Details

analyze1.5s (5.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4997	203
1	4997	203
0	4	4
1	4	4

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 (0.2%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune4.0ms (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

11.6b

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)
0.5b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite500.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

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×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `associate-/l/_binary64_25` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `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 → 173

Calls

4 calls:

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

Compiler

Compiled 6194 to 4307 computations (30.5% saved)

series2.4s (9%)

Error

2.5b

Counts

4 → 64

Calls

4 calls:

1.0s	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
981.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
152.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
111.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 6293 to 5582 computations (11.3% saved)

simplify93.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5493	8408

prune517.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	229	8	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	230	8	238

Error

0.6b

Counts

238 → 8

Compiler

Compiled 7160 to 4883 computations (31.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.5b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
0.6b	(asin.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
10.4b	(sqrt.f64 (/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))

rewrite1.9s (7.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

639×	`times-frac_binary64_84`
518×	`add-sqr-sqrt_binary64_100`
385×	`*-un-lft-identity_binary64_78`
236×	`add-cube-cbrt_binary64_113`
210×	`difference-of-squares_binary64_47`
149×	`sqrt-prod_binary64_94`
97×	`unpow-prod-down_binary64_157`
48×	`associate-/r*_binary64_22`
43×	`unpow2_binary64_143` `sqr-pow_binary64_50`
21×	`distribute-lft-out--_binary64_30`
18×	`add-exp-log_binary64_116`
16×	`associate-/r/_binary64_24`
10×	`div-inv_binary64_75`
9×	`add-cbrt-cube_binary64_114`
8×	`pow1_binary64_139` `div-exp_binary64_129`
7×	`flip3--_binary64_82` `flip--_binary64_53`
5×	`rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117`
3×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`inv-pow_binary64_163` `pow-flip_binary64_152` `1-exp_binary64_122` `rec-exp_binary64_128` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-div_binary64_95` `asin-acos_binary64_258` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 419

Calls

4 calls:

33.0ms	(sqrt.f64 (/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
23.0ms	(/.f64 1 (/.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 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))

Compiler

Compiled 18257 to 13364 computations (26.8% saved)

series2.3s (8.9%)

Error

0.6b

Counts

4 → 64

Calls

4 calls:

1.0s	(/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
942.0ms	(sqrt.f64 (/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
163.0ms	(asin.f64 (sqrt.f64 (/.f64 1 (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))))
103.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 6329 to 5618 computations (11.2% saved)

simplify234.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4955	21303
1	4955	21303

prune1.4s (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	483	0	483
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	483	8	491

Error

0.6b

Counts

491 → 8

Compiler

Compiled 17073 to 11854 computations (30.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.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	(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))))))
10.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite518.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

155×	`add-sqr-sqrt_binary64_100` `sqrt-prod_binary64_94`
125×	`times-frac_binary64_84`
112×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
63×	`add-cube-cbrt_binary64_113`
41×	`unpow-prod-down_binary64_157`
17×	`associate-/l*_binary64_23`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114` `sqrt-div_binary64_95` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `div-inv_binary64_75` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 194

Calls

4 calls:

19.0ms	(/.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 t l) 2)
3.0ms	(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))))))

Compiler

Compiled 7390 to 5278 computations (28.6% saved)

series1.6s (5.9%)

Error

0.6b

Counts

4 → 55

Calls

4 calls:

955.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
222.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
166.0ms	(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))))))
116.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 5153 to 4571 computations (11.3% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5566	9351

prune536.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	249	8	257

Error

0.6b

Counts

257 → 8

Compiler

Compiled 7869 to 5510 computations (30% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
7.2b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
10.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite705.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

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

Counts

4 → 146

Calls

4 calls:

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

Compiler

Compiled 8808 to 6286 computations (28.6% saved)

series2.8s (10.7%)

Error

0.6b

Counts

4 → 68

Calls

4 calls:

994.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
968.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
331.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
328.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 11714 to 9980 computations (14.8% saved)

simplify106.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	8668
1	4967	8668

prune756.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	212	10	222

Error

0.6b

Counts

222 → 10

Compiler

Compiled 11050 to 7787 computations (29.5% saved)

regimes3.9s (14.9%)

Accuracy

Total 0.2b remaining (21.9%)

Threshold costs 0.2b (21.9%)

Compiler

Compiled 51393 to 44145 computations (14.1% saved)

bsearch4.0ms (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	91	99
1	91	99

end0.0ms (0%)

sample4.2s (16%)

Algorithm

1×

intervals

Results

761.0ms	8000×	body	128	valid
415.0ms	4746×	body	128	nan

Compiler

Compiled 2982 to 2566 computations (14% saved)

Details

analyze1.5s (5.9%)

sample52.0ms (0.2%)

simplify56.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite500.0ms (1.9%)

series2.4s (9%)

simplify93.0ms (0.4%)

prune517.0ms (2%)

localize15.0ms (0.1%)

rewrite1.9s (7.3%)

series2.3s (8.9%)

simplify234.0ms (0.9%)

prune1.4s (5.3%)

localize17.0ms (0.1%)

rewrite518.0ms (2%)

series1.6s (5.9%)

simplify100.0ms (0.4%)

prune536.0ms (2%)

localize19.0ms (0.1%)

rewrite705.0ms (2.7%)

series2.8s (10.7%)

simplify106.0ms (0.4%)

prune756.0ms (2.9%)

regimes3.9s (14.9%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.2s (16%)

Profiling