Details

sample140.0ms

Algorithm

intervals

Results

35.0ms	255×	body	80	nan
31.0ms	111×	body	160	valid
20.0ms	145×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
8.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

rewrite165.0ms

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:

10.0ms	(pow (/ t l) 2.0)
67.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
73.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

series964.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (/ t l) 2.0)
319.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))
39.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
511.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))

simplify1.3s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	2435
1	755
0	317

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.9b	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))
8.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.2b	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
647×	`sqrt-prod`
560×	`add-sqr-sqrt`
325×	`*-un-lft-identity`
253×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
19×	`sqrt-div`
14×	`associate-/r/`
9×	`rem-sqrt-square` `flip3-+` `flip-+`
7×	`pow1` `div-inv`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos`

Counts

4 → 385

Calls

4 calls:

1.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))
123.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

38.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))))
472.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))))
257.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
249.0ms	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

simplify832.0ms

Counts

397 → 397

Iterations

Iter	Nodes
done	5000
1	1617
0	904

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize73.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.9b	(sqrt (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.2b	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

95×	`sqrt-prod`
88×	`add-sqr-sqrt`
56×	`times-frac`
43×	`*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
11×	`sqrt-div`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
2×	`associate-/r/`
1×	`div-inv`

Counts

4 → 118

Calls

4 calls:

49.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.0ms	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

483.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
388.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0))))
263.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
276.0ms	(sqrt (+ 1.0 (* (pow (/ t l) 2.0) 2.0)))

simplify760.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1493
1	548
0	293

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize83.0ms

Local error

Found 4 expressions with local error:

9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 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))))

series1.3s

Counts

4 → 12

Calls

4 calls:

311.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
244.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
371.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
419.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	3901
2	658
1	195
0	86

prune994.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.1b

regimes2.3s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	8231×	body	80	nan
1.1s	3798×	body	160	valid
628.0ms	4202×	body	80	valid