Details

analyze1.5s

Algorithm: search

sample72.0ms

Algorithm

intervals

Results

23.0ms	120×	body	160	valid
16.0ms	163×	body	80	nan
13.0ms	136×	body	80	valid

simplify129.0ms

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

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: 8.9b

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))))))
8.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite24.0ms

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))))))
11.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(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))))))
138.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	724	1249
1	2152	1176
2	5001	1152

prune326.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	9	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 8.8b

Counts

119 → 9

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))))))
8.0b	(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 (/ t l) 2.0)
14.0ms	(/ (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))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
136.0ms	(/ (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))))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	693	2519
1	2331	2342
2	5001	2330

prune419.0ms

Filtered

107 candidates to 163 candidates (-52.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	163	9	172

Merged error: 8.8b

Counts

172 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

1.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
16.0ms	(sqrt (/ (- 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))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
131.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
67.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	618	2081
1	1575	1993
2	5001	1980

prune527.0ms

Filtered

100 candidates to 113 candidates (-13.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 8.8b

Counts

122 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.8b	(sqrt (pow (/ Om Omc) 2.0))
19.8b	(sqrt (pow (/ Om Omc) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series192.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
50.0ms	(sqrt (pow (/ Om Omc) 2.0))
47.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	448	784
1	1229	764
2	5001	758

prune457.0ms

Filtered

88 candidates to 102 candidates (-15.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Merged error: 8.8b

Counts

111 → 9

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 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

analyze1.5s

Algorithm: search

sample2.0s

Algorithm

intervals

Results

750.0ms	3802×	body	160	valid
447.0ms	4653×	body	80	nan
402.0ms	4198×	body	80	valid

Details

analyze1.5s

sample72.0ms

simplify129.0ms

prune5.0ms

localize14.0ms

rewrite24.0ms

series177.0ms

simplify56.0ms

prune326.0ms

localize15.0ms

rewrite30.0ms

series209.0ms

simplify69.0ms

prune419.0ms

localize20.0ms

rewrite26.0ms

series288.0ms

simplify54.0ms

prune527.0ms

localize25.0ms

rewrite16.0ms

series192.0ms

simplify40.0ms

prune457.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.5s

sample2.0s

Profiling