Details

sample62.0ms

Algorithm

intervals

Results

16.0ms	245×	body	80	nan
16.0ms	125×	body	160	valid
9.0ms	131×	body	80	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite39.0ms

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:

4.0ms	(pow (/ t l) 2.0)
16.0ms	(/ (- 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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ t l) 2.0)
212.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
312.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune614.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms

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:

5.0ms	(pow (/ t l) 2.0)
17.0ms	(/ (- 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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
212.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune799.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

713×	`times-frac`
674×	`sqrt-prod`
641×	`add-sqr-sqrt`
364×	`*-un-lft-identity`
278×	`add-cube-cbrt`
172×	`difference-of-squares`
86×	`unpow-prod-down`
43×	`distribute-lft-out--` `sqr-pow`
21×	`sqrt-div`
16×	`associate-/r/`
10×	`flip3-+` `flip-+`
9×	`rem-sqrt-square`
8×	`div-inv` `associate-/l*`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--`

Counts

4 → 464

Calls

4 calls:

21.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series984.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
176.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
171.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
315.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify186.0ms

Algorithm

egg-herbie

Counts

476 → 476

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1572	14491
1	4817	14013
2	5001	14001

prune1.3s

Filtered

476 candidates to 196 candidates (41.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.4b

localize34.0ms

Local error

Found 4 expressions with local error:

15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.3b	(sqrt (pow (/ Om Omc) 2.0))
18.3b	(sqrt (pow (/ Om Omc) 2.0))

rewrite21.0ms

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` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 94

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))
8.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
265.0ms	(sqrt (pow (/ Om Omc) 2.0))
263.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	379	880
1	1012	844
2	4180	836
3	5001	834

prune884.0ms

Filtered

106 candidates to 92 candidates (86.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.4b

regimes651.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	19
1	22	19

end0.0ms

sample1.9s

Algorithm

intervals

Results

566.0ms	8227×	body	80	nan
521.0ms	3766×	body	160	valid
308.0ms	4234×	body	80	valid