Details

analyze1.5s (15.3%)

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)

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
14.0ms	145×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify225.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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: 12.4b

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 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))))))
11.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite72.0ms (0.7%)

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

series591.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

339.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
165.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
60.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4927	6661
1	4927	6661

prune568.0ms (5.9%)

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: 12.3b

Counts

186 → 10

Compiler

Compiled 9725 to 7451 computations (23.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.5b	(asin.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
11.5b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite85.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-sqr-sqrt_binary64_101`
156×	`sqrt-prod_binary64_95`
127×	`times-frac_binary64_85`
111×	`*-un-lft-identity_binary64_79`
70×	`difference-of-squares_binary64_48`
62×	`add-cube-cbrt_binary64_114`
41×	`unpow-prod-down_binary64_158`
17×	`associate-/l*_binary64_24`
15×	`unpow2_binary64_144` `sqr-pow_binary64_51`
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` `rem-sqrt-square_binary64_92` `sqrt-div_binary64_96`
2×	`pow-exp_binary64_147` `div-exp_binary64_130` `flip-+_binary64_53` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `asin-acos_binary64_259` `pow-pow_binary64_151` `flip--_binary64_54` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90`

Counts

4 → 194

Calls

4 calls:

24.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
20.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))

series886.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

555.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
233.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
69.0ms	(asin.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
29.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5392	8340

prune614.0ms (6.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	205	11	216

Merged error: 12.3b

Counts

216 → 11

Compiler

Compiled 9459 to 6701 computations (29.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.5b	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
11.5b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_101`
72×	`times-frac_binary64_85`
65×	`*-un-lft-identity_binary64_79`
37×	`add-cube-cbrt_binary64_114`
30×	`sqrt-prod_binary64_95`
28×	`difference-of-squares_binary64_48`
13×	`unpow-prod-down_binary64_158`
9×	`add-exp-log_binary64_117`
8×	`associate-/l*_binary64_24`
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` `unpow2_binary64_144` `sqr-pow_binary64_51` `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 → 131

Calls

4 calls:

14.0ms	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))

series483.0ms (5%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
157.0ms	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
64.0ms	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
33.0ms	(pow.f64 (/.f64 t l) 2)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4927	4522
1	4927	4522

prune406.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	144	10	154

Merged error: 12.3b

Counts

154 → 10

Compiler

Compiled 7332 to 5224 computations (28.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.6b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
11.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64_95` `add-sqr-sqrt_binary64_101`
125×	`times-frac_binary64_85`
112×	`*-un-lft-identity_binary64_79`
70×	`difference-of-squares_binary64_48`
63×	`add-cube-cbrt_binary64_114`
41×	`unpow-prod-down_binary64_158`
17×	`associate-/l*_binary64_24`
15×	`unpow2_binary64_144` `sqr-pow_binary64_51`
9×	`add-exp-log_binary64_117`
7×	`distribute-lft-out--_binary64_31`
6×	`associate-/r*_binary64_23` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96` `pow1_binary64_140`
4×	`add-log-exp_binary64_118`
3×	`pow-unpow_binary64_156`
2×	`pow-exp_binary64_147` `div-exp_binary64_130` `flip-+_binary64_53` `div-inv_binary64_76` `associate-/r/_binary64_25` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `asin-acos_binary64_259` `pow-pow_binary64_151` `flip--_binary64_54` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90` `sqrt-undiv_binary64_100`

Counts

4 → 194

Calls

4 calls:

24.0ms	(/.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)
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

series483.0ms (5%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
72.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
58.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5022	8052

prune535.0ms (5.5%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	5	6
Picked	0	1	1
Done	0	3	3
Total	205	11	216

Merged error: 5.1b

Counts

216 → 11

Compiler

Compiled 8685 to 6424 computations (26% saved)

regimes573.0ms (5.9%)

Compiler: Compiled 6126 to 5548 computations (9.4% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	63
1	39	63

end0.0ms (0%)

sample2.0s (21%)

Algorithm

1×

intervals

Results

795.0ms	8000×	body	128	valid
449.0ms	4576×	body	128	nan

Compiler

Compiled 389 to 348 computations (10.5% saved)

Details

analyze1.5s (15.3%)

sample55.0ms (0.6%)

simplify225.0ms (2.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite72.0ms (0.7%)

series591.0ms (6.1%)

simplify99.0ms (1%)

prune568.0ms (5.9%)

localize18.0ms (0.2%)

rewrite85.0ms (0.9%)

series886.0ms (9.2%)

simplify107.0ms (1.1%)

prune614.0ms (6.4%)

localize16.0ms (0.2%)

rewrite56.0ms (0.6%)

series483.0ms (5%)

simplify80.0ms (0.8%)

prune406.0ms (4.2%)

localize15.0ms (0.2%)

rewrite63.0ms (0.7%)

series483.0ms (5%)

simplify103.0ms (1.1%)

prune535.0ms (5.5%)

regimes573.0ms (5.9%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (21%)

Profiling