Details

analyze2.6s (6.3%)

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)

sample111.0ms (0.3%)

Algorithm

1×

intervals

Results

49.0ms	256×	body	128	valid
28.0ms	174×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify104.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune6.0ms (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

10.8b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(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))))))
0.5b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite720.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

10.7b

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` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `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 → 173

Calls

4 calls:

33.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
32.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.0ms	(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)

series3.2s (7.7%)

Error

1.3b

Counts

4 → 67

Calls

4 calls:

1.5s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
994.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
212.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
129.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 9524 to 8165 computations (14.3% saved)

simplify195.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5083	10882

prune840.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	231	9	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Error

0.6b

Counts

241 → 9

Compiler

Compiled 8826 to 5959 computations (32.5% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 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))))))
0.8b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite818.0ms (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` `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:

38.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.0ms	(pow.f64 (/.f64 t l) 2)
6.0ms	(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)

series2.1s (5%)

Error

0.5b

Counts

4 → 61

Calls

4 calls:

1.2s	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (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))))
181.0ms	(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))))))
111.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 8144 to 6980 computations (14.3% saved)

simplify272.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4957	11509
1	4957	11509

prune894.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	251	4	255
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	254	10	264

Error

0.5b

Counts

264 → 10

Compiler

Compiled 9404 to 6541 computations (30.4% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.5b	(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)))))))
9.5b	(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)))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite929.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

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:

37.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
33.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(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)))))))
2.0ms	(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)

series4.0s (9.7%)

Error

0.5b

Counts

4 → 68

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)))))
1.4s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
346.0ms	(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)))))))
314.0ms	(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 16922 to 14168 computations (16.3% saved)

simplify225.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4954	12364
1	4954	12364

prune1.6s (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	215	9	224

Error

0.5b

Counts

224 → 9

Compiler

Compiled 13711 to 9578 computations (30.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.5b	(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)))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite2.2s (5.4%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

186×	`add-sqr-sqrt_binary64_100`
147×	`sqrt-prod_binary64_94` `times-frac_binary64_84`
122×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
59×	`add-cube-cbrt_binary64_113`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
8×	`pow1_binary64_139`
7×	`rem-sqrt-square_binary64_91`
6×	`associate-/r/_binary64_24`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96`
3×	`sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 193

Calls

4 calls:

31.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
29.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
23.0ms	(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)))))))

Compiler

Compiled 15811 to 11273 computations (28.7% saved)

series6.0s (14.5%)

Error

0.5b

Counts

4 → 78

Calls

4 calls:

1.5s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.5s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.4s	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
375.0ms	(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 26238 to 21366 computations (18.6% saved)

simplify343.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4954	16938
1	4954	16938

prune3.0s (7.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	270	10	280

Error

0.5b

Counts

280 → 10

Compiler

Compiled 23586 to 16454 computations (30.2% saved)

regimes4.9s (11.8%)

Accuracy

Total 0.3b remaining (37.3%)

Threshold costs 0.3b (37.3%)

Compiler

Compiled 40103 to 34626 computations (13.7% saved)

bsearch4.0ms (0%)

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	145	114
1	145	114

end0.0ms (0%)

sample6.2s (15%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
669.0ms	4745×	body	128	nan

Compiler

Compiled 2358 to 2034 computations (13.7% saved)

Details

analyze2.6s (6.3%)

sample111.0ms (0.3%)

simplify104.0ms (0.2%)

prune6.0ms (0%)

localize28.0ms (0.1%)

rewrite720.0ms (1.7%)

series3.2s (7.7%)

simplify195.0ms (0.5%)

prune840.0ms (2%)

localize30.0ms (0.1%)

rewrite818.0ms (2%)

series2.1s (5%)

simplify272.0ms (0.7%)

prune894.0ms (2.2%)

localize33.0ms (0.1%)

rewrite929.0ms (2.2%)

series4.0s (9.7%)

simplify225.0ms (0.5%)

prune1.6s (3.9%)

localize24.0ms (0.1%)

rewrite2.2s (5.4%)

series6.0s (14.5%)

simplify343.0ms (0.8%)

prune3.0s (7.2%)

regimes4.9s (11.8%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.2s (15%)

Profiling