Details

sample102.0ms

Algorithm

intervals

Results

27.0ms	260×	body	80	nan
20.0ms	122×	body	160	valid
12.0ms	134×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	265	19
5	798	19
6	3016	19
done	5001	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 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))))
11.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite181.0ms

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×	`cbrt-undiv` `pow-to-exp` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `clear-num` `flip--`

Counts

4 → 130

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
96.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
57.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series934.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
345.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
490.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.1s

Counts

142 → 142

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	308	3657
1	633	3542
2	1484	3367
3	4468	3355
done	5000	3352

prune896.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
0.6b	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
11.0b	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `times-frac`
16×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `associate-/r/`
13×	`unpow-prod-down`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`associate-r/` `associate-l/` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `div-exp` `div-inv` `difference-of-squares`
2×	`cbrt-undiv` `pow-exp` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
62.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
53.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow (/ Om Omc) 2.0)
49.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
748.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
1.2s	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify1.3s

Counts

109 → 109

Iterations

Useful iterations: 2 (415.0ms)

Iter	Nodes	Cost
0	299	3802
1	786	3283
2	2916	2986
done	5000	2986

prune706.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) (* 2 2.0))
0.3b	(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
0.6b	(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
11.3b	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
52×	`add-sqr-sqrt`
47×	`sqrt-prod`
32×	`add-cube-cbrt` `*-un-lft-identity`
23×	`unpow-prod-down`
20×	`difference-of-squares`
18×	`sqrt-div`
12×	`flip3-+` `flip-+`
10×	`associate-/l*`
9×	`add-exp-log`
8×	`pow1` `frac-times` `associate-/r/`
6×	`add-cbrt-cube` `sqr-pow`
4×	`associate-r/` `associate-l/` `associate-/r*` `add-log-exp`
2×	`sqrt-pow1` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `pow-unpow` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `pow1/2` `pow-prod-down` `clear-num` `flip--`

Counts

4 → 130

Calls

4 calls:

9.0ms	(pow (/ Om Omc) (* 2 2.0))
1.0ms	(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
115.0ms	(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
28.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (/ Om Omc) (* 2 2.0))
28.0ms	(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
644.0ms	(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
465.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

simplify1.1s

Counts

142 → 142

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	353	5383
1	739	5144
2	2058	4877
done	5000	4839

prune949.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

localize52.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
7.4b	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
11.3b	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
11.3b	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-div`
24×	`flip3-+` `flip-+`
18×	`pow1`
16×	`frac-times` `sqrt-pow1`
12×	`sqrt-prod`
8×	`add-sqr-sqrt` `associate-r/` `associate-l/`
6×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
4×	`add-exp-log` `pow-prod-down` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 88

Calls

4 calls:

25.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
28.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
30.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
36.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
293.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
495.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
462.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

simplify830.0ms

Counts

100 → 100

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	145	3104
1	339	2728
2	1077	2604
done	5000	2594

prune870.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

regimes611.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	24	35
done	24	35

end0.0ms

sample2.5s

Algorithm

intervals

Results

648.0ms	8238×	body	80	nan
596.0ms	3815×	body	160	valid
324.0ms	4185×	body	80	valid