Details

sample110.0ms

Algorithm

intervals

Results

25.0ms	115×	body	160	valid
22.0ms	230×	body	80	nan
13.0ms	141×	body	80	valid

simplify125.0ms

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: 11.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.1b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms

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

series261.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
95.0ms	(/ (- 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))))))
139.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	662	1889
1	2099	1789
2	5002	1774

prune442.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	132	10	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	11	143

Merged error: 11.0b

Counts

143 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
1.0b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.1b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

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))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 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))))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

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

prune421.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	162	12	174

Merged error: 11.0b

Counts

174 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

9.7b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

28.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
68.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	1002	6281
1	3059	6183
2	5001	6175

prune1.3s

Filtered

160 candidates to 192 candidates (-20.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	192	12	204

Merged error: 11.0b

Counts

204 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.3b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.9b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.9b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
13.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
143.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
147.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
149.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	532	2819
1	1231	2727
2	4288	2718
3	5001	2695

prune694.0ms

Filtered

125 candidates to 145 candidates (-16.0%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	145	12	157

Merged error: 11.0b

Counts

157 → 12

regimes1.5s

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.5s

Algorithm

intervals

Results

743.0ms	7834×	body	80	nan
703.0ms	3813×	body	160	valid
390.0ms	4187×	body	80	valid

Details

sample110.0ms

simplify125.0ms

prune5.0ms

localize14.0ms

rewrite37.0ms

series261.0ms

simplify65.0ms

prune442.0ms

localize17.0ms

rewrite28.0ms

series210.0ms

simplify73.0ms

prune421.0ms

localize19.0ms

rewrite49.0ms

series331.0ms

simplify108.0ms

prune1.3s

localize18.0ms

rewrite42.0ms

series467.0ms

simplify130.0ms

prune694.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling