Details

analyze1.5s (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)

sample56.0ms (0.2%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
13.0ms	157×	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 (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

10.5b

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 t l) 2)
0.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite452.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

10.4b

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:

17.0ms	(/.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)))))
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)

series1.5s (6.1%)

Error

2.8b

Counts

4 → 59

Calls

4 calls:

603.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
602.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
109.0ms	(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)

Compiler

Compiled 6111 to 5380 computations (12% saved)

simplify103.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5653	8349

prune437.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	225	7	232
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	225	8	233

Error

0.3b

Counts

233 → 8

Compiler

Compiled 7039 to 4760 computations (32.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.4b	(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)))))))
8.4b	(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)))))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite642.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

21.0ms	(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)

series1.8s (7.3%)

Error

0.3b

Counts

4 → 58

Calls

4 calls:

581.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
563.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
242.0ms	(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)))))))
237.0ms	(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 10358 to 8816 computations (14.9% saved)

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4967	8262
1	4967	8262

prune648.0ms (2.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	201	11	212

Error

0.3b

Counts

212 → 11

Compiler

Compiled 10840 to 7668 computations (29.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.4b	(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)))))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite1.5s (6.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

20.0ms	(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)))))
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)))))))

Compiler

Compiled 16197 to 11659 computations (28% saved)

series2.3s (9.3%)

Error

0.3b

Counts

4 → 63

Calls

4 calls:

590.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
589.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
588.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
255.0ms	(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 16299 to 13371 computations (18% saved)

simplify131.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4967	10785
1	4967	10785

prune1.6s (6.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	256	11	267

Error

0.3b

Counts

267 → 11

Compiler

Compiled 19740 to 14106 computations (28.5% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.4b	(sqrt.f64 (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)))))))
9.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite937.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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` `sqrt-div_binary64_95` `associate-/r/_binary64_24`
3×	`flip3-+_binary64_81` `flip-+_binary64_52`
2×	`div-inv_binary64_75`

Counts

4 → 148

Calls

4 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(sqrt.f64 (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 12426 to 9001 computations (27.6% saved)

series1.9s (7.9%)

Error

0.3b

Counts

4 → 64

Calls

4 calls:

609.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
606.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
259.0ms	(sqrt.f64 (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)))))))
222.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 14792 to 12062 computations (18.5% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5216	8106

prune1.2s (5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	212	11	223

Error

0.3b

Counts

223 → 11

Compiler

Compiled 15976 to 11465 computations (28.2% saved)

regimes3.1s (13%)

Accuracy

Total 0.1b remaining (12.4%)

Threshold costs 0.1b (12.4%)

Compiler

Compiled 46868 to 40117 computations (14.4% 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	99
1	91	99

end0.0ms (0%)

sample4.1s (16.7%)

Algorithm

1×

intervals

Results

768.0ms	8000×	body	128	valid
440.0ms	4826×	body	128	nan

Compiler

Compiled 2763 to 2362 computations (14.5% saved)

Details

analyze1.5s (6.3%)

sample56.0ms (0.2%)

simplify56.0ms (0.2%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite452.0ms (1.9%)

series1.5s (6.1%)

simplify103.0ms (0.4%)

prune437.0ms (1.8%)

localize18.0ms (0.1%)

rewrite642.0ms (2.6%)

series1.8s (7.3%)

simplify110.0ms (0.5%)

prune648.0ms (2.7%)

localize21.0ms (0.1%)

rewrite1.5s (6.3%)

series2.3s (9.3%)

simplify131.0ms (0.5%)

prune1.6s (6.8%)

localize28.0ms (0.1%)

rewrite937.0ms (3.9%)

series1.9s (7.9%)

simplify91.0ms (0.4%)

prune1.2s (5%)

regimes3.1s (13%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.1s (16.7%)

Profiling