Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	254×	body	80	nan
13.0ms	116×	body	160	valid
8.0ms	140×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	108	18
4	279	18
5	835	18
6	3116	18
done	5000	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
28×	`sqrt-prod` `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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `div-exp` `pow-exp` `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 → 134

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
64.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
3.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
34.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ t l) 2.0)
180.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
12.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
294.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.3s

Counts

146 → 146

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	285	3461
1	527	3355
2	1126	3196
3	3232	3196
done	5001	3193

prune575.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
10.4b	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-div`
2×	`rem-sqrt-square`
1×	`frac-times` `asin-acos` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 56

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
163.0ms	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 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))
2.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series527.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
294.0ms	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
109.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
109.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify2.2s

Counts

68 → 68

Iterations

Useful iterations: 5 (1.4s)

Iter	Nodes	Cost
0	109	1947
1	184	1825
2	321	1048
3	706	976
4	1666	958
5	4046	950
done	5000	950

prune262.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.5b

localize22.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (* (/ 1 (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
17.1b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
17.1b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
17.1b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-div`
2×	`sqrt-pow1`
1×	`frac-times` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod`

Counts

4 → 55

Calls

4 calls:

56.0ms	(sqrt (* (/ 1 (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series746.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(sqrt (* (/ 1 (* (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
132.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
129.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
130.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.3s

Counts

67 → 67

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	94	1415
1	168	1299
2	332	1003
3	865	961
4	2506	925
done	5000	915

prune306.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.5b

localize31.0ms

Local error

Found 4 expressions with local error:

10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.9b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series442.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
109.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
108.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
113.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: 5 (780.0ms)

Iter	Nodes	Cost
0	54	924
1	93	808
2	163	772
3	384	772
4	943	736
5	2465	720
done	5000	720

prune357.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.5b

regimes336.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	48
1	21	48
done	21	48

end0.0ms

sample1.8s

Algorithm

intervals

Results

474.0ms	8153×	body	80	nan
438.0ms	3789×	body	160	valid
243.0ms	4211×	body	80	valid