Details

analyze1.6s (15.7%)

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)

sample51.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
13.0ms	147×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

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

9.9b

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)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.8b	(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	(/.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)))))
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))))))

series319.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(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))))
31.0ms	(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)

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4950	6453
1	4950	6453

prune339.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	176	9	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Error

9.8b

Counts

186 → 9

Compiler

Compiled 5808 to 3991 computations (31.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.2b	(/.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	(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))))))
8.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435`
125×	`times-frac_binary64_425`
112×	`*-un-lft-identity_binary64_419`
70×	`difference-of-squares_binary64_388`
63×	`add-cube-cbrt_binary64_454`
41×	`unpow-prod-down_binary64_498`
17×	`associate-/l*_binary64_364`
15×	`sqr-pow_binary64_391` `unpow2_binary64_484`
9×	`add-exp-log_binary64_457`
7×	`distribute-lft-out--_binary64_371`
6×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `associate-/r*_binary64_363` `pow1_binary64_480`
4×	`add-log-exp_binary64_458`
3×	`pow-unpow_binary64_496`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `pow-exp_binary64_487` `associate-/r/_binary64_365` `flip-+_binary64_393` `div-exp_binary64_470` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sqrt-undiv_binary64_440` `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` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

Counts

4 → 194

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(pow.f64 (/.f64 t l) 2)
3.0ms	(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))))))

series256.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
45.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
32.0ms	(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))))))
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify133.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4985	7842
1	4985	7842

prune408.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	207	8	215

Error

4.5b

Counts

215 → 8

Compiler

Compiled 6750 to 4754 computations (29.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.8b	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.8b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_441`
72×	`times-frac_binary64_425`
65×	`*-un-lft-identity_binary64_419`
37×	`add-cube-cbrt_binary64_454`
30×	`sqrt-prod_binary64_435`
28×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
9×	`add-exp-log_binary64_457`
8×	`associate-/l*_binary64_364`
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` `sqr-pow_binary64_391` `flip3--_binary64_423` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `flip--_binary64_394` `unpow2_binary64_484` `asin-acos_binary64_599` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

4 → 131

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.0ms	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))

series263.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
86.0ms	(/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
34.0ms	(asin.f64 (.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5136	4494

prune259.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	143	8	151

Error

4.5b

Counts

151 → 8

Compiler

Compiled 5100 to 3288 computations (35.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.0b	(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)))))))
7.0b	(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)))))))
8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite67.0ms (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:

19.0ms	(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)))))))

series488.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
163.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
83.0ms	(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)))))))
73.0ms	(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)))))))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5138	6552

prune475.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	158	8	166

Error

4.5b

Counts

166 → 8

Compiler

Compiled 8412 to 5929 computations (29.5% saved)

regimes1.8s (18.1%)

Accuracy

Total 0.1b remaining (1.7%)

Threshold costs 0.1b (1.7%)

Compiler

Compiled 27380 to 23572 computations (13.9% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	66
1	40	66

end0.0ms (0%)

sample2.9s (29.2%)

Algorithm

1×

intervals

Results

748.0ms	8000×	body	128	valid
393.0ms	4602×	body	128	nan

Compiler

Compiled 1612 to 1387 computations (14% saved)

Details

analyze1.6s (15.7%)

sample51.0ms (0.5%)

simplify146.0ms (1.5%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite66.0ms (0.7%)

series319.0ms (3.2%)

simplify104.0ms (1%)

prune339.0ms (3.4%)

localize15.0ms (0.1%)

rewrite54.0ms (0.5%)

series256.0ms (2.5%)

simplify133.0ms (1.3%)

prune408.0ms (4.1%)

localize16.0ms (0.2%)

rewrite50.0ms (0.5%)

series263.0ms (2.6%)

simplify89.0ms (0.9%)

prune259.0ms (2.6%)

localize18.0ms (0.2%)

rewrite67.0ms (0.7%)

series488.0ms (4.8%)

simplify87.0ms (0.9%)

prune475.0ms (4.7%)

regimes1.8s (18.1%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.9s (29.2%)

Profiling