Details

analyze1.5s

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

sample70.0ms

Algorithm

intervals

Results

27.0ms	126×	body	160	valid
13.0ms	140×	body	80	nan
12.0ms	130×	body	80	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	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: 10.2b

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))))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b	(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 (/ Om Omc) 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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
98.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
139.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5030	3354

prune405.0ms

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: 10.2b

Counts

143 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

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)
15.0ms	(/ (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))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
137.0ms	(/ (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))))))
51.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4984	4133
1	4984	4133

prune385.0ms

Filtered

105 candidates to 163 candidates (-55.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	163	8	171

Merged error: 10.2b

Counts

171 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.7b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

190×	`sqrt-prod`
164×	`add-sqr-sqrt`
112×	`times-frac`
78×	`*-un-lft-identity`
54×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`distribute-lft-out--` `sqr-pow`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`

Counts

4 → 180

Calls

4 calls:

15.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
150.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
136.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
140.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5159	5618

prune869.0ms

Filtered

152 candidates to 192 candidates (-26.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	192	8	200

Merged error: 10.2b

Counts

200 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

9.3b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

32.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
69.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify95.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5361	10323

prune1.1s

Filtered

159 candidates to 192 candidates (-20.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	192	8	200

Merged error: 10.2b

Counts

200 → 8

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

720.0ms	3737×	body	160	valid
465.0ms	4816×	body	80	nan
409.0ms	4263×	body	80	valid

Details

analyze1.5s

sample70.0ms

simplify42.0ms

prune5.0ms

localize15.0ms

rewrite39.0ms

series265.0ms

simplify62.0ms

prune405.0ms

localize18.0ms

rewrite30.0ms

series215.0ms

simplify66.0ms

prune385.0ms

localize18.0ms

rewrite67.0ms

series575.0ms

simplify72.0ms

prune869.0ms

localize19.0ms

rewrite54.0ms

series337.0ms

simplify95.0ms

prune1.1s

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

Profiling