Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	245×	body	80	nan
23.0ms	126×	body	160	valid
12.0ms	130×	body	80	valid

simplify130.0ms

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

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: 10.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(pow (/ Om Omc) 2.0)
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
8.0ms	(pow (/ Om Omc) 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)))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ t l) 2.0)
66.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
333.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune579.0ms

Filtered

118 candidates to 92 candidates (78.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	11	119

Merged error: 9.9b

Counts

119 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.6b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

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

series581.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ Om Omc) 2.0)
323.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	605	2493
1	1954	2321
2	5001	2311

prune463.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	166	8	174

Merged error: 9.9b

Counts

174 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.1b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(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:

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

series858.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
247.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune352.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 9.9b

Counts

92 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(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)))))))
29.0b	(cbrt (pow (/ t l) 2.0))
29.0b	(cbrt (pow (/ t l) 2.0))
29.0b	(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:

321.0ms	(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)))))))
269.0ms	(cbrt (pow (/ t l) 2.0))
260.0ms	(cbrt (pow (/ t l) 2.0))
265.0ms	(cbrt (pow (/ t l) 2.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	516	2189
1	1205	2120
2	4816	2084
3	5001	2075

prune542.0ms

Filtered

129 candidates to 103 candidates (79.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

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

Merged error: 9.9b

Counts

137 → 8

regimes638.0ms

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

sample2.3s

Algorithm

intervals

Results

724.0ms	7869×	body	80	nan
710.0ms	3838×	body	160	valid
380.0ms	4162×	body	80	valid

Details

sample82.0ms

simplify130.0ms

prune3.0ms

localize14.0ms

rewrite29.0ms

series476.0ms

simplify62.0ms

prune579.0ms

localize16.0ms

rewrite29.0ms

series581.0ms

simplify71.0ms

prune463.0ms

localize21.0ms

rewrite13.0ms

series858.0ms

simplify87.0ms

prune352.0ms

localize19.0ms

rewrite29.0ms

series1.1s

simplify125.0ms

prune542.0ms

regimes638.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling