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

sample76.0ms

Algorithm

intervals

Results

24.0ms	128×	body	160	valid
22.0ms	182×	body	80	nan
12.0ms	128×	body	80	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

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: 9.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(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))))))
8.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite25.0ms

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 (/ Om Omc) 2.0)
4.0ms	(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)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(pow (/ t l) 2.0)
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
136.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5008	2152

prune333.0ms

Filtered

94 candidates to 118 candidates (-25.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 8.9b

Counts

119 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.7b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

320×	`sqrt-prod`
192×	`add-sqr-sqrt`
152×	`times-frac`
100×	`*-un-lft-identity`
76×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
10×	`sqrt-div`
8×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`div-inv`

Counts

4 → 204

Calls

4 calls:

17.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.0ms	(sqrt (/ (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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
145.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
52.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5101	6750

prune877.0ms

Filtered

128 candidates to 216 candidates (-68.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	216	9	225

Merged error: 8.9b

Counts

225 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.0b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
91×	`cbrt-prod`
76×	`times-frac`
72×	`sqrt-prod`
53×	`*-un-lft-identity`
41×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 121

Calls

4 calls:

1.0ms	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
19.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 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))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
142.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
62.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5497	4449

prune765.0ms

Filtered

120 candidates to 133 candidates (-10.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	133	9	142

Merged error: 8.9b

Counts

142 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
90×	`sqrt-prod`
84×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
7×	`pow1`
6×	`rem-sqrt-square` `associate-/r/`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 137

Calls

4 calls:

1.0ms	(cbrt (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)))))
12.0ms	(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)))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
135.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
131.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
131.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5283	4323

prune969.0ms

Filtered

124 candidates to 149 candidates (-20.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	5	5
Picked	1	0	1
Done	1	2	3
Total	147	11	158

Merged error: 8.9b

Counts

158 → 11

regimes1.6s

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 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	18	19

end0.0ms

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

sample2.0s

Algorithm

intervals

Results

733.0ms	3832×	body	160	valid
476.0ms	4802×	body	80	nan
409.0ms	4168×	body	80	valid

Details

analyze1.5s

sample76.0ms

simplify63.0ms

prune5.0ms

localize14.0ms

rewrite25.0ms

series174.0ms

simplify74.0ms

prune333.0ms

localize20.0ms

rewrite50.0ms

series388.0ms

simplify85.0ms

prune877.0ms

localize19.0ms

rewrite30.0ms

series296.0ms

simplify58.0ms

prune765.0ms

localize20.0ms

rewrite45.0ms

series459.0ms

simplify50.0ms

prune969.0ms

regimes1.6s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.5s

sample2.0s

Profiling