Details

analyze2.8s (8.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4997	203
1	4997	203
0	4	4
1	4	4

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)

sample97.0ms (0.3%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
27.0ms	179×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

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

9.9b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite118.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_100`
108×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
49×	`add-cube-cbrt_binary64_113`
48×	`sqrt-prod_binary64_94`
41×	`unpow-prod-down_binary64_157`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
14×	`associate-/l*_binary64_23`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`pow-exp_binary64_146` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `flip3--_binary64_82` `frac-2neg_binary64_89` `pow-pow_binary64_150` `flip--_binary64_53` `sqrt-div_binary64_95` `clear-num_binary64_77` `asin-acos_binary64_258` `div-sub_binary64_83` `pow1/2_binary64_158`

Counts

4 → 173

Calls

4 calls:

33.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
33.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.0ms	(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))))))

series2.4s (7%)

Counts

4 → 58

Calls

4 calls:

1.1s	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
892.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
220.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
142.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 4123 to 3757 computations (8.9% saved)

simplify196.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5645	8270

prune951.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	225	6	231
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	225	7	232

Error

0.6b

Counts

232 → 7

Compiler

Compiled 7020 to 4740 computations (32.5% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.1b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
15.2b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.2b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite203.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`add-sqr-sqrt_binary64_100`
146×	`cbrt-prod_binary64_109`
145×	`times-frac_binary64_84`
122×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
59×	`add-cube-cbrt_binary64_113`
51×	`sqrt-prod_binary64_94`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
6×	`associate-/r/_binary64_24`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`cbrt-div_binary64_110` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/3_binary64_160` `div-inv_binary64_75` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96`
1×	`sqrt-div_binary64_95` `asin-acos_binary64_258` `pow1/2_binary64_158`

Counts

4 → 187

Calls

4 calls:

43.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
39.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
34.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

series8.6s (25.3%)

Counts

4 → 69

Calls

4 calls:

2.9s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.6s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.6s	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
447.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 14780 to 12686 computations (14.2% saved)

simplify285.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5185	14671

prune1.9s (5.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	256	7	263

Error

0.6b

Counts

263 → 7

Compiler

Compiled 15391 to 10669 computations (30.7% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.5b	(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)))))))
7.5b	(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)))))))
9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite119.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64_100`
102×	`sqrt-prod_binary64_94`
98×	`times-frac_binary64_84`
84×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
42×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
8×	`pow1_binary64_139`
6×	`rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `add-exp-log_binary64_116` `associate-/r/_binary64_24` `pow1/2_binary64_158`
2×	`flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `flip3-+_binary64_81`

Counts

4 → 146

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
30.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(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)))))))
2.0ms	(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)))))))

series2.5s (7.4%)

Counts

4 → 56

Calls

4 calls:

858.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
857.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
400.0ms	(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)))))))
386.0ms	(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)))))))

Compiler

Compiled 6922 to 6098 computations (11.9% saved)

simplify197.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5013	8098

prune1.3s (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	198	4	202
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	200	9	209

Error

0.5b

Counts

209 → 9

Compiler

Compiled 10722 to 7579 computations (29.3% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.5b	(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)))))))
9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.9b	(cbrt.f64 (pow.f64 (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))))))) 3))

rewrite124.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt_binary64_100`
105×	`sqrt-prod_binary64_94`
98×	`times-frac_binary64_84`
88×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
46×	`add-cube-cbrt_binary64_113`
30×	`unpow-prod-down_binary64_157`
18×	`cbrt-prod_binary64_109`
13×	`sqr-pow_binary64_50`
12×	`unpow2_binary64_143`
7×	`pow1_binary64_139`
6×	`distribute-lft-out--_binary64_30` `cube-prod_binary64_106`
5×	`rem-sqrt-square_binary64_91`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `associate-/r/_binary64_24`
3×	`sqrt-pow1_binary64_96` `pow1/2_binary64_158`
2×	`flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `flip3-+_binary64_81`
1×	`cube-mult_binary64_108` `rem-cbrt-cube_binary64_102` `pow1/3_binary64_160` `unpow3_binary64_144`

Counts

4 → 160

Calls

4 calls:

34.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
30.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(cbrt.f64 (pow.f64 (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))))))) 3))
2.0ms	(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)))))))

series2.5s (7.5%)

Counts

4 → 56

Calls

4 calls:

868.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
855.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
420.0ms	(cbrt.f64 (pow.f64 (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))))))) 3))
405.0ms	(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)))))))

Compiler

Compiled 7162 to 6338 computations (11.5% saved)

simplify229.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5004	8893

prune1.6s (4.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	216	9	225

Error

0.5b

Counts

225 → 9

Compiler

Compiled 11733 to 8422 computations (28.2% saved)

regimes2.8s (8.2%)

Accuracy

Total 0.1b remaining (9.1%)

Threshold costs 0.1b (9.1%)

Compiler

Compiled 21875 to 18899 computations (13.6% saved)

bsearch147.0ms (0.4%)

Steps

Iters	Range		Point
6	8.810224470902786e+133	1.33853881495266e+135	8.948713621136704e+133
10	-9.482900424380452e+155	-1.2067687766485158e+144	-9.402290212995132e+153

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	73	99
1	73	99

end0.0ms (0%)

sample4.7s (13.9%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
685.0ms	4763×	body	128	nan

Compiler

Compiled 1281 to 1100 computations (14.1% saved)

Details

analyze2.8s (8.1%)

sample97.0ms (0.3%)

simplify105.0ms (0.3%)

prune6.0ms (0%)

localize35.0ms (0.1%)

rewrite118.0ms (0.3%)

series2.4s (7%)

simplify196.0ms (0.6%)

prune951.0ms (2.8%)

localize40.0ms (0.1%)

rewrite203.0ms (0.6%)

series8.6s (25.3%)

simplify285.0ms (0.8%)

prune1.9s (5.6%)

localize35.0ms (0.1%)

rewrite119.0ms (0.3%)

series2.5s (7.4%)

simplify197.0ms (0.6%)

prune1.3s (3.8%)

localize37.0ms (0.1%)

rewrite124.0ms (0.4%)

series2.5s (7.5%)

simplify229.0ms (0.7%)

prune1.6s (4.6%)

regimes2.8s (8.2%)

bsearch147.0ms (0.4%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.7s (13.9%)

Profiling