Details

analyze1.7s (4.2%)

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)

sample54.0ms (0.1%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
12.0ms	147×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

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

13.3b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(pow.f64 (/.f64 t l) 2)
0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
12.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite431.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

13.3b

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:

21.0ms	(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)
4.0ms	(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 3950 to 2735 computations (30.8% saved)

series2.4s (5.8%)

Error

2.5b

Counts

4 → 48

Calls

4 calls:

2.0s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
166.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
109.0ms	(pow.f64 (/.f64 t l) 2)
108.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5767 to 5137 computations (10.9% saved)

simplify102.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4982	5848
1	4982	5848

prune274.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	6	175

Error

0.4b

Counts

175 → 6

Compiler

Compiled 3215 to 2263 computations (29.6% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
2.1b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
12.9b	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite340.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

44×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
40×	`times-frac_binary64_84`
32×	`add-cube-cbrt_binary64_113`
27×	`sqrt-prod_binary64_94`
26×	`unpow-prod-down_binary64_157`
22×	`log-pow_binary64_167`
18×	`exp-prod_binary64_130`
10×	`pow1_binary64_139`
7×	`add-exp-log_binary64_116`
6×	`difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
3×	`div-inv_binary64_75` `log-prod_binary64_164` `pow-unpow_binary64_155`
2×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-log-exp_binary64_119` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129`

Counts

4 → 106

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.0ms	(pow.f64 (/.f64 t l) 2)
7.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 3233 to 2317 computations (28.3% saved)

series3.8s (9%)

Error

0.4b

Counts

4 → 50

Calls

4 calls:

3.0s	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
329.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
172.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
113.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 7635 to 6798 computations (11% saved)

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5253	6167

prune336.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Error

0.4b

Counts

162 → 6

Compiler

Compiled 4116 to 2983 computations (27.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.5b	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
12.5b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
12.5b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite540.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

110×	`sqrt-prod_binary64_94`
70×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
64×	`times-frac_binary64_84`
40×	`add-cube-cbrt_binary64_113`
12×	`difference-of-squares_binary64_47`
10×	`sqrt-div_binary64_95`
8×	`pow1_binary64_139` `rem-sqrt-square_binary64_91`
6×	`distribute-lft-out_binary64_29` `distribute-lft-out--_binary64_30`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24`
2×	`div-inv_binary64_75`

Counts

4 → 128

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.0ms	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (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 5588 to 3668 computations (34.4% saved)

series3.4s (8.1%)

Error

0.4b

Counts

4 → 62

Calls

4 calls:

1.4s	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
1.4s	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
220.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
210.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7112 to 5644 computations (20.6% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4949	7230
1	4949	7230

prune491.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	189	7	196

Error

0.4b

Counts

196 → 7

Compiler

Compiled 6046 to 3985 computations (34.1% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
12.5b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
12.5b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
12.5b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite391.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

19×	`sqrt-prod_binary64_94`
14×	`add-sqr-sqrt_binary64_100`
10×	`sqrt-div_binary64_95`
9×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`sqrt-pow1_binary64_96`
5×	`pow1/2_binary64_158` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 66

Calls

4 calls:

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

Compiler

Compiled 4332 to 2929 computations (32.4% saved)

series1.3s (3%)

Error

0.4b

Counts

4 → 54

Calls

4 calls:

401.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
232.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
228.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
228.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7758 to 5927 computations (23.6% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4949	2928
1	4949	2928

prune503.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Error

0.4b

Counts

127 → 7

Compiler

Compiled 5951 to 4000 computations (32.8% saved)

regimes23.3s (55.8%)

Accuracy

Total 0.1b remaining (12.3%)

Threshold costs 0.1b (12.3%)

Compiler

Compiled 278282 to 237815 computations (14.5% saved)

bsearch26.0ms (0.1%)

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	106	103
1	106	103

end8.0ms (0%)

Compiler: Compiled 66 to 50 computations (24.2% saved)

sample2.0s (4.8%)

Algorithm

1×

intervals

Results

742.0ms	8000×	body	128	valid
414.0ms	4747×	body	128	nan

Compiler

Compiled 351 to 309 computations (12% saved)

Details

analyze1.7s (4.2%)

sample54.0ms (0.1%)

simplify53.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0%)

rewrite431.0ms (1%)

series2.4s (5.8%)

simplify102.0ms (0.2%)

prune274.0ms (0.7%)

localize16.0ms (0%)

rewrite340.0ms (0.8%)

series3.8s (9%)

simplify87.0ms (0.2%)

prune336.0ms (0.8%)

localize21.0ms (0.1%)

rewrite540.0ms (1.3%)

series3.4s (8.1%)

simplify108.0ms (0.3%)

prune491.0ms (1.2%)

localize30.0ms (0.1%)

rewrite391.0ms (0.9%)

series1.3s (3%)

simplify95.0ms (0.2%)

prune503.0ms (1.2%)

regimes23.3s (55.8%)

bsearch26.0ms (0.1%)

simplify4.0ms (0%)

end8.0ms (0%)

sample2.0s (4.8%)

Profiling