Details

analyze1.4s (8.4%)

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 (0.3%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
11.0ms	136×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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

Error

11.1b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
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))))
10.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite503.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

11.0b

Rules

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

Counts

4 → 194

Calls

4 calls:

22.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
18.0ms	(sqrt.f64 (/.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)
5.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 6678 to 4618 computations (30.8% saved)

series908.0ms (5.5%)

Error

1.3b

Counts

4 → 39

Calls

4 calls:

412.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
303.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
78.0ms	(pow.f64 (/.f64 t l) 2)
70.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 2992 to 2740 computations (8.4% saved)

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5039	6991

prune413.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	227	6	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	228	6	234

Error

0.2b

Counts

234 → 6

Compiler

Compiled 6631 to 4496 computations (32.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.2b	(pow.f64 (/.f64 t l) 2)
0.2b	(pow.f64 (/.f64 Om Omc) 2)
10.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite583.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

163×	`add-sqr-sqrt_binary64_100`
155×	`sqrt-prod_binary64_94`
134×	`times-frac_binary64_84`
120×	`*-un-lft-identity_binary64_78`
71×	`add-cube-cbrt_binary64_113`
70×	`difference-of-squares_binary64_47`
54×	`unpow-prod-down_binary64_157`
17×	`associate-/l*_binary64_23`
16×	`unpow2_binary64_143` `sqr-pow_binary64_50`
12×	`add-exp-log_binary64_116`
7×	`pow1_binary64_139` `distribute-lft-out--_binary64_30`
6×	`add-cbrt-cube_binary64_114` `sqrt-div_binary64_95` `pow-unpow_binary64_155` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117` `pow-exp_binary64_146`
3×	`div-inv_binary64_75` `div-exp_binary64_129`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `associate-/l/_binary64_25` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53`

Counts

4 → 215

Calls

4 calls:

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)))))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
5.0ms	(pow.f64 (/.f64 t l) 2)
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7890 to 5605 computations (29% saved)

series650.0ms (4%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

298.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
155.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
78.0ms	(pow.f64 (/.f64 Om Omc) 2)
72.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 2824 to 2545 computations (9.9% saved)

simplify117.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5017	8317

prune461.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	253	7	260

Error

0.1b

Counts

260 → 7

Compiler

Compiled 7677 to 5359 computations (30.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.0b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite1.3s (7.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

4 → 252

Calls

4 calls:

22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
20.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
20.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 15204 to 10786 computations (29.1% saved)

series1.7s (10.1%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

471.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
468.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
315.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
313.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 8006 to 6876 computations (14.1% saved)

simplify150.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	12750
1	4979	12750

prune1.2s (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	300	7	307

Error

0.1b

Counts

307 → 7

Compiler

Compiled 15633 to 10930 computations (30.1% saved)

localize15.0ms (0.1%)

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 (.f64 t (/.f64 (/.f64 t l) l)))))
3.8b	(*.f64 t (/.f64 (/.f64 t l) l))
10.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 t (/.f64 (/.f64 t l) l))))))

rewrite523.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

188×	`add-sqr-sqrt_binary64_100`
177×	`times-frac_binary64_84`
134×	`*-un-lft-identity_binary64_78`
85×	`add-cube-cbrt_binary64_113`
70×	`difference-of-squares_binary64_47`
48×	`sqrt-prod_binary64_94`
43×	`associate-r_binary64_18`
41×	`unpow-prod-down_binary64_157`
18×	`add-exp-log_binary64_116`
15×	`add-cbrt-cube_binary64_114` `unpow2_binary64_143` `sqr-pow_binary64_50`
14×	`associate-/l*_binary64_23`
8×	`pow1_binary64_139`
7×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75`
5×	`div-exp_binary64_129`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24` `cbrt-undiv_binary64_112`
3×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `associate-l_binary64_19` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `-commutative_binary64_9` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 230

Calls

4 calls:

22.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 t (/.f64 (/.f64 t l) l)))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 t (/.f64 (/.f64 t l) l))))))
17.0ms	(*.f64 t (/.f64 (/.f64 t l) l))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 8512 to 4572 computations (46.3% saved)

series899.0ms (5.5%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

410.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 t (/.f64 (/.f64 t l) l)))))
287.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 t (/.f64 (/.f64 t l) l))))))
91.0ms	(*.f64 t (/.f64 (/.f64 t l) l))
67.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 3028 to 2730 computations (9.8% saved)

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4992	8424
1	4992	8424

prune392.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	269	7	276

Error

0.1b

Counts

276 → 7

Compiler

Compiled 8325 to 4318 computations (48.1% saved)

regimes1.6s (10%)

Accuracy

Total 0.1b remaining (17.9%)

Threshold costs 0.1b (17.9%)

Compiler

Compiled 21711 to 19551 computations (9.9% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	99
1	91	99

end0.0ms (0%)

sample3.2s (19.3%)

Algorithm

1×

intervals

Results

740.0ms	8000×	body	128	valid
630.0ms	4851×	body	128	nan

Compiler

Compiled 1359 to 1220 computations (10.2% saved)

Details

analyze1.4s (8.4%)

sample52.0ms (0.3%)

simplify148.0ms (0.9%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite503.0ms (3.1%)

series908.0ms (5.5%)

simplify110.0ms (0.7%)

prune413.0ms (2.5%)

localize14.0ms (0.1%)

rewrite583.0ms (3.6%)

series650.0ms (4%)

simplify117.0ms (0.7%)

prune461.0ms (2.8%)

localize17.0ms (0.1%)

rewrite1.3s (7.9%)

series1.7s (10.1%)

simplify150.0ms (0.9%)

prune1.2s (7.2%)

localize15.0ms (0.1%)

rewrite523.0ms (3.2%)

series899.0ms (5.5%)

simplify125.0ms (0.8%)

prune392.0ms (2.4%)

regimes1.6s (10%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (19.3%)

Profiling