Details

analyze1.4s

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

sample69.0ms

Algorithm

intervals

Results

23.0ms	123×	body	160	valid
13.0ms	139×	body	80	nan
12.0ms	133×	body	80	valid

simplify41.0ms

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: 10.1b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 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))))))
9.2b	(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 (/ t l) 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)))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
100.0ms	(/ (- 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))))))
146.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4953	3362
1	4953	3362

prune475.0ms

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: 10.0b

Counts

143 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.1b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.1b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.1b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 133

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
14.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
153.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
155.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
153.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4965	4796
1	4965	4796

prune981.0ms

Filtered

128 candidates to 145 candidates (-13.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	145	9	154

Merged error: 10.0b

Counts

154 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.3b	(sqrt (pow (/ Om Omc) 2.0))
17.3b	(sqrt (pow (/ Om Omc) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series232.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms	(sqrt (pow (/ Om Omc) 2.0))
50.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4957	1244
1	4957	1244

prune655.0ms

Filtered

88 candidates to 98 candidates (-11.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	98	9	107

Merged error: 10.0b

Counts

107 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.3b	(sqrt (pow (/ Om Omc) 2.0))
17.3b	(sqrt (pow (/ Om Omc) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

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

series230.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms	(sqrt (pow (/ Om Omc) 2.0))
47.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify33.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4957	1244
1	4957	1244

prune750.0ms

Filtered

88 candidates to 98 candidates (-11.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	98	9	107

Merged error: 10.0b

Counts

107 → 9

regimes1.4s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample1.9s

Algorithm

intervals

Results

725.0ms	3840×	body	160	valid
418.0ms	4489×	body	80	nan
390.0ms	4160×	body	80	valid

Details

analyze1.4s

sample69.0ms

simplify41.0ms

prune5.0ms

localize15.0ms

rewrite36.0ms

series275.0ms

simplify73.0ms

prune475.0ms

localize19.0ms

rewrite48.0ms

series489.0ms

simplify56.0ms

prune981.0ms

localize26.0ms

rewrite18.0ms

series232.0ms

simplify34.0ms

prune655.0ms

localize29.0ms

rewrite20.0ms

series230.0ms

simplify33.0ms

prune750.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.9s

Profiling