Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	119×	body	160	valid
15.0ms	211×	body	80	nan
10.0ms	137×	body	80	valid

simplify121.0ms

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	4432	10
6	5002	10

prune3.0ms

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: 11.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.6b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`sqrt-div`
4×	`associate-/r/` `associate-/l/`
3×	`sqrt-prod` `div-inv`
2×	`flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+`
1×	`pow-to-exp` `unpow-prod-down` `asin-acos` `pow1/2` `div-sub` `sqr-pow`

Counts

4 → 21

Calls

4 calls:

2.0ms	(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))))))
5.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(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))))))
201.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
323.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	303	309
1	856	300
2	3763	296
3	5001	296

prune179.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Merged error: 11.0b

Counts

34 → 4

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
0.7b	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
10.1b	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

19×	`sqrt-prod`
18×	`sqrt-div`
13×	`sqr-pow`
12×	`flip3-+` `flip-+`
8×	`frac-times` `associate-/r/`
6×	`times-frac` `difference-of-squares`
5×	`*-commutative`
4×	`unpow-prod-down` `associate-r/` `associate-l/`
3×	`difference-cubes` `associate-/l*`
2×	`associate-/r*` `div-inv` `associate-/l/`
1×	`pow-to-exp` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `pow1/2` `clear-num` `flip--`

Counts

4 → 40

Calls

4 calls:

2.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
22.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
17.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ t l) 2.0)
42.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
864.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
507.0ms	(sqrt (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	607	1288
1	2391	1271
2	5002	1270

prune334.0ms

Filtered

52 candidates to 48 candidates (92.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	52	4	56

Merged error: 11.0b

Counts

56 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0))
10.1b	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0)))
15.2b	(/ (pow t 2) (pow l 2))
15.9b	(/ (pow Om 2) (pow Omc 2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`unpow2` `sqr-pow`
8×	`times-frac`
5×	`sqrt-div`
4×	`pow-to-exp` `frac-2neg` `clear-num` `associate-/r` `associate-/r/` `div-inv` `associate-/l/` `associate-/l`
3×	`sqrt-prod`
2×	`flip3--` `flip3-+` `div-exp` `flip--` `flip-+`
1×	`pow1/2` `div-sub`

Counts

4 → 41

Calls

4 calls:

13.0ms	(/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0))
13.0ms	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0)))
4.0ms	(/ (pow t 2) (pow l 2))
4.0ms	(/ (pow Om 2) (pow Omc 2))

series2.0s

Counts

4 → 12

Calls

4 calls:

829.0ms	(/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0))
1.1s	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ (pow t 2) (pow l 2)))) 1.0)))
30.0ms	(/ (pow t 2) (pow l 2))
26.0ms	(/ (pow Om 2) (pow Omc 2))

simplify178.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (164.0ms)

Iter	Nodes	Cost
0	236	412
1	752	411
2	4506	411
3	5001	410

prune221.0ms

Filtered

53 candidates to 37 candidates (69.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	52	5	57

Merged error: 11.0b

Counts

57 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b	(/ t (/ (pow l 2) t))
6.4b	(/ (pow l 2) t)
10.1b	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ t (/ (pow l 2) t)))) 1.0)))
15.9b	(/ (pow Om 2) (pow Omc 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`unpow2` `sqr-pow`
7×	`associate-/r/`
6×	`associate-/l*`
5×	`frac-2neg` `sqrt-div` `clear-num` `div-inv`
4×	`times-frac`
3×	`associate-/r*` `sqrt-prod`
2×	`pow-to-exp` `associate-/l/`
1×	`flip3--` `flip3-+` `pow1/2` `div-exp` `flip--` `flip-+`

Counts

4 → 35

Calls

4 calls:

4.0ms	(/ t (/ (pow l 2) t))
3.0ms	(/ (pow l 2) t)
12.0ms	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ t (/ (pow l 2) t)))) 1.0)))
4.0ms	(/ (pow Om 2) (pow Omc 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ t (/ (pow l 2) t))
24.0ms	(/ (pow l 2) t)
1.1s	(sqrt (/ (- 1.0 (/ (pow Om 2) (pow Omc 2))) (+ (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (/ t (/ (pow l 2) t)))) 1.0)))
25.0ms	(/ (pow Om 2) (pow Omc 2))

simplify207.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	224	283
1	745	283
2	4703	281
3	5001	281

prune182.0ms

Filtered

47 candidates to 32 candidates (68.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	47	5	52

Merged error: 11.0b

Counts

52 → 5

regimes517.0ms

Accuracy

0% (0.0b remaining)

Error of 11.0b against oracle of 10.9b and baseline of 11.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

604.0ms	7924×	body	80	nan
564.0ms	3719×	body	160	valid
332.0ms	4281×	body	80	valid