Details

analyze1.3s (13.9%)

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)

sample48.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
11.0ms	133×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify350.0ms (3.6%)

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

Merged error: 10.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(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))))
1.2b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_441`
108×	`times-frac_binary64_425`
98×	`*-un-lft-identity_binary64_419`
70×	`difference-of-squares_binary64_388`
49×	`add-cube-cbrt_binary64_454`
48×	`sqrt-prod_binary64_435`
41×	`unpow-prod-down_binary64_498`
15×	`sqr-pow_binary64_391` `unpow2_binary64_484`
14×	`associate-/l*_binary64_364`
9×	`add-exp-log_binary64_457`
7×	`distribute-lft-out--_binary64_371`
6×	`add-cbrt-cube_binary64_455` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`div-inv_binary64_416` `pow-unpow_binary64_496` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `pow-exp_binary64_487` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `associate-/l/_binary64_366`
1×	`sqrt-div_binary64_436` `clear-num_binary64_418` `pow1/2_binary64_499` `flip3--_binary64_423` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `flip--_binary64_394` `asin-acos_binary64_599` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

4 → 173

Calls

4 calls:

18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(/.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))))))

series318.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
91.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
32.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4950	6453
1	4950	6453

prune344.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	6	186

Merged error: 10.4b

Counts

186 → 6

Compiler

Compiled 5737 to 3923 computations (31.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2)))))))
30.7b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
30.7b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
30.7b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-sqr-sqrt_binary64_441`
76×	`times-frac_binary64_425`
67×	`*-un-lft-identity_binary64_419`
54×	`cbrt-prod_binary64_450`
51×	`unpow-prod-down_binary64_498`
48×	`sqrt-prod_binary64_435`
46×	`add-cube-cbrt_binary64_454`
30×	`difference-of-squares_binary64_388`
9×	`sqr-pow_binary64_391` `unpow2_binary64_484`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/3_binary64_501` `distribute-lft-out--_binary64_371`
2×	`associate-/r/_binary64_365` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437`

Counts

4 → 138

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2)))))))
6.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

series397.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (cbrt.f64 (pow.f64 (/.f64 t l) 2)))))))
74.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
72.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
70.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4913	4188
1	4913	4188

prune310.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Merged error: 10.4b

Counts

156 → 7

Compiler

Compiled 5829 to 3793 computations (34.9% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4)) (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))))
22.9b	(cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4))
30.7b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
30.7b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`cbrt-prod_binary64_450`
106×	`add-sqr-sqrt_binary64_441`
103×	`times-frac_binary64_425`
85×	`*-un-lft-identity_binary64_419`
78×	`unpow-prod-down_binary64_498`
64×	`add-cube-cbrt_binary64_454`
48×	`sqrt-prod_binary64_435`
30×	`difference-of-squares_binary64_388`
9×	`sqr-pow_binary64_391`
8×	`unpow2_binary64_484`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/3_binary64_501` `distribute-lft-out--_binary64_371`
2×	`associate-/r/_binary64_365` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437`

Counts

4 → 164

Calls

4 calls:

18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4)) (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))))
10.0ms	(cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

series407.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 t l) 2)) (cbrt.f64 (pow.f64 (/.f64 t l) 2))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4)) (cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 2))))))))
82.0ms	(cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) 4))
73.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
71.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5698	9781

prune631.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	176	7	183

Merged error: 10.4b

Counts

183 → 7

Compiler

Compiled 11100 to 6414 computations (42.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.0b	(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)))))))
6.0b	(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)))))))
8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64_441`
102×	`sqrt-prod_binary64_435`
98×	`times-frac_binary64_425`
84×	`*-un-lft-identity_binary64_419`
60×	`difference-of-squares_binary64_388`
42×	`add-cube-cbrt_binary64_454`
24×	`unpow-prod-down_binary64_498`
12×	`sqr-pow_binary64_391` `unpow2_binary64_484`
8×	`pow1_binary64_480`
6×	`distribute-lft-out--_binary64_371` `rem-sqrt-square_binary64_432`
4×	`add-log-exp_binary64_458` `pow1/2_binary64_499` `associate-/r/_binary64_365` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-pow1_binary64_437`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `div-inv_binary64_416` `flip-+_binary64_393`

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)))))
18.0ms	(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)))))))

series506.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
177.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
76.0ms	(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)))))))
74.0ms	(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)))))))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5138	6552

prune529.0ms (5.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	156	9	165

Merged error: 10.3b

Counts

165 → 9

Compiler

Compiled 8412 to 5929 computations (29.5% saved)

regimes1.1s (11.2%)

Compiler: Compiled 17386 to 14806 computations (14.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	29
1	29	29

end0.0ms (0%)

sample2.6s (27.2%)

Algorithm

1×

intervals

Results

729.0ms	8000×	body	128	valid
409.0ms	4708×	body	128	nan

Compiler

Compiled 1267 to 1083 computations (14.5% saved)

Details

analyze1.3s (13.9%)

sample48.0ms (0.5%)

simplify350.0ms (3.6%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite66.0ms (0.7%)

series318.0ms (3.3%)

simplify103.0ms (1.1%)

prune344.0ms (3.5%)

localize17.0ms (0.2%)

rewrite53.0ms (0.5%)

series397.0ms (4.1%)

simplify140.0ms (1.4%)

prune310.0ms (3.2%)

localize31.0ms (0.3%)

rewrite67.0ms (0.7%)

series407.0ms (4.2%)

simplify123.0ms (1.3%)

prune631.0ms (6.5%)

localize17.0ms (0.2%)

rewrite66.0ms (0.7%)

series506.0ms (5.2%)

simplify81.0ms (0.8%)

prune529.0ms (5.5%)

regimes1.1s (11.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (27.2%)

Profiling