Details

analyze1.3s (13.2%)

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)

sample52.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
14.0ms	159×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	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: 10.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite61.0ms (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:

17.0ms	(/.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)))))
4.0ms	(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))))))

series329.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
93.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
38.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5043	6451

prune343.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	6	186

Merged error: 10.3b

Counts

186 → 6

Compiler

Compiled 5759 to 3940 computations (31.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
9.2b	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
9.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_139`
8×	`add-sqr-sqrt_binary64_100`
7×	`sqrt-prod_binary64_94` `sqrt-div_binary64_95`
6×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `add-exp-log_binary64_116`
3×	`pow1/2_binary64_158`
2×	`flip-+_binary64_52` `rem-sqrt-square_binary64_91` `flip3-+_binary64_81`
1×	`frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `asin-acos_binary64_258`

Counts

4 → 52

Calls

4 calls:

27.0ms	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

series294.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
36.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
36.0ms	(asin.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
34.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5126	1551

prune121.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	63	7	70

Merged error: 10.3b

Counts

70 → 7

Compiler

Compiled 2548 to 1741 computations (31.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))
9.2b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))

rewrite121.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64_84`
412×	`*-un-lft-identity_binary64_78`
404×	`add-sqr-sqrt_binary64_100`
182×	`add-cube-cbrt_binary64_113`
125×	`sqrt-prod_binary64_94`
108×	`difference-of-squares_binary64_47`
61×	`distribute-lft-out_binary64_29`
30×	`associate-/r*_binary64_22`
27×	`distribute-lft-out--_binary64_30`
20×	`associate-/r/_binary64_24`
13×	`unpow-prod-down_binary64_157`
12×	`div-inv_binary64_75` `add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53`
6×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `div-exp_binary64_129` `associate-/l*_binary64_23`
3×	`cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `pow-unpow_binary64_155`
2×	`pow-exp_binary64_146` `associate-/l/_binary64_25`
1×	`pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `unpow2_binary64_143` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `sqrt-div_binary64_95` `clear-num_binary64_77` `asin-acos_binary64_258` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 346

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))
23.0ms	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
5.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))

series339.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))
99.0ms	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
33.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))
15.0ms	(pow.f64 (/.f64 t l) 2)

simplify196.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5018	19218

prune921.0ms (9.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	355	3	358
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	356	9	365

Merged error: 10.3b

Counts

365 → 9

Compiler

Compiled 15028 to 9386 computations (37.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))))
1.8b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))
14.6b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.6b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite275.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

461×	`times-frac_binary64_84`
357×	`*-un-lft-identity_binary64_78`
354×	`add-sqr-sqrt_binary64_100`
221×	`sqrt-prod_binary64_94`
153×	`add-cube-cbrt_binary64_113`
103×	`cbrt-prod_binary64_109`
96×	`difference-of-squares_binary64_47`
54×	`distribute-lft-out_binary64_29`
24×	`distribute-lft-out--_binary64_30`
9×	`associate-/r/_binary64_24`
5×	`div-inv_binary64_75` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-log-exp_binary64_117` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
2×	`flip-+_binary64_52` `pow1/3_binary64_160` `flip3-+_binary64_81`
1×	`sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `pow1/2_binary64_158`

Counts

4 → 269

Calls

4 calls:

201.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))
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))))
1.0ms	(asin.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))))

series545.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))
104.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
99.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
80.0ms	(asin.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (-.f64 1 (/.f64 Om Omc)))))))

simplify184.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5033	18248

prune1.3s (13%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	281	9	290

Merged error: 10.3b

Counts

290 → 9

Compiler

Compiled 16728 to 11354 computations (32.1% saved)

regimes951.0ms (9.4%)

Compiler: Compiled 13773 to 12057 computations (12.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms (0%)

sample2.3s (23%)

Algorithm

1×

intervals

Results

750.0ms	8000×	body	128	valid
412.0ms	4742×	body	128	nan

Compiler

Compiled 888 to 775 computations (12.7% saved)

Details

analyze1.3s (13.2%)

sample52.0ms (0.5%)

simplify140.0ms (1.4%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite61.0ms (0.6%)

series329.0ms (3.2%)

simplify102.0ms (1%)

prune343.0ms (3.4%)

localize18.0ms (0.2%)

rewrite40.0ms (0.4%)

series294.0ms (2.9%)

simplify70.0ms (0.7%)

prune121.0ms (1.2%)

localize17.0ms (0.2%)

rewrite121.0ms (1.2%)

series339.0ms (3.3%)

simplify196.0ms (1.9%)

prune921.0ms (9.1%)

localize21.0ms (0.2%)

rewrite275.0ms (2.7%)

series545.0ms (5.4%)

simplify184.0ms (1.8%)

prune1.3s (13%)

regimes951.0ms (9.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (23%)

Profiling