Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	119×	body	160	valid
14.0ms	211×	body	80	nan
9.0ms	137×	body	80	valid

simplify132.0ms

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	4371	10
6	5001	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

localize15.0ms

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)))))

rewrite13.0ms

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

series620.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
212.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
325.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	294	309
1	818	300
2	3472	300
3	5002	299

prune137.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	5	34

Merged error: 11.0b

Counts

34 → 5

localize26.0ms

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))))))

rewrite47.0ms

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)))))))
20.0ms	(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))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
41.0ms	(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))))))))
1.0s	(/ (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)))))))
537.0ms	(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))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	585	1290
1	2257	1274
2	5001	1274

prune343.0ms

Filtered

52 candidates to 48 candidates (92.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	52	5	57

Merged error: 11.0b

Counts

57 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 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 2.0) (pow (/ 1 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 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))
15.6b	(* (pow t 2.0) (pow (/ 1 l) 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

1.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
24.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
21.0ms	(sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))
5.0ms	(* (pow t 2.0) (pow (/ 1 l) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

46.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
887.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
581.0ms	(sqrt (* (+ 1.0 (* 2.0 (* (pow t 2.0) (pow (/ 1 l) 2.0)))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))
319.0ms	(* (pow t 2.0) (pow (/ 1 l) 2.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	719	1477
1	2748	1465
2	5001	1465

prune411.0ms

Filtered

56 candidates to 51 candidates (91.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	2	2
Picked	1	0	1
Done	1	1	2
Total	56	5	61

Merged error: 11.0b

Counts

61 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
0.3b	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 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 (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 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 (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqr-pow`
19×	`sqrt-prod`
18×	`sqrt-div`
17×	`div-inv`
14×	`associate-r` `pow-prod-down`
12×	`pow-unpow` `flip3-+` `flip-+`
10×	`associate-l` `*-commutative`
8×	`frac-times` `associate-/r/`
7×	`unpow-prod-down` `unswap-sqr`
6×	`times-frac` `swap-sqr` `difference-of-squares`
4×	`pow-to-exp` `associate-r/` `associate-l/`
3×	`difference-cubes` `prod-exp` `associate-/l*`
2×	`associate-/r*` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`pow2` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `pow1/2` `clear-num` `flip--`

Counts

4 → 65

Calls

4 calls:

18.0ms	(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
1.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
29.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
27.0ms	(sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))))
48.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
902.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
535.0ms	(sqrt (* (+ 1.0 (* 2.0 (* (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2))) (* (pow t (/ 2.0 2)) (pow (/ 1 l) (/ 2.0 2)))))) (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))

simplify120.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	834	2115
1	3611	2070
2	5001	2070

prune501.0ms

Filtered

77 candidates to 64 candidates (83.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	77	5	82

Merged error: 11.0b

Counts

82 → 5

regimes579.0ms

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

sample1.8s

Algorithm

intervals

Results

558.0ms	7924×	body	80	nan
517.0ms	3719×	body	160	valid
302.0ms	4281×	body	80	valid