Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample67.0ms

Algorithm

intervals

Results

23.0ms	118×	body	160	valid
14.0ms	138×	body	80	nan
13.0ms	138×	body	80	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	19

prune8.0ms

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: 10.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite26.0ms

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:

4.0ms	(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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
12.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
137.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4938	2150
1	4938	2150

prune322.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Merged error: 10.3b

Counts

119 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(/ (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))))))
9.4b	(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))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
134.0ms	(/ (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))))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	4133
1	4984	4133

prune409.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	162	8	170

Merged error: 10.3b

Counts

170 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
3.4b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`asin-acos` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
4.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
65.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
67.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5506	1389

prune400.0ms

Filtered

61 candidates to 66 candidates (-8.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 10.3b

Counts

74 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.5b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (* (* (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0))))) (/ (cbrt (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))) (fabs (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4952	1410
1	4952	1410

prune355.0ms

Filtered

57 candidates to 64 candidates (-12.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	64	8	72

Merged error: 10.3b

Counts

72 → 8

regimes1.5s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

755.0ms	3733×	body	160	valid
489.0ms	4830×	body	80	nan
427.0ms	4267×	body	80	valid

Details

analyze1.5s

sample67.0ms

simplify41.0ms

prune8.0ms

localize16.0ms

rewrite26.0ms

series178.0ms

simplify63.0ms

prune322.0ms

localize16.0ms

rewrite30.0ms

series210.0ms

simplify65.0ms

prune409.0ms

localize29.0ms

rewrite12.0ms

series221.0ms

simplify33.0ms

prune400.0ms

localize29.0ms

rewrite13.0ms

series202.0ms

simplify55.0ms

prune355.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

Profiling