Details

sample153.0ms

Algorithm

intervals

Results

57.0ms	130×	body	160	valid
46.0ms	277×	body	80	nan
20.0ms	126×	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite53.0ms

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:

18.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
21.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ Om Omc) (/ Om Omc))
19.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
96.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
134.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify1.1s

Counts

164 → 164

Iterations

Iter	Nodes
2	2120
1	708
0	267

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
12.4b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite63.0ms

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:

25.0ms	(* (/ Om Omc) (/ Om Omc))
2.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
25.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ Om Omc) (/ Om Omc))
17.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
145.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
90.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify2.8s

Counts

185 → 185

Iterations

Iter	Nodes
3	6139
2	1857
1	677
0	281

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

rewrite184.0ms

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:

23.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
67.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
88.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ Om Omc) (/ Om Omc))
20.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
132.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))
178.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

simplify1.0s

Counts

164 → 164

Iterations

Iter	Nodes
2	2096
1	702
0	267

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize39.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
6.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

136×	`sqrt-prod`
68×	`add-sqr-sqrt`
64×	`times-frac`
54×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

4 → 148

Calls

4 calls:

10.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
14.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
24.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
285.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
157.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
139.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify932.0ms

Counts

160 → 160

Iterations

Iter	Nodes
3	2379
2	767
1	366
0	206

prune3.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

regimes634.0ms

Accuracy

98.4% (0.1b remaining)

Error of 5.3b against oracle of 5.3b and baseline of 9.5b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	25

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.3s	3859×	body	160	valid
1.8s	8015×	body	80	nan
884.0ms	4141×	body	80	valid