Details

sample56.0ms

Algorithm

intervals

Results

14.0ms	251×	body	80	nan
14.0ms	123×	body	160	valid
8.0ms	133×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	106	18
4	252	18
5	760	18
6	2815	18
done	5000	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
28×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 112

Calls

4 calls:

3.0ms	(pow (/ Om Omc) 2.0)
4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ Om Omc) 2.0)
59.0ms	(pow (/ t l) 2.0)
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
263.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify834.0ms

Counts

124 → 124

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	319	2298
1	586	2196
2	1363	2088
done	5000	2062

prune493.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
4.1b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
22×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp`

Counts

4 → 107

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
67.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
11.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
64.0ms	(log (exp (pow (/ Om Omc) 2.0)))
265.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.1s

Counts

119 → 119

Iterations

Useful iterations: 3 (994.0ms)

Iter	Nodes	Cost
0	301	2146
1	515	1868
2	1211	1755
3	4675	1723
done	5000	1723

prune468.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
4.1b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `log-pow`
17×	`exp-prod`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `sqrt-prod`
2×	`pow-exp` `div-inv` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series244.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ t l) 2.0)
12.0ms	(asin (fabs (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
66.0ms	(log (exp (pow (/ Om Omc) 2.0)))
104.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: 3 (962.0ms)

Iter	Nodes	Cost
0	254	1275
1	437	1122
2	1052	1037
3	3972	1035
done	5000	1035

prune471.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
1.3b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
13.5b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
13.5b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
86×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
31×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 135

Calls

4 calls:

0.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
31.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
13.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
13.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
308.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
309.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
311.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify953.0ms

Counts

147 → 147

Iterations

Useful iterations: 3 (328.0ms)

Iter	Nodes	Cost
0	251	4840
1	399	4725
2	785	4553
3	2335	4489
done	5000	4489

prune784.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.3b

regimes493.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

460.0ms	7939×	body	80	nan
440.0ms	3848×	body	160	valid
239.0ms	4152×	body	80	valid