Details

sample83.0ms

Algorithm

intervals

Results

21.0ms	126×	body	160	valid
20.0ms	232×	body	80	nan
11.0ms	130×	body	80	valid

simplify127.0ms

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

prune12.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 8.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.6b	(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)
13.0ms	(/ (- 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)))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (/ t l) 2.0)
219.0ms	(/ (- 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))))))
337.0ms	(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 (44.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774

prune1.6s

Filtered

142 candidates to 114 candidates (19.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	133	9	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	9	143

Merged error: 8.1b

Counts

143 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(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)))))
0.8b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

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:

5.0ms	(pow (/ t l) 2.0)
16.0ms	(/ (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))))

series630.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(pow (/ t l) 2.0)
334.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
207.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	619	2493
1	1983	2321
2	5001	2311

prune1.3s

Filtered

163 candidates to 107 candidates (34.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	163	9	172

Merged error: 8.1b

Counts

172 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(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))))))))
2.4b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0b	(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)))))
14.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(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))))))))
375.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
373.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
363.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	532	2819
1	1231	2727
2	4288	2718
3	5001	2695

prune1.9s

Filtered

145 candidates to 125 candidates (13.8%)

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: 8.1b

Counts

154 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.7b	(sqrt (pow (/ Om Omc) 2.0))
18.7b	(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))))
2.0ms	(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))

series1.2s

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
283.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
300.0ms	(sqrt (pow (/ Om Omc) 2.0))
294.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	371	842
1	977	808
2	4022	800
3	5001	798

prune1.3s

Filtered

98 candidates to 82 candidates (16.3%)

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: 8.1b

Counts

107 → 9

regimes1.7s

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	19	11
1	19	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

695.0ms	8069×	body	80	nan
651.0ms	3795×	body	160	valid
359.0ms	4205×	body	80	valid

Details

sample83.0ms

simplify127.0ms

prune12.0ms

localize25.0ms

rewrite36.0ms

series645.0ms

simplify63.0ms

prune1.6s

localize17.0ms

rewrite31.0ms

series630.0ms

simplify64.0ms

prune1.3s

localize18.0ms

rewrite48.0ms

series1.1s

simplify123.0ms

prune1.9s

localize25.0ms

rewrite20.0ms

series1.2s

simplify96.0ms

prune1.3s

regimes1.7s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

Profiling