Details

sample189.0ms

Algorithm

intervals

Results

77.0ms	284×	body	80	nan
54.0ms	126×	body	160	valid
27.0ms	130×	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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.6b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.8b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite57.0ms

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:

13.0ms	(* (/ Om Omc) (/ Om Omc))
26.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
14.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ Om Omc) (/ Om Omc))
110.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
21.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
140.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify920.0ms

Counts

164 → 164

Iterations

Iter	Nodes
2	2110
1	708
0	267

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.6b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.7b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite46.0ms

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:

24.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
3.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ Om Omc) (/ Om Omc))
146.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
20.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
110.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify3.0s

Counts

185 → 185

Iterations

Iter	Nodes
3	6232
2	1862
1	677
0	281

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.6b	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
2.5b	(log (exp (* (/ Om Omc) (/ Om Omc))))
7.7b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
70×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
60×	`times-frac`
42×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1`
10×	`log-pow` `associate-/l*`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`log-prod`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `exp-prod` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `exp-to-pow` `pow1/2` `div-exp` `rem-log-exp` `div-inv` `flip--`

Counts

4 → 134

Calls

4 calls:

32.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
3.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
17.0ms	(asin (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
30.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
83.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify864.0ms

Counts

146 → 146

Iterations

Iter	Nodes
3	2347
2	741
1	347
0	201

prune3.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize82.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.7b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.3b	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
9.3b	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

7.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.0ms	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0ms	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
88.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
182.0ms	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
187.0ms	(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify3.6s

Counts

88 → 88

Iterations

Iter	Nodes
4	4491
3	1360
2	418
1	169
0	84

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

regimes611.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	32
1	32
0	29

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	3829×	body	160	valid
1.6s	8015×	body	80	nan
851.0ms	4171×	body	80	valid