Details

sample71.0ms

Algorithm

intervals

Results

23.0ms	290×	body	80	nan
15.0ms	110×	body	160	valid
11.0ms	146×	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

prune4.0ms

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: 11.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite30.0ms

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:

8.0ms	(pow (/ t l) 2.0)
4.0ms	(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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
65.0ms	(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))))))
329.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

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

prune590.0ms

Filtered

118 candidates to 92 candidates (78.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Merged error: 11.3b

Counts

119 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite34.0ms

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)
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (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)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
322.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	609	2507
1	1958	2333
2	5001	2323

prune615.0ms

Filtered

163 candidates to 107 candidates (65.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	164	7	171

Merged error: 11.3b

Counts

171 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b	(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)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series867.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
248.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	201	726
1	658	700
2	2858	696
3	5002	688

prune434.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	84	7	91

Merged error: 11.3b

Counts

91 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.7b	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
24×	`cbrt-prod`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
9×	`unpow-prod-down` `cube-prod`
8×	`pow1`
6×	`sqrt-pow1`
4×	`add-exp-log` `rem-sqrt-square` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`cube-div` `cbrt-div`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

series863.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	320	914
1	1108	893
2	5001	879

prune472.0ms

Filtered

98 candidates to 66 candidates (67.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	98	7	105

Merged error: 11.3b

Counts

105 → 7

regimes643.0ms

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	18	10
1	18	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

572.0ms	8139×	body	80	nan
541.0ms	3793×	body	160	valid
300.0ms	4207×	body	80	valid