Details

sample63.0ms

Algorithm

intervals

Results

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

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

series593.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(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))))))
206.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
308.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

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

prune547.0ms

Filtered

142 candidates to 114 candidates (80.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 11.0b

Counts

143 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.1b	(sqrt (pow (/ Om Omc) 2.0))
18.1b	(sqrt (pow (/ Om Omc) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series897.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
270.0ms	(sqrt (pow (/ Om Omc) 2.0))
262.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	366	816
1	964	796
2	3840	796
3	5001	796

prune574.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 11.0b

Counts

109 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
29.4b	(cbrt (pow (/ t l) 2.0))
29.4b	(cbrt (pow (/ t l) 2.0))
29.4b	(cbrt (pow (/ t l) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

318.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
266.0ms	(cbrt (pow (/ t l) 2.0))
265.0ms	(cbrt (pow (/ t l) 2.0))
267.0ms	(cbrt (pow (/ t l) 2.0))

simplify131.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	516	2189
1	1205	2120
2	4830	2084
3	5001	2075

prune642.0ms

Filtered

129 candidates to 103 candidates (79.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	129	8	137

Merged error: 11.0b

Counts

137 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

16.9b	(sqrt (pow (/ t l) 2.0))
16.9b	(sqrt (pow (/ t l) 2.0))
29.4b	(cbrt (pow (/ t l) 2.0))
29.4b	(cbrt (pow (/ t l) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

56×	`unpow-prod-down`
44×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
34×	`cbrt-prod` `sqrt-prod`
8×	`rem-sqrt-square`
6×	`sqr-pow`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 110

Calls

4 calls:

5.0ms	(sqrt (pow (/ t l) 2.0))
5.0ms	(sqrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

261.0ms	(sqrt (pow (/ t l) 2.0))
259.0ms	(sqrt (pow (/ t l) 2.0))
260.0ms	(cbrt (pow (/ t l) 2.0))
262.0ms	(cbrt (pow (/ t l) 2.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	346	1048
1	707	1024
2	1791	1020
3	4800	1014
4	5001	1014

prune698.0ms

Filtered

122 candidates to 98 candidates (80.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	4	4
Picked	0	1	1
Done	1	2	3
Total	122	8	130

Merged error: 11.0b

Counts

130 → 8

regimes717.0ms

Accuracy

0% (0.1b 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

sample1.9s

Algorithm

intervals

Results

592.0ms	7924×	body	80	nan
545.0ms	3719×	body	160	valid
315.0ms	4281×	body	80	valid