Details

sample174.0ms

Algorithm

intervals

Results

69.0ms	129×	body	160	valid
52.0ms	267×	body	80	nan
26.0ms	127×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

26.0ms	(* (/ Om Omc) (/ Om Omc))
38.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
16.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ Om Omc) (/ Om Omc))
57.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
21.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
176.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.2s

Counts

195 → 195

Iterations

Iter	Nodes
done	2002
2	2002
1	971
0	370

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

42.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
7.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
14.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
16.0ms	(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
46.0ms	(log (exp (* (/ Om Omc) (/ Om Omc))))
167.0ms	(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.4s

Counts

148 → 148

Iterations

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

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

12.0ms	(* (/ Om Omc) (/ Om Omc))
34.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
3.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

series138.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ Om Omc) (/ Om Omc))
38.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
11.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
62.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

simplify854.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	2002
2	2002
1	860
0	304

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.9b

localize42.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
7.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
7.1b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
7.1b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))

rewrite67.0ms

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:

15.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
15.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
17.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
16.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
153.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
315.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
254.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))

simplify1.1s

Counts

160 → 160

Iterations

Iter	Nodes
done	2001
3	2001
2	810
1	365
0	206

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.9b

regimes378.0ms

Accuracy

98.3% (0.1b remaining)

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

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	8206×	body	80	nan
1.5s	3807×	body	160	valid
1.2s	4193×	body	80	valid