Details

sample165.0ms

Algorithm

intervals

Results

57.0ms	273×	body	80	nan
37.0ms	124×	body	160	valid
19.0ms	132×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 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))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite169.0ms

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 (/ Om Omc) 2.0)
114.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
7.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
36.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series787.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow (/ Om Omc) 2.0)
231.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
456.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.0s

Counts

146 → 146

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	276	3461
1	512	3355
2	1095	3196
3	3178	3184
done	5001	3181

prune772.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
9.0b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
37×	`times-frac`
34×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`unpow-prod-down`
16×	`difference-of-squares`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `sqrt-prod`
2×	`div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `flip--`

Counts

4 → 107

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
126.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
3.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow (/ Om Omc) 2.0)
212.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
15.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
1.3s	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

simplify2.2s

Counts

119 → 119

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	253	2588
1	511	2426
2	1162	2288
3	3398	2273
done	5001	2268

prune535.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.8b

localize41.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.4b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`div-inv`

Counts

4 → 94

Calls

4 calls:

2.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
3.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
15.0ms	(sqrt (pow (/ Om Omc) 2.0))
14.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

175.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
145.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
400.0ms	(sqrt (pow (/ Om Omc) 2.0))
385.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	171	1478
1	320	1364
2	606	1338
3	1346	1338
4	3326	1320
done	5001	1312

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.8b

localize42.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
13.9b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

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))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))
10.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
174.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
425.0ms	(sqrt (pow (/ Om Omc) 2.0))
416.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify2.5s

Counts

102 → 102

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	171	1478
1	329	1404
2	620	1356
3	1358	1350
4	3344	1332
done	5001	1324

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.8b

regimes660.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	3695×	body	160	valid
1.1s	8083×	body	80	nan
1.0s	4305×	body	80	valid