Details

sample88.0ms

Algorithm

intervals

Results

23.0ms	126×	body	160	valid
23.0ms	250×	body	80	nan
12.0ms	130×	body	80	valid

simplify126.0ms

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

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: 11.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.8b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms

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

series271.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
97.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
143.0ms	(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 (43.0ms)

Iter	Nodes	Cost
0	649	1889
1	2079	1797
2	5001	1774

prune440.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 11.6b

Counts

143 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)))))
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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)
17.0ms	(/ (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))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
142.0ms	(/ (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))))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	689	2520
1	2332	2350
2	5001	2330

prune441.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	161	9	170

Merged error: 11.6b

Counts

170 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.5b	(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))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
65.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
49.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify110.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	262	796
1	822	778
2	3917	772
3	5002	764

prune333.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	83	10	93

Merged error: 11.6b

Counts

93 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`sqrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`cbrt-prod` `sqrt-div`
5×	`sqrt-pow1`
4×	`add-exp-log` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2`
2×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

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

series250.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
49.0ms	(sqrt (+ 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))))

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	317	762
1	1036	731
2	5001	718

prune378.0ms

Filtered

65 candidates to 74 candidates (-13.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	74	10	84

Merged error: 11.6b

Counts

84 → 10

regimes1.5s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.6s

Algorithm

intervals

Results

738.0ms	8056×	body	80	nan
712.0ms	3858×	body	160	valid
381.0ms	4142×	body	80	valid

Details

sample88.0ms

simplify126.0ms

prune5.0ms

localize19.0ms

rewrite37.0ms

series271.0ms

simplify63.0ms

prune440.0ms

localize16.0ms

rewrite32.0ms

series217.0ms

simplify69.0ms

prune441.0ms

localize22.0ms

rewrite13.0ms

series230.0ms

simplify110.0ms

prune333.0ms

localize28.0ms

rewrite12.0ms

series250.0ms

simplify40.0ms

prune378.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling