Details

sample60.0ms

Algorithm

intervals

Results

15.0ms	251×	body	80	nan
14.0ms	111×	body	160	valid
9.0ms	145×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	107	18
4	266	18
5	839	18
6	3147	18
done	5000	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite43.0ms

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:

4.0ms	(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))))
30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ Om Omc) 2.0)
62.0ms	(pow (/ t l) 2.0)
11.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
267.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify619.0ms

Counts

124 → 124

Iterations

Useful iterations: done (614.0ms)

Iter	Nodes	Cost
0	319	2298
1	590	2196
2	1568	2088
done	5001	2082

prune526.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
8.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

rewrite42.0ms

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 (pow (/ t l) 2.0) 1) 1.0))))
30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
60.0ms	(pow (/ t l) 2.0)
11.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0))))
271.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (pow (/ t l) 2.0) 1) 1.0)))

simplify742.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	321	2460
1	595	2196
2	1610	2088
done	5000	2088

prune644.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-div` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 155

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
43.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series458.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ t l) 2.0)
275.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
11.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
106.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify640.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (173.0ms)

Iter	Nodes	Cost
0	300	4354
1	513	4047
2	1350	3908
done	5000	3908

prune634.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.7b	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
14.8b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
14.8b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`asin-acos` `pow1/2`

Counts

4 → 56

Calls

4 calls:

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

series428.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
125.0ms	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
145.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
139.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify829.0ms

Counts

68 → 68

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	112	1316
1	201	1261
2	437	1115
3	1301	1109
done	5000	1082

prune327.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

regimes402.0ms

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	16	19
done	16	19

end0.0ms

sample1.8s

Algorithm

intervals

Results

518.0ms	8170×	body	80	nan
497.0ms	3852×	body	160	valid
268.0ms	4148×	body	80	valid