Details

sample5.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.148682%

Guaranteed chance to sample good point: 44.585494%

Results

25.0ms	130×	body	160	valid
14.0ms	136×	body	80	nan
12.0ms	126×	body	80	valid

simplify129.0ms

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

prune8.0ms

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: 8.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite36.0ms

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 (/ Om Omc) 2.0)
12.0ms	(/ (- 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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
95.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(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)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	649	1889
1	2079	1797
2	5001	1774

prune407.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 8.1b

Counts

143 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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

series211.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
138.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	689	2519
1	2333	2350
2	5001	2330

prune408.0ms

Filtered

105 candidates to 163 candidates (-55.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	163	9	172

Merged error: 8.1b

Counts

172 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

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))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	262	796
1	822	778
2	3917	772
3	5002	764

prune309.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	83	10	93

Merged error: 8.1b

Counts

93 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

33×	`sqrt-prod`
18×	`add-sqr-sqrt`
14×	`sqrt-div`
13×	`sqrt-pow1`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
7×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 78

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
68.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
64.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	262	856
1	822	837
2	3917	828
3	5002	818

prune367.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	90	10	100

Merged error: 8.1b

Counts

100 → 10

regimes1.4s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample7.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.148682%

Guaranteed chance to sample good point: 44.585494%

Results

743.0ms	3818×	body	160	valid
471.0ms	4502×	body	80	nan
426.0ms	4182×	body	80	valid

Details

sample5.1s

simplify129.0ms

prune8.0ms

localize15.0ms

rewrite36.0ms

series259.0ms

simplify63.0ms

prune407.0ms

localize16.0ms

rewrite32.0ms

series211.0ms

simplify69.0ms

prune408.0ms

localize19.0ms

rewrite13.0ms

series229.0ms

simplify110.0ms

prune309.0ms

localize23.0ms

rewrite15.0ms

series246.0ms

simplify116.0ms

prune367.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.5s

Profiling