Details

sample118.0ms

Algorithm

intervals

Results

31.0ms	121×	body	160	valid
27.0ms	225×	body	80	nan
16.0ms	135×	body	80	valid

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	16	19
1	39	19
2	159	18
3	1282	18
done	5001	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`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` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `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 → 138

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
94.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
70.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow (/ t l) 2.0)
351.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
33.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
602.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.7s

Counts

150 → 150

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	325	3783
1	2107	3650
done	5002	3331

prune974.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b	(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.8b	(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
10.3b	(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

143.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.0ms	(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms	(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
2.0ms	(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

series851.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
248.0ms	(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
16.0ms	(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
345.0ms	(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

simplify5.1s

Counts

100 → 100

Iterations

Useful iterations: done (5.1s)

Iter	Nodes	Cost
0	170	2462
1	781	2311
done	5000	2162

prune545.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize51.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
29.5b	(cbrt (pow (/ t l) 2.0))
29.5b	(cbrt (pow (/ t l) 2.0))
29.5b	(cbrt (pow (/ t l) 2.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 125

Calls

4 calls:

67.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
10.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))
10.0ms	(cbrt (pow (/ t l) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

482.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
391.0ms	(cbrt (pow (/ t l) 2.0))
384.0ms	(cbrt (pow (/ t l) 2.0))
460.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.3s

Counts

137 → 137

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	273	4113
1	1045	3957
done	5000	2719

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.6b

localize53.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
19.4b	(sqrt (pow (/ Om Omc) 2.0))
19.4b	(sqrt (pow (/ Om Omc) 2.0))

rewrite57.0ms

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:

3.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
3.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
29.0ms	(sqrt (pow (/ Om Omc) 2.0))
16.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
151.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
417.0ms	(sqrt (pow (/ Om Omc) 2.0))
505.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify14.0s

Counts

106 → 106

Iterations

Useful iterations: done (14.0s)

Iter	Nodes	Cost
0	171	1478
1	587	1364
done	5001	1338

prune788.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 11.6b

regimes569.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	3767×	body	160	valid
1.0s	7895×	body	80	nan
611.0ms	4233×	body	80	valid