Details

analyze1.4s (12.2%)

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)

sample51.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
12.0ms	124×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify217.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4891	29
1	4891	29

prune3.0ms (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

Merged error: 8.5b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(/.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))))))
7.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite73.0ms (0.6%)

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:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
19.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(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))))))

series586.0ms (5%)

Counts

4 → 12

Calls

4 calls:

330.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
164.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
62.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
29.0ms	(pow.f64 (/.f64 t l) 2)

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4939	6661
1	4939	6661

prune339.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	179	7	186

Merged error: 8.5b

Counts

186 → 7

Compiler

Compiled 5888 to 4016 computations (31.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_109`
7×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`cbrt-div_binary64_110`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`flip-+_binary64_52` `pow1/3_binary64_160` `sqrt-div_binary64_95` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96`
1×	`sqrt-prod_binary64_94` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `pow1/2_binary64_158`

Counts

4 → 53

Calls

4 calls:

33.0ms	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series1.3s (10.7%)

Counts

4 → 12

Calls

4 calls:

691.0ms	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
196.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
188.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
184.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify98.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5010	1444

prune156.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	65	7	72

Merged error: 8.5b

Counts

72 → 7

Compiler

Compiled 3198 to 2370 computations (25.9% saved)

localize20.0ms (0.2%)

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))))))))
1.0b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
12.9b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
12.9b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite100.0ms (0.8%)

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:

21.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
17.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(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))))))))

series1.6s (13.4%)

Counts

4 → 12

Calls

4 calls:

491.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
488.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
477.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
126.0ms	(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))))))))

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4925	10005
1	4925	10005

prune670.0ms (5.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	199	7	206

Merged error: 8.5b

Counts

206 → 7

Compiler

Compiled 11276 to 7886 computations (30.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_109`
8×	`cbrt-div_binary64_110` `add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `pow1/3_binary64_160` `add-exp-log_binary64_116` `pow1_binary64_139` `flip3-+_binary64_81`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series710.0ms (6%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
182.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
173.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
169.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4904	1336
1	4904	1336

prune256.0ms (2.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	64	7	71

Merged error: 8.5b

Counts

71 → 7

Compiler

Compiled 4832 to 3590 computations (25.7% saved)

regimes1.1s (9.7%)

Compiler: Compiled 14796 to 12804 computations (13.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	29
1	29	29

end0.0ms (0%)

sample2.6s (22.2%)

Algorithm

1×

intervals

Results

777.0ms	8000×	body	128	valid
461.0ms	4737×	body	128	nan

Compiler

Compiled 1082 to 940 computations (13.1% saved)

Details

analyze1.4s (12.2%)

sample51.0ms (0.4%)

simplify217.0ms (1.8%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite73.0ms (0.6%)

series586.0ms (5%)

simplify102.0ms (0.9%)

prune339.0ms (2.9%)

localize20.0ms (0.2%)

rewrite50.0ms (0.4%)

series1.3s (10.7%)

simplify98.0ms (0.8%)

prune156.0ms (1.3%)

localize20.0ms (0.2%)

rewrite100.0ms (0.8%)

series1.6s (13.4%)

simplify144.0ms (1.2%)

prune670.0ms (5.7%)

localize24.0ms (0.2%)

rewrite27.0ms (0.2%)

series710.0ms (6%)

simplify76.0ms (0.6%)

prune256.0ms (2.2%)

regimes1.1s (9.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (22.2%)

Profiling