Details

sample202.0ms

Algorithm

intervals

Results

67.0ms	122×	body	160	valid
66.0ms	276×	body	80	nan
32.0ms	134×	body	80	valid

simplify1.4s

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: 7.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
0.2b	(* (+ (/ t l) (/ t l)) (/ t l))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite128.0ms

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:

25.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
79.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
16.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ Om Omc) (/ Om Omc))
21.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
45.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
209.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify1.4s

Counts

195 → 195

Iterations

Iter	Nodes
done	2002
2	2002
1	972
0	370

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
0.2b	(* (+ (/ t l) (/ t l)) (/ t l))
0.3b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
7.5b	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
92×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
65×	`sqrt-prod`
36×	`associate-l`
15×	`distribute-rgt-out`
14×	`difference-of-squares`
13×	`associate-r` `distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l*`
7×	`pow1`
6×	`associate-/r*` `sqrt-div` `div-inv`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`frac-times` `associate-*l/`
2×	`cbrt-undiv` `distribute-lft1-in` `div-exp` `frac-add` `distribute-rgt1-in` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `count-2` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 177

Calls

4 calls:

2.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
67.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
12.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
3.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
63.0ms	(* (+ (/ t l) (/ t l)) (/ t l))
196.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
114.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

simplify1.8s

Counts

189 → 189

Iterations

Iter	Nodes
done	2001
3	2001
2	1647
1	667
0	316

prune976.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize67.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ 1 (* (* (cbrt (* (+ (/ t l) (/ t l)) (/ t l))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l)))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l))))))
27.6b	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
27.6b	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
27.6b	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

3.0ms	(sqrt (+ 1 (* (* (cbrt (* (+ (/ t l) (/ t l)) (/ t l))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l)))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l))))))
15.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
14.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
16.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (+ 1 (* (* (cbrt (* (+ (/ t l) (/ t l)) (/ t l))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l)))) (cbrt (* (+ (/ t l) (/ t l)) (/ t l))))))
176.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
158.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))
142.0ms	(cbrt (* (+ (/ t l) (/ t l)) (/ t l)))

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	2009
4	2009
3	1508
2	478
1	227
0	117

prune567.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (fabs (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
3.2b	(sqrt (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
14.3b	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
14.3b	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

58×	`sqrt-prod`
38×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-cube-cbrt`
11×	`associate-/l*`
10×	`cbrt-prod`
8×	`difference-of-squares`
6×	`cbrt-div` `add-cbrt-cube` `sqrt-div` `add-exp-log`
5×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*` `flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `pow1/2` `div-exp` `div-inv` `flip--`

Counts

4 → 111

Calls

4 calls:

15.0ms	(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (fabs (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
6.0ms	(sqrt (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
3.0ms	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
3.0ms	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (fabs (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
183.0ms	(sqrt (cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
184.0ms	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
183.0ms	(cbrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

simplify1.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	2000
3	2000
2	994
1	429
0	239

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.6b

regimes514.0ms

Accuracy

97.9% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.1b

bsearch3.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.0s	3797×	body	160	valid
1.6s	8081×	body	80	nan
1.1s	4203×	body	80	valid