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

24.0ms	130×	body	160	valid
16.0ms	169×	body	80	nan
12.0ms	126×	body	80	valid

simplify128.0ms

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

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: 8.3b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 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))))))
7.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms

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)
15.0ms	(/ (- 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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
93.0ms	(/ (- 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))))))
133.0ms	(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 (46.0ms)

Iter	Nodes	Cost
0	662	1889
1	2099	1789
2	5002	1774

prune425.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Merged error: 8.2b

Counts

143 → 8

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)))))
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

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)
14.0ms	(/ (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))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
129.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
49.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	693	2519
1	2331	2342
2	5001	2330

prune402.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Merged error: 8.2b

Counts

171 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.6b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.6b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
74×	`times-frac`
56×	`*-un-lft-identity`
54×	`sqrt-prod`
44×	`add-cube-cbrt`
43×	`cbrt-prod`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`add-exp-log` `cbrt-div`
6×	`pow1` `associate-/r*` `distribute-lft-out--` `sqr-pow`
5×	`add-cbrt-cube`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `pow1/3` `associate-/l*`
2×	`pow-flip` `div-exp` `div-inv`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `clear-num` `inv-pow`

Counts

4 → 139

Calls

4 calls:

5.0ms	(/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
130.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
63.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	578	2308
1	1561	2226
2	5001	2146

prune551.0ms

Filtered

105 candidates to 151 candidates (-43.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	151	7	158

Merged error: 8.2b

Counts

158 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.4b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.4b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.4b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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

series319.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
63.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
63.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
61.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	398	1463
1	940	1367
2	3376	1358
3	5002	1343

prune503.0ms

Filtered

73 candidates to 87 candidates (-19.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	85	9	94

Merged error: 8.1b

Counts

94 → 9

regimes1.5s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample7.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.148682%

Guaranteed chance to sample good point: 44.585494%

Results

759.0ms	3838×	body	160	valid
471.0ms	4681×	body	80	nan
422.0ms	4162×	body	80	valid

Details

sample5.1s

simplify128.0ms

prune5.0ms

localize14.0ms

rewrite37.0ms

series253.0ms

simplify66.0ms

prune425.0ms

localize15.0ms

rewrite28.0ms

series203.0ms

simplify71.0ms

prune402.0ms

localize22.0ms

rewrite30.0ms

series333.0ms

simplify60.0ms

prune551.0ms

localize22.0ms

rewrite17.0ms

series319.0ms

simplify93.0ms

prune503.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.4s

Profiling