Details

sample199.0ms

Algorithm

intervals

Results

85.0ms	127×	body	160	valid
34.0ms	247×	body	80	nan
18.0ms	129×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	108	18
4	292	18
5	1583	18
done	5001	18

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
6.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite154.0ms

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×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 134

Calls

4 calls:

10.0ms	(pow (/ t l) 2.0)
91.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
43.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow (/ t l) 2.0)
298.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
413.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify985.0ms

Counts

146 → 146

Iterations

Useful iterations: 2 (326.0ms)

Iter	Nodes	Cost
0	285	3461
1	628	3355
2	1798	3196
done	5001	3196

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.7b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
6.8b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

rewrite99.0ms

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×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `flip--`

Counts

4 → 107

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
87.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
2.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

116.0ms	(pow (/ t l) 2.0)
238.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
27.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
1.5s	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

simplify973.0ms

Counts

119 → 119

Iterations

Useful iterations: done (965.0ms)

Iter	Nodes	Cost
0	270	2588
1	648	2424
2	1889	2295
done	5000	2289

prune948.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
6.8b	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
7.1b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
7.1b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(asin (sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
7.0ms	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series866.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(asin (sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
512.0ms	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
153.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
186.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify698.0ms

Counts

67 → 67

Iterations

Useful iterations: done (691.0ms)

Iter	Nodes	Cost
0	105	1590
1	173	1397
2	358	1237
3	1101	951
done	5001	930

prune565.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize59.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
7.6b	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
7.6b	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
7.6b	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`add-sqr-sqrt` `sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 63

Calls

4 calls:

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

series702.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
158.0ms	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
158.0ms	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
231.0ms	(cbrt (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify1.2s

Counts

75 → 75

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	72	1179
1	121	1096
2	227	1021
3	604	1012
4	2468	976
done	5000	960

prune755.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.8b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	7987×	body	80	nan
1.1s	3791×	body	160	valid
1.0s	4209×	body	80	valid