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

sample108.0ms

Algorithm

intervals

Results

24.0ms	137×	body	160	valid
11.0ms	119×	body	80	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	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: 8.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite39.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
16.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
94.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(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)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5030	3354

prune410.0ms

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: 8.1b

Counts

143 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0b	(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))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
131.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms	(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))))

simplify65.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	4133
1	4984	4133

prune390.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	163	7	170

Merged error: 8.1b

Counts

170 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b	(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))))))))
1.4b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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))))))))
17.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(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))))))))
146.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5290	4449

prune728.0ms

Filtered

120 candidates to 133 candidates (-10.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	133	7	140

Merged error: 8.1b

Counts

140 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.5b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.5b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.5b	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
30×	`sqrt-prod`
28×	`times-frac`
25×	`*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`cbrt-prod`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--` `sqr-pow`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 75

Calls

4 calls:

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

series322.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
61.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
63.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
63.0ms	(cbrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5281	2449

prune530.0ms

Filtered

76 candidates to 87 candidates (-14.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	84	10	94

Merged error: 8.0b

Counts

94 → 10

regimes1.7s

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

724.0ms	3919×	body	160	valid
361.0ms	4081×	body	80	valid

Details

analyze1.5s

sample108.0ms

simplify42.0ms

prune5.0ms

localize17.0ms

rewrite39.0ms

series256.0ms

simplify61.0ms

prune410.0ms

localize18.0ms

rewrite30.0ms

series206.0ms

simplify65.0ms

prune390.0ms

localize22.0ms

rewrite32.0ms

series300.0ms

simplify56.0ms

prune728.0ms

localize24.0ms

rewrite19.0ms

series322.0ms

simplify50.0ms

prune530.0ms

regimes1.7s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling