Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample66.0ms

Algorithm

intervals

Results

24.0ms	130×	body	160	valid
14.0ms	151×	body	80	nan
11.0ms	126×	body	80	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune5.0ms

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: 12.4b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.2b	(pow (/ t l) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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:

12.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(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))))))
11.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms	(pow (/ t l) 2.0)
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
137.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4971	3360
1	4971	3360

prune412.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 12.3b

Counts

143 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 151

Calls

4 calls:

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
134.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4988	4130
1	4988	4130

prune404.0ms

Filtered

107 candidates to 163 candidates (-52.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	162	8	170

Merged error: 12.3b

Counts

170 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (/ -1 l) (/ -1 t)) 2.0)
0.3b	(/ (/ -1 l) (/ -1 t))
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
11.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

852×	`times-frac`
423×	`add-sqr-sqrt`
402×	`*-un-lft-identity`
396×	`add-cube-cbrt`
180×	`unpow-prod-down`
57×	`div-inv`
30×	`sqrt-prod`
29×	`add-exp-log`
16×	`div-exp` `add-cbrt-cube`
13×	`associate-/r` `associate-/l`
12×	`difference-of-squares`
8×	`cbrt-undiv`
6×	`pow1`
5×	`pow-exp`
4×	`associate-/r/` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `distribute-lft-out--`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `asin-acos` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 457

Calls

4 calls:

25.0ms	(pow (/ (/ -1 l) (/ -1 t)) 2.0)
10.0ms	(/ (/ -1 l) (/ -1 t))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
11.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ (/ -1 l) (/ -1 t)) 2.0)
2.0ms	(/ (/ -1 l) (/ -1 t))
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0))))))
139.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ (/ -1 l) (/ -1 t)) 2.0)))))

simplify132.0ms

Algorithm

egg-herbie

Counts

469 → 469

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4983	8957
1	4983	8957

prune1.7s

Filtered

386 candidates to 469 candidates (-21.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	468	1	469
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	470	7	477

Merged error: 12.3b

Counts

477 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 l) t)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0)))))
0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))))
11.3b	(sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
95×	`sqrt-prod`
84×	`times-frac`
66×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
15×	`add-exp-log`
14×	`unpow-prod-down`
13×	`associate-l`
11×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `sqr-pow`
6×	`sqrt-div` `associate-/r*`
4×	`prod-exp` `add-log-exp`
3×	`div-exp` `associate-r` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `associate-/r/` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`rem-sqrt-square` `rec-exp` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--`

Counts

4 → 158

Calls

4 calls:

7.0ms	(* (/ 1 l) t)
14.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0)))))
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (/ 1 l) t)
129.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0)))))
13.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))))
38.0ms	(sqrt (+ 1.0 (* 2.0 (pow (* (/ 1 l) t) 2.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4955	4030
1	4955	4030

prune375.0ms

Filtered

113 candidates to 170 candidates (-50.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	170	7	177

Merged error: 12.3b

Counts

177 → 7

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	22
1	23	22

end0.0ms

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample1.9s

Algorithm

intervals

Results

717.0ms	3835×	body	160	valid
446.0ms	4657×	body	80	nan
389.0ms	4165×	body	80	valid

Details

analyze1.4s

sample66.0ms

simplify60.0ms

prune5.0ms

localize18.0ms

rewrite34.0ms

series256.0ms

simplify60.0ms

prune412.0ms

localize15.0ms

rewrite31.0ms

series207.0ms

simplify66.0ms

prune404.0ms

localize16.0ms

rewrite80.0ms

series168.0ms

simplify132.0ms

prune1.7s

localize17.0ms

rewrite33.0ms

series182.0ms

simplify100.0ms

prune375.0ms

regimes1.6s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze1.4s

sample1.9s

Profiling