Details

sample74.0ms

Algorithm

intervals

Results

19.0ms	257×	body	80	nan
16.0ms	109×	body	160	valid
11.0ms	147×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2725
5	723
4	243
3	97
2	49
1	29
0	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.6b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 130

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
75.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
69.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series935.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (/ t l) 2.0)
24.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
342.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
465.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	1754
1	745
0	317

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.8b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

713×	`times-frac`
674×	`sqrt-prod`
641×	`add-sqr-sqrt`
364×	`*-un-lft-identity`
278×	`add-cube-cbrt`
172×	`difference-of-squares`
86×	`unpow-prod-down`
43×	`distribute-lft-out--` `sqr-pow`
21×	`sqrt-div`
16×	`associate-/r/`
10×	`flip3-+` `flip-+`
9×	`rem-sqrt-square`
8×	`div-inv` `associate-/l*`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `flip--`

Counts

4 → 456

Calls

4 calls:

83.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
107.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

513.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
287.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
491.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify3.1s

Counts

468 → 468

Iterations

Iter	Nodes
done	5001
2	3291
1	1523
0	873

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 10.8b

localize146.0ms

Local error

Found 4 expressions with local error:

10.0b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.1b	(sqrt (/ 1 (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`sqrt-prod`
13×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-div`
8×	`sqrt-pow1`
6×	`cbrt-prod`
4×	`cbrt-div` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `times-frac` `pow1/2`
2×	`pow1/3` `associate-*l/` `associate-/r/` `pow-flip`
1×	`pow-prod-down` `div-inv` `inv-pow`

Counts

4 → 70

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
18.0ms	(sqrt (/ 1 (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
502.0ms	(sqrt (/ 1 (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
312.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
318.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1095
1	376
0	182

prune849.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 10.8b

localize74.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.1b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
66×	`sqrt-prod`
56×	`times-frac`
42×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`pow1`
6×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate-/r/` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

1.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
36.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
59.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
62.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
420.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
472.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	2251
2	808
1	390
0	205

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.8b

regimes1.9s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	7945×	body	80	nan
1.2s	3771×	body	160	valid
540.0ms	4229×	body	80	valid