	3805×	body	160	valid
810.0ms	4195×	body	80	valid