Details

analyze1.3s (5.7%)

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)

sample55.0ms (0.2%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
11.0ms	143×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify145.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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

9.6b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.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))))))
8.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite415.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

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	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (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 6194 to 4303 computations (30.5% saved)

series1.8s (7.8%)

Error

1.6b

Counts

4 → 65

Calls

4 calls:

727.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
723.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
119.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
79.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 7644 to 6687 computations (12.5% saved)

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4981	9980
1	4981	9980

prune473.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	231	7	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

0.7b

Counts

239 → 7

Compiler

Compiled 8151 to 5628 computations (31% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (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 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
2.8b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
8.5b	(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)))))

rewrite309.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

64×	`*-un-lft-identity_binary64_78`
60×	`add-sqr-sqrt_binary64_100`
52×	`times-frac_binary64_84`
36×	`add-cube-cbrt_binary64_113`
27×	`sqrt-prod_binary64_94`
26×	`log-pow_binary64_167`
18×	`exp-prod_binary64_130`
14×	`difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30`
13×	`pow1_binary64_139` `unpow-prod-down_binary64_157`
7×	`associate-/l*_binary64_23`
6×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `log-prod_binary64_164` `associate-/r*_binary64_22`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `unpow2_binary64_143` `sqr-pow_binary64_50` `rem-log-exp_binary64_119` `asin-acos_binary64_258` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53`

Counts

4 → 125

Calls

4 calls:

22.0ms	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
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	(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 4583 to 3340 computations (27.1% saved)

series2.3s (10.2%)

Error

0.7b

Counts

4 → 62

Calls

4 calls:

1.0s	(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)))))
810.0ms	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
205.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
113.0ms	(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 7770 to 6841 computations (12% saved)

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5000	7340

prune392.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Error

0.7b

Counts

194 → 7

Compiler

Compiled 6348 to 4440 computations (30.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.7b	(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 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite682.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

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` `flip-+_binary64_52` `associate-/r/_binary64_24`
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))))))
10.0ms	(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)

series1.6s (6.8%)

Error

0.7b

Counts

4 → 69

Calls

4 calls:

766.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
289.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
159.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
158.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 8599 to 7409 computations (13.8% saved)

simplify149.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4937	9293
1	4937	9293

prune832.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	244	8	252

Error

0.7b

Counts

252 → 8

Compiler

Compiled 11336 to 8298 computations (26.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(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 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))

rewrite2.0s (8.6%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

403×	`sqrt-prod_binary64_94`
355×	`add-sqr-sqrt_binary64_100`
290×	`times-frac_binary64_84`
240×	`*-un-lft-identity_binary64_78`
192×	`cbrt-prod_binary64_109`
180×	`difference-of-squares_binary64_47`
165×	`unpow-prod-down_binary64_157`
114×	`add-cube-cbrt_binary64_113`
93×	`cube-prod_binary64_106`
37×	`sqr-pow_binary64_50`
36×	`unpow2_binary64_143`
18×	`distribute-lft-out--_binary64_30`
12×	`sqrt-div_binary64_95`
7×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24`
5×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`div-inv_binary64_75` `pow1/2_binary64_158` `sqrt-pow1_binary64_96`
1×	`pow1/3_binary64_160` `cube-div_binary64_107` `cbrt-div_binary64_110` `unpow3_binary64_144` `cube-mult_binary64_108` `rem-cbrt-cube_binary64_102`

Counts

4 → 335

Calls

4 calls:

41.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (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 20361 to 15361 computations (24.6% saved)

series2.1s (9.1%)

Error

0.7b

Counts

4 → 78

Calls

4 calls:

780.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
777.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
160.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
151.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 10734 to 9363 computations (12.8% saved)

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

413 → 413

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5309	19554

prune1.8s (7.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	413	0	413
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	413	8	421

Error

0.7b

Counts

421 → 8

Compiler

Compiled 20583 to 14925 computations (27.5% saved)

regimes2.7s (11.7%)

Accuracy

Total 0.1b remaining (14.3%)

Threshold costs 0.1b (14.3%)

Compiler

Compiled 36651 to 32612 computations (11% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	101
1	91	101

end0.0ms (0%)

sample3.5s (15.1%)

Algorithm

1×

intervals

Results

727.0ms	8000×	body	128	valid
383.0ms	4663×	body	128	nan

Compiler

Compiled 2122 to 1888 computations (11% saved)

Details

analyze1.3s (5.7%)

sample55.0ms (0.2%)

simplify145.0ms (0.6%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite415.0ms (1.8%)

series1.8s (7.8%)

simplify123.0ms (0.5%)

prune473.0ms (2%)

localize16.0ms (0.1%)

rewrite309.0ms (1.3%)

series2.3s (10.2%)

simplify104.0ms (0.5%)

prune392.0ms (1.7%)

localize20.0ms (0.1%)

rewrite682.0ms (3%)

series1.6s (6.8%)

simplify149.0ms (0.6%)

prune832.0ms (3.6%)

localize22.0ms (0.1%)

rewrite2.0s (8.6%)

series2.1s (9.1%)

simplify198.0ms (0.9%)

prune1.8s (7.9%)

regimes2.7s (11.7%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (15.1%)

Profiling