Details

sample63.0ms

Algorithm

intervals

Results

17.0ms	127×	body	160	valid
17.0ms	241×	body	80	nan
9.0ms	129×	body	80	valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 10.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite42.0ms

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×	`associate-/r/` `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 → 130

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
13.0ms	(/ (- 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))))))
18.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
213.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
330.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774

prune592.0ms

Filtered

142 candidates to 114 candidates (80.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 10.6b

Counts

143 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.4b	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `asin-acos` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
19.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
386.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
320.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	265	790
1	811	728
2	3959	726
3	5002	726

prune323.0ms

Filtered

64 candidates to 54 candidates (84.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	63	9	72

Merged error: 10.6b

Counts

72 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))))
9.4b	(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
16.0b	(sqrt (pow (/ Om Omc) 2.0))
16.0b	(sqrt (pow (/ Om Omc) 2.0))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

621×	`sqrt-prod`
533×	`times-frac`
481×	`add-sqr-sqrt`
431×	`*-un-lft-identity`
167×	`add-cube-cbrt`
150×	`difference-of-squares`
102×	`distribute-lft-out`
90×	`unpow-prod-down`
34×	`sqr-pow`
30×	`distribute-lft-out--`
11×	`rem-sqrt-square` `associate-/r/`
8×	`div-inv`
5×	`pow1` `flip3--` `flip--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos` `sqrt-div`

Counts

4 → 341

Calls

4 calls:

1.0ms	(asin (sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))))
56.0ms	(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

44.0ms	(asin (sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))))
630.0ms	(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
263.0ms	(sqrt (pow (/ Om Omc) 2.0))
265.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify178.0ms

Algorithm

egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1199	10664
1	4952	10436
2	5002	10436

prune1.1s

Filtered

353 candidates to 159 candidates (45.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	351	2	353
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	353	9	362

Merged error: 10.6b

Counts

362 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

3.0ms	(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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	140	600
1	436	584
2	1753	584
3	5002	580

prune419.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 10.6b

Counts

81 → 9

regimes633.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms

sample1.9s

Algorithm

intervals

Results

570.0ms	8130×	body	80	nan
538.0ms	3742×	body	160	valid
304.0ms	4258×	body	80	valid