Details

analyze1.5s (8.5%)

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

Symmetry

Compiler

Compiled 20 to 20 computations (0% saved)

sample55.0ms (0.3%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
11.0ms	132×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

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

8.5b

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 Om Omc) 2)
0.3b	(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))))))
8.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite280.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

Rules

80×	`add-sqr-sqrt_binary64_100`
67×	`times-frac_binary64_84`
59×	`*-un-lft-identity_binary64_78`
48×	`sqrt-prod_binary64_94`
38×	`add-cube-cbrt_binary64_113` `unpow-prod-down_binary64_157`
30×	`difference-of-squares_binary64_47`
10×	`add-exp-log_binary64_116`
8×	`unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `pow-exp_binary64_146`
3×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75`
2×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `asin-acos_binary64_258`

Counts

4 → 126

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)))))
8.0ms	(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))))))

Compiler

Compiled 4135 to 2867 computations (30.7% saved)

series1.8s (10.2%)

Error

1.3b

Counts

4 → 56

Calls

4 calls:

1.4s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
113.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
77.0ms	(pow.f64 (/.f64 t l) 2)
72.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 8886 to 7684 computations (13.5% saved)

simplify102.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4972	7292
1	4972	7292

prune386.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	10	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Error

0.4b

Counts

183 → 10

Compiler

Compiled 6490 to 4540 computations (30% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.4b	(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)))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite472.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

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` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 194

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 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)

series1.9s (11%)

Error

0.3b

Counts

4 → 69

Calls

4 calls:

1.4s	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
175.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
118.0ms	(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))))))
72.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 9709 to 8369 computations (13.8% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5064	11771

prune587.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	262	11	273

Error

0.3b

Counts

273 → 11

Compiler

Compiled 9613 to 6802 computations (29.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.9b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

rewrite682.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

174×	`sqrt-prod_binary64_94`
146×	`add-sqr-sqrt_binary64_100`
120×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
54×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
10×	`pow1_binary64_139` `sqrt-div_binary64_95` `rem-sqrt-square_binary64_91`
9×	`sqrt-pow1_binary64_96`
6×	`distribute-lft-out--_binary64_30`
5×	`pow1/2_binary64_158`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `associate-/r/_binary64_24` `flip-+_binary64_52`
3×	`pow-flip_binary64_152`
2×	`div-inv_binary64_75`
1×	`inv-pow_binary64_163`

Counts

4 → 176

Calls

4 calls:

22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.0ms	(sqrt.f64 (/.f64 1 (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))))

Compiler

Compiled 9163 to 6797 computations (25.8% saved)

series2.2s (12.6%)

Error

0.3b

Counts

4 → 93

Calls

4 calls:

1.2s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
396.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
188.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
177.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 11377 to 9755 computations (14.3% saved)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5043	10253

prune851.0ms (4.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	269	11	280

Error

0.3b

Counts

280 → 11

Compiler

Compiled 12520 to 9175 computations (26.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.4b	(asin.f64 (-.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (pow.f64 (/.f64 Om Omc) 2)))))
8.0b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.0b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite262.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

34×	`add-sqr-sqrt_binary64_100`
31×	`times-frac_binary64_84`
30×	`sqrt-prod_binary64_94`
28×	`*-un-lft-identity_binary64_78`
26×	`add-cube-cbrt_binary64_113`
13×	`unpow-prod-down_binary64_157`
9×	`pow1_binary64_139`
7×	`add-exp-log_binary64_116`
6×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `pow-unpow_binary64_155`
2×	`pow1/2_binary64_158` `inv-pow_binary64_163` `pow-flip_binary64_152` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `pow-exp_binary64_146`
1×	`asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 97

Calls

4 calls:

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

Compiler

Compiled 4404 to 3287 computations (25.4% saved)

series611.0ms (3.5%)

Error

0.3b

Counts

4 → 41

Calls

4 calls:

221.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
175.0ms	(asin.f64 (-.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (pow.f64 (/.f64 Om Omc) 2)))))
78.0ms	(pow.f64 (/.f64 t l) 2)
65.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 4255 to 3751 computations (11.8% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5003	2980

prune289.0ms (1.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	138	11	149

Error

0.3b

Counts

149 → 11

Compiler

Compiled 5207 to 3843 computations (26.2% saved)

regimes1.8s (10.2%)

Accuracy

Total 0.5b remaining (44.4%)

Threshold costs 0.5b (44.4%)

Compiler

Compiled 25407 to 22243 computations (12.5% saved)

bsearch3.0ms (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	101
1	91	101

Removed

()

end0.0ms (0%)

sample3.2s (18.5%)

Algorithm

1×

intervals

Results

936.0ms	8000×	body	128	valid
399.0ms	4741×	body	128	nan

Compiler

Compiled 1571 to 1370 computations (12.8% saved)

Details

analyze1.5s (8.5%)

sample55.0ms (0.3%)

simplify56.0ms (0.3%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite280.0ms (1.6%)

series1.8s (10.2%)

simplify102.0ms (0.6%)

prune386.0ms (2.2%)

localize17.0ms (0.1%)

rewrite472.0ms (2.7%)

series1.9s (11%)

simplify136.0ms (0.8%)

prune587.0ms (3.4%)

localize20.0ms (0.1%)

rewrite682.0ms (3.9%)

series2.2s (12.6%)

simplify133.0ms (0.8%)

prune851.0ms (4.9%)

localize18.0ms (0.1%)

rewrite262.0ms (1.5%)

series611.0ms (3.5%)

simplify76.0ms (0.4%)

prune289.0ms (1.7%)

regimes1.8s (10.2%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (18.5%)

Profiling