Details

analyze2.5s (5.6%)

Algorithm

1×

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

Compiler

Compiled 20 to 20 computations (0% saved)

sample109.0ms (0.2%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
25.0ms	167×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify245.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune6.0ms (0%)

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

Error

9.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(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)))))

rewrite544.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

80×	`add-sqr-sqrt_binary64_100`
67×	`times-frac_binary64_84`
59×	`*-un-lft-identity_binary64_78`
48×	`sqrt-prod_binary64_94`
38×	`add-cube-cbrt_binary64_113` `unpow-prod-down_binary64_157`
30×	`difference-of-squares_binary64_47`
10×	`add-exp-log_binary64_116`
8×	`unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `pow-exp_binary64_146`
3×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75`
2×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `asin-acos_binary64_258`

Counts

4 → 126

Calls

4 calls:

39.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.0ms	(pow.f64 (/.f64 t l) 2)
8.0ms	(pow.f64 (/.f64 Om Omc) 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))))))

Compiler

Compiled 4135 to 2867 computations (30.7% saved)

series2.3s (5.1%)

Error

2.3b

Counts

4 → 45

Calls

4 calls:

1.6s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
215.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
145.0ms	(pow.f64 (/.f64 t l) 2)
141.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5833 to 5095 computations (12.7% saved)

simplify203.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	5017	5324

prune626.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Error

0.4b

Counts

172 → 6

Compiler

Compiled 5065 to 3450 computations (31.9% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.7b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite707.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

88×	`add-sqr-sqrt_binary64_100`
77×	`times-frac_binary64_84`
65×	`*-un-lft-identity_binary64_78`
57×	`sqrt-prod_binary64_94`
44×	`add-cube-cbrt_binary64_113`
43×	`cbrt-prod_binary64_109`
38×	`unpow-prod-down_binary64_157`
30×	`difference-of-squares_binary64_47`
10×	`add-exp-log_binary64_116`
8×	`unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `pow-exp_binary64_146`
3×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75` `rem-sqrt-square_binary64_91`
2×	`associate-/r/_binary64_24` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `asin-acos_binary64_258`

Counts

4 → 136

Calls

4 calls:

34.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.0ms	(pow.f64 (/.f64 t l) 2)
9.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 6150 to 4345 computations (29.3% saved)

series2.2s (4.9%)

Error

0.4b

Counts

4 → 45

Calls

4 calls:

1.3s	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
409.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
149.0ms	(pow.f64 (/.f64 t l) 2)
144.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5133 to 4535 computations (11.7% saved)

simplify196.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5049	5864

prune737.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	181	6	187

Error

0.4b

Counts

187 → 6

Compiler

Compiled 7098 to 4984 computations (29.8% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.6b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.6b	(sqrt.f64 (/.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))))

rewrite1.4s (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

174×	`sqrt-prod_binary64_94`
146×	`add-sqr-sqrt_binary64_100`
120×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
54×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
10×	`pow1_binary64_139` `sqrt-div_binary64_95` `rem-sqrt-square_binary64_91`
9×	`sqrt-pow1_binary64_96`
6×	`distribute-lft-out--_binary64_30`
5×	`pow1/2_binary64_158`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24`
3×	`pow-flip_binary64_152`
2×	`div-inv_binary64_75`
1×	`inv-pow_binary64_163`

Counts

4 → 176

Calls

4 calls:

39.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
18.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9163 to 6797 computations (25.8% saved)

series2.6s (5.8%)

Error

0.4b

Counts

4 → 69

Calls

4 calls:

1.3s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
380.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
350.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
333.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7353 to 6357 computations (13.5% saved)

simplify224.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4945	8217
1	4945	8217

prune1.5s (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	245	6	251

Error

0.4b

Counts

251 → 6

Compiler

Compiled 10614 to 7781 computations (26.7% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.3b	(cbrt.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)))))
8.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite2.3s (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

185×	`add-sqr-sqrt_binary64_100`
147×	`times-frac_binary64_84`
144×	`sqrt-prod_binary64_94`
122×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
59×	`add-cube-cbrt_binary64_113`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
7×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `cbrt-prod_binary64_109`
1×	`pow1/3_binary64_160`

Counts

4 → 191

Calls

4 calls:

36.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
32.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
31.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 15683 to 11181 computations (28.7% saved)

series7.9s (17.5%)

Error

0.4b

Counts

4 → 75

Calls

4 calls:

1.8s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.8s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.8s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.8s	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 22125 to 18045 computations (18.4% saved)

simplify284.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4995	12294
1	4995	12294

prune3.1s (6.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	263	3	266
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	264	8	272

Error

0.4b

Counts

272 → 8

Compiler

Compiled 20294 to 14257 computations (29.7% saved)

regimes6.2s (13.8%)

Accuracy

Total 0.1b remaining (18%)

Threshold costs 0.1b (18%)

Compiler

Compiled 51587 to 43249 computations (16.2% saved)

bsearch8.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	101
1	91	101

end0.0ms (0%)

sample8.9s (19.9%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
1.1s	4735×	body	128	nan

Compiler

Compiled 2954 to 2479 computations (16.1% saved)

Details

analyze2.5s (5.6%)

sample109.0ms (0.2%)

simplify245.0ms (0.5%)

prune6.0ms (0%)

localize27.0ms (0.1%)

rewrite544.0ms (1.2%)

series2.3s (5.1%)

simplify203.0ms (0.5%)

prune626.0ms (1.4%)

localize35.0ms (0.1%)

rewrite707.0ms (1.6%)

series2.2s (4.9%)

simplify196.0ms (0.4%)

prune737.0ms (1.6%)

localize36.0ms (0.1%)

rewrite1.4s (3.1%)

series2.6s (5.8%)

simplify224.0ms (0.5%)

prune1.5s (3.3%)

localize40.0ms (0.1%)

rewrite2.3s (5.2%)

series7.9s (17.5%)

simplify284.0ms (0.6%)

prune3.1s (6.8%)

regimes6.2s (13.8%)

bsearch8.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample8.9s (19.9%)

Profiling