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

sample72.0ms

Algorithm

intervals

Results

26.0ms	139×	body	160	valid
15.0ms	117×	body	80	valid
14.0ms	151×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4892	19
1	4892	19

prune3.0ms

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: 10.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
98×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
49×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
41×	`unpow-prod-down_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
14×	`associate-/l*_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 173

Calls

4 calls:

8.0ms	(pow.f64 (/.f64 t l) 2)
16.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
43.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
70.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4953	4274
1	4953	4274

prune172.0ms

Filtered

101 candidates to 185 candidates (-83.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	8	186

Merged error: 9.9b

Counts

186 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.5b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.9b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
125×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
63×	`add-cube-cbrt_binary64`
41×	`unpow-prod-down_binary64`
17×	`associate-/l*_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 194

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 t l) 2)
20.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 t l) 2)
70.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
11.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify84.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	5066
1	4973	5066

prune148.0ms

Filtered

96 candidates to 206 candidates (-114.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	206	8	214

Merged error: 5.7b

Counts

214 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

5.3b	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.3b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

183×	`sqrt-prod_binary64`
148×	`add-sqr-sqrt_binary64`
126×	`times-frac_binary64`
98×	`*-un-lft-identity_binary64`
86×	`cbrt-prod_binary64`
60×	`difference-of-squares_binary64`
56×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
12×	`unpow2_binary64` `sqr-pow_binary64`
10×	`rem-sqrt-square_binary64` `sqrt-div_binary64`
8×	`pow1_binary64`
6×	`distribute-lft-out--_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`div-inv_binary64`

Counts

4 → 178

Calls

4 calls:

27.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
24.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
113.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
11.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
11.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5146	5601

prune306.0ms

Filtered

105 candidates to 190 candidates (-81.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	190	8	198

Merged error: 5.7b

Counts

198 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
5.8b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64`
102×	`sqrt-prod_binary64`
98×	`times-frac_binary64`
84×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`
42×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
12×	`unpow2_binary64` `sqr-pow_binary64`
8×	`pow1_binary64`
6×	`rem-sqrt-square_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 146

Calls

4 calls:

1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
34.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
70.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
76.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4928	4274
1	4928	4274

prune166.0ms

Filtered

80 candidates to 158 candidates (-97.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	0	5	5
Picked	1	0	1
Done	2	0	2
Total	158	8	166

Merged error: 5.7b

Counts

166 → 8

regimes985.0ms

Accuracy

88.6% (0.6b remaining)

Error of 6.4b against oracle of 5.8b and baseline of 10.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	64
1	44	64

end0.0ms

sample2.0s

Algorithm

intervals

Results

732.0ms	3840×	body	160	valid
453.0ms	4654×	body	80	nan
397.0ms	4160×	body	80	valid

Details

analyze1.5s

sample72.0ms

simplify44.0ms

prune3.0ms

localize14.0ms

rewrite51.0ms

series131.0ms

simplify68.0ms

prune172.0ms

localize15.0ms

rewrite40.0ms

series102.0ms

simplify84.0ms

prune148.0ms

localize25.0ms

rewrite73.0ms

series246.0ms

simplify60.0ms

prune306.0ms

localize18.0ms

rewrite47.0ms

series212.0ms

simplify77.0ms

prune166.0ms

regimes985.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling