Details

sample81.0ms

Algorithm

intervals

Results

25.0ms	276×	body	80	nan
21.0ms	120×	body	160	valid
12.0ms	136×	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

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: 10.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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

series625.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
219.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
323.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	634	1882
1	2017	1787
2	5001	1774

prune661.0ms

Filtered

142 candidates to 114 candidates (80.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 10.0b

Counts

143 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.7b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-cube-cbrt`
25×	`log-pow`
24×	`sqrt-prod`
17×	`exp-prod`
14×	`distribute-lft-out--`
13×	`pow1` `unpow-prod-down`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`associate-/r/` `add-log-exp`
3×	`log-prod` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `asin-acos` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

15.0ms	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(log (exp (pow (/ Om Omc) 2.0)))
14.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
61.0ms	(log (exp (pow (/ Om Omc) 2.0)))
321.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	552	1751
1	1657	1613
2	5002	1583

prune428.0ms

Filtered

129 candidates to 99 candidates (76.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Merged error: 10.0b

Counts

136 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.1b	(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))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ Om Omc) 2.0)
314.0ms	(/ (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))))))
206.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (43.0ms)

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

prune466.0ms

Filtered

163 candidates to 107 candidates (65.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	163	7	170

Merged error: 10.0b

Counts

170 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (/ (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)))))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
21×	`add-sqr-sqrt`
18×	`cbrt-div`
14×	`times-frac`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `pow1/3`
2×	`unpow-prod-down` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

17.0ms	(sqrt (/ (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)))))))
2.0ms	(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))))

series1.2s

Counts

4 → 12

Calls

4 calls:

446.0ms	(sqrt (/ (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)))))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
239.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
242.0ms	(cbrt (+ 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	367	1353
1	817	1301
2	2924	1289
3	5002	1286

prune416.0ms

Filtered

87 candidates to 74 candidates (85.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	87	7	94

Merged error: 10.0b

Counts

94 → 7

regimes685.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

705.0ms	7898×	body	80	nan
685.0ms	3790×	body	160	valid
383.0ms	4210×	body	80	valid