Details

sample169.0ms

Algorithm

intervals

Results

60.0ms	129×	body	80	valid
29.0ms	247×	body	80	nan
27.0ms	127×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	101	19
4	277	19
5	1551	19
done	5001	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite135.0ms

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:

6.0ms	(pow (/ t l) 2.0)
79.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
43.0ms	(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:

70.0ms	(pow (/ t l) 2.0)
352.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
38.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
567.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.2s

Counts

142 → 142

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	317	3657
1	755	3534
2	2435	3369
done	5000	3367

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
6.8b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
58.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
4.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

59.0ms	(asin (sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
595.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
275.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
261.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify604.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	124	1871
1	255	1741
2	880	1378
done	5000	1378

prune673.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

localize63.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
15×	`sqrt-prod`
13×	`pow1`
11×	`add-sqr-sqrt` `sqrt-pow1`
10×	`*-un-lft-identity`
9×	`cbrt-prod` `flip3-+` `pow1/3` `add-cube-cbrt` `flip-+` `pow-flip`
8×	`associate-/r/`
5×	`times-frac`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `pow1/2` `sqrt-div` `div-inv` `inv-pow`

Counts

4 → 77

Calls

4 calls:

39.0ms	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

440.0ms	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
394.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
364.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
392.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: 3 (711.0ms)

Iter	Nodes	Cost
0	142	2121
1	289	1879
2	752	1754
3	3511	1739
done	5001	1739

prune743.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

localize77.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
56×	`times-frac`
54×	`sqrt-prod`
41×	`*-un-lft-identity`
31×	`cbrt-prod`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 101

Calls

4 calls:

2.0ms	(asin (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
74.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

36.0ms	(asin (* (/ 1 (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
585.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
387.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
435.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify871.0ms

Counts

113 → 113

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	302	3717
1	562	3588
2	1495	3386
done	5001	3376

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.8b

regimes1.5s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	18	19
done	18	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	3791×	body	160	valid
1.1s	7987×	body	80	nan
688.0ms	4209×	body	80	valid