Details

sample62.0ms

Algorithm

intervals

Results

15.0ms	260×	body	80	nan
14.0ms	122×	body	160	valid
8.0ms	134×	body	80	valid

simplify122.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10
done	5002	10

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)))))

rewrite116.0ms

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:

6.0ms	(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))))))
59.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
44.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
229.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
344.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	634	1882
1	2017	1787
2	5001	1774
done	5001	1774

prune582.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize19.0ms

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)))))

rewrite90.0ms

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:

8.0ms	(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))))))
43.0ms	(/ (- (* 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))))
35.0ms	(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)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
31.0ms	(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))))))
625.0ms	(/ (- (* 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))))
799.0ms	(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)))))

simplify85.0ms

Counts

109 → 109

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	789	1849
1	3446	1677
2	5003	1677
done	5003	1677

prune500.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

localize20.0ms

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)))) (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) 2.0) (pow (/ Om Omc) 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))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (/ (sqrt (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
42.0ms	(/ (sqrt (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
22.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ Om Omc) 2.0)
31.0ms	(asin (/ (sqrt (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
807.0ms	(/ (sqrt (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
361.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

simplify78.0ms

Counts

129 → 129

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	699	2489
1	2640	2361
2	5001	2361
done	5001	2361

prune595.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

localize29.0ms

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))))

rewrite99.0ms

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:

24.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
27.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
23.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
22.0ms	(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:

243.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
240.0ms	(sqrt (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))
362.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
369.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))

simplify46.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	336	1526
1	1143	1492
2	5001	1486
done	5001	1486

prune606.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

regimes436.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18
done	24	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

476.0ms	8238×	body	80	nan
454.0ms	3815×	body	160	valid
247.0ms	4185×	body	80	valid