Details

analyze1.5s (10.7%)

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)

sample56.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
15.0ms	153×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify226.0ms (1.7%)

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: 8.6b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))))
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite73.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_101`
108×	`times-frac_binary64_85`
98×	`*-un-lft-identity_binary64_79`
70×	`difference-of-squares_binary64_48`
49×	`add-cube-cbrt_binary64_114`
48×	`sqrt-prod_binary64_95`
41×	`unpow-prod-down_binary64_158`
15×	`unpow2_binary64_144` `sqr-pow_binary64_51`
14×	`associate-/l*_binary64_24`
9×	`add-exp-log_binary64_117`
7×	`distribute-lft-out--_binary64_31`
6×	`add-cbrt-cube_binary64_115` `pow1_binary64_140`
4×	`associate-/r/_binary64_25` `add-log-exp_binary64_118`
3×	`associate-/r*_binary64_23` `pow-unpow_binary64_156` `div-inv_binary64_76`
2×	`pow-exp_binary64_147` `div-exp_binary64_130` `flip-+_binary64_53` `rem-sqrt-square_binary64_92` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `asin-acos_binary64_259` `div-sub_binary64_84` `pow-pow_binary64_151` `flip--_binary64_54` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90`

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)))))
20.0ms	(/.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))))))

series590.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

336.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
166.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
61.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
28.0ms	(pow.f64 (/.f64 t l) 2)

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	6661
1	4939	6661

prune816.0ms (6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	9	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Merged error: 8.5b

Counts

186 → 10

Compiler

Compiled 15094 to 12048 computations (20.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
0.4b	(/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
7.7b	(sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`times-frac_binary64_85` `add-sqr-sqrt_binary64_101`
16×	`sqrt-prod_binary64_95` `add-cube-cbrt_binary64_114` `associate-/r/_binary64_25` `*-un-lft-identity_binary64_79`
13×	`unpow-prod-down_binary64_158`
12×	`add-exp-log_binary64_117` `flip-+_binary64_53` `flip3-+_binary64_82`
9×	`add-cbrt-cube_binary64_115`
8×	`frac-times_binary64_89`
6×	`pow1_binary64_140`
4×	`associate-/l_binary64_24` `associate-l/_binary64_22` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
3×	`div-exp_binary64_130` `pow-unpow_binary64_156` `div-inv_binary64_76` `difference-of-squares_binary64_48`
2×	`pow-exp_binary64_147` `cbrt-undiv_binary64_113` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `pow-to-exp_binary64_148` `unpow2_binary64_144` `sqr-pow_binary64_51` `asin-acos_binary64_259` `div-sub_binary64_84` `pow-pow_binary64_151` `flip--_binary64_54` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90`

Counts

4 → 98

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
28.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
5.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

series875.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

496.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
273.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
80.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 Om Omc) 2))) (.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) (+.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
25.0ms	(pow.f64 (/.f64 t l) 2)

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4950	3526
1	4950	3526

prune269.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	110	10	120

Merged error: 8.5b

Counts

120 → 10

Compiler

Compiled 5318 to 3775 computations (29% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite127.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

297×	`cbrt-prod_binary64_110`
281×	`add-sqr-sqrt_binary64_101`
234×	`times-frac_binary64_85`
194×	`*-un-lft-identity_binary64_79`
130×	`difference-of-squares_binary64_48`
108×	`sqrt-prod_binary64_95`
103×	`add-cube-cbrt_binary64_114`
52×	`unpow-prod-down_binary64_158`
26×	`unpow2_binary64_144` `sqr-pow_binary64_51`
17×	`associate-/l*_binary64_24`
13×	`distribute-lft-out--_binary64_31`
10×	`cbrt-div_binary64_111`
6×	`associate-/r*_binary64_23` `add-exp-log_binary64_117`
5×	`rem-sqrt-square_binary64_92` `pow1_binary64_140`
4×	`add-cbrt-cube_binary64_115` `flip-+_binary64_53` `associate-/r/_binary64_25` `add-log-exp_binary64_118` `flip3-+_binary64_82`
2×	`div-inv_binary64_76` `pow1/3_binary64_161` `associate-/l/_binary64_26`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip--_binary64_54` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90`

Counts

4 → 290

Calls

4 calls:

28.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
23.0ms	(/.f64 (cbrt.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))))

series1.3s (10%)

Counts

4 → 12

Calls

4 calls:

492.0ms	(/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
492.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
187.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
177.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify205.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4901	15453
1	4901	15453

prune1.5s (10.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	302	0	302
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	302	10	312

Merged error: 8.5b

Counts

312 → 10

Compiler

Compiled 18151 to 12977 computations (28.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.7b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
15.1b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.1b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.1b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite176.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`add-sqr-sqrt_binary64_101`
144×	`times-frac_binary64_85` `cbrt-prod_binary64_110`
121×	`*-un-lft-identity_binary64_79`
90×	`difference-of-squares_binary64_48`
58×	`add-cube-cbrt_binary64_114`
36×	`unpow-prod-down_binary64_158`
24×	`pow1_binary64_140`
18×	`unpow2_binary64_144` `sqr-pow_binary64_51`
15×	`cbrt-div_binary64_111` `sqrt-pow1_binary64_97`
12×	`pow1/3_binary64_161`
9×	`distribute-lft-out--_binary64_31` `pow-prod-up_binary64_149`
7×	`sqrt-div_binary64_96`
6×	`associate-/r/_binary64_25` `pow-plus_binary64_142`
5×	`frac-times_binary64_89` `associate-*l/_binary64_22` `pow-prod-down_binary64_150`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`flip-+_binary64_53` `div-inv_binary64_76` `associate-*r/_binary64_21` `pow-sqr_binary64_52` `flip3-+_binary64_82`
2×	`pow2_binary64_160`
1×	`sqrt-prod_binary64_95` `pow3_binary64_162` `pow1/2_binary64_159`

Counts

4 → 202

Calls

4 calls:

63.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
24.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
20.0ms	(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)))))

series1.8s (13.4%)

Counts

4 → 12

Calls

4 calls:

492.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
487.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
479.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
351.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

simplify168.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4887	9554
1	4887	9554

prune1.1s (8.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	214	10	224

Merged error: 8.5b

Counts

224 → 10

Compiler

Compiled 14822 to 10275 computations (30.7% saved)

regimes413.0ms (3.1%)

Compiler: Compiled 5416 to 4712 computations (13% 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%)

sample2.0s (14.7%)

Algorithm

1×

intervals

Results

778.0ms	8000×	body	128	valid
458.0ms	4703×	body	128	nan

Compiler

Compiled 412 to 362 computations (12.1% saved)

Details

analyze1.5s (10.7%)

sample56.0ms (0.4%)

simplify226.0ms (1.7%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite73.0ms (0.5%)

series590.0ms (4.4%)

simplify104.0ms (0.8%)

prune816.0ms (6%)

localize19.0ms (0.1%)

rewrite80.0ms (0.6%)

series875.0ms (6.5%)

simplify96.0ms (0.7%)

prune269.0ms (2%)

localize21.0ms (0.2%)

rewrite127.0ms (0.9%)

series1.3s (10%)

simplify205.0ms (1.5%)

prune1.5s (10.8%)

localize31.0ms (0.2%)

rewrite176.0ms (1.3%)

series1.8s (13.4%)

simplify168.0ms (1.2%)

prune1.1s (8.1%)

regimes413.0ms (3.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (14.7%)

Profiling