Details

sample80.0ms

Algorithm

intervals

Results

22.0ms	248×	body	80	nan
21.0ms	117×	body	160	valid
12.0ms	139×	body	80	valid

simplify124.0ms

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: 9.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
8.0ms	(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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ Om Omc) 2.0)
65.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune430.0ms

Filtered

118 candidates to 92 candidates (78.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 9.4b

Counts

119 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.9b	(log (exp (pow (/ Om Omc) 2.0)))
8.8b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 101

Calls

4 calls:

5.0ms	(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))))))
6.0ms	(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)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(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))))))
59.0ms	(log (exp (pow (/ Om Omc) 2.0)))
319.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	624	1169
1	1863	1079
2	5002	1061

prune413.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	113	8	121

Merged error: 9.4b

Counts

121 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)))))
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(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 (/ t l) 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))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (/ t l) 2.0)
325.0ms	(/ (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))))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (43.0ms)

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

prune614.0ms

Filtered

163 candidates to 107 candidates (65.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	164	7	171

Merged error: 9.4b

Counts

171 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

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)))))
5.0ms	(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))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
232.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
171.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
172.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune329.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 9.4b

Counts

91 → 7

regimes630.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

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

699.0ms	3883×	body	160	valid
688.0ms	7818×	body	80	nan
362.0ms	4117×	body	80	valid

Details

sample80.0ms

simplify124.0ms

prune3.0ms

localize14.0ms

rewrite31.0ms

series461.0ms

simplify57.0ms

prune430.0ms

localize16.0ms

rewrite30.0ms

series460.0ms

simplify54.0ms

prune413.0ms

localize15.0ms

rewrite30.0ms

series579.0ms

simplify71.0ms

prune614.0ms

localize18.0ms

rewrite15.0ms

series812.0ms

simplify87.0ms

prune329.0ms

regimes630.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling