Details

analyze1.6s (18.7%)

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)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
13.0ms	150×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify148.0ms (1.8%)

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: 8.8b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64_441`
67×	`times-frac_binary64_425`
59×	`*-un-lft-identity_binary64_419`
48×	`sqrt-prod_binary64_435`
38×	`unpow-prod-down_binary64_498` `add-cube-cbrt_binary64_454`
30×	`difference-of-squares_binary64_388`
10×	`add-exp-log_binary64_457`
8×	`sqr-pow_binary64_391` `unpow2_binary64_484`
7×	`pow1_binary64_480`
6×	`pow-unpow_binary64_496`
4×	`add-log-exp_binary64_458` `pow-exp_binary64_487` `add-cbrt-cube_binary64_455`
3×	`div-inv_binary64_416` `distribute-lft-out--_binary64_371`
2×	`associate-/r/_binary64_365` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `rem-sqrt-square_binary64_432` `div-exp_binary64_470`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `asin-acos_binary64_599`

Counts

4 → 126

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)))))
5.0ms	(pow.f64 (/.f64 Om Omc) 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))))))

series235.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt.f64 (/.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)
14.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5089	3793

prune222.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Merged error: 8.7b

Counts

139 → 7

Compiler

Compiled 3985 to 2729 computations (31.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.4b	(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))))))
8.0b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite57.0ms (0.7%)

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 Om Omc) 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))))))

series260.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
40.0ms	(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 Om Omc) 2)

simplify121.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5039	7842

prune378.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	205	8	213

Merged error: 3.6b

Counts

213 → 8

Compiler

Compiled 6750 to 4752 computations (29.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.0b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.0b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.6b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`sqrt-prod_binary64_435`
146×	`add-sqr-sqrt_binary64_441`
120×	`times-frac_binary64_425`
98×	`*-un-lft-identity_binary64_419`
60×	`difference-of-squares_binary64_388`
54×	`add-cube-cbrt_binary64_454`
24×	`unpow-prod-down_binary64_498`
12×	`sqr-pow_binary64_391` `unpow2_binary64_484`
10×	`sqrt-div_binary64_436` `pow1_binary64_480` `rem-sqrt-square_binary64_432`
9×	`sqrt-pow1_binary64_437`
6×	`distribute-lft-out--_binary64_371`
5×	`pow1/2_binary64_499`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `associate-/r/_binary64_365` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-flip_binary64_493`
2×	`div-inv_binary64_416`
1×	`inv-pow_binary64_504`

Counts

4 → 176

Calls

4 calls:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.0ms	(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))))

series427.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
106.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
37.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
36.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5031	7135

prune584.0ms (7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	188	8	196

Merged error: 3.6b

Counts

196 → 8

Compiler

Compiled 8776 to 6432 computations (26.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.0b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.0b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
11.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
11.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_435`
16×	`add-sqr-sqrt_binary64_441`
12×	`sqrt-div_binary64_436`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `sqrt-pow1_binary64_437` `pow1_binary64_480`
6×	`pow1/2_binary64_499` `rem-sqrt-square_binary64_432`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(sqrt.f64 (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))))

series274.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
95.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
36.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
35.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4920	1536
1	4920	1536

prune169.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	84	8	92

Merged error: 3.6b

Counts

92 → 8

Compiler

Compiled 3226 to 2380 computations (26.2% saved)

regimes1.0s (12.5%)

Compiler: Compiled 13928 to 12668 computations (9% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	63
1	39	63

end0.0ms (0%)

sample2.3s (27.9%)

Algorithm

1×

intervals

Results

739.0ms	8000×	body	128	valid
406.0ms	4866×	body	128	nan

Compiler

Compiled 840 to 758 computations (9.8% saved)

Details

analyze1.6s (18.7%)

sample52.0ms (0.6%)

simplify148.0ms (1.8%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite49.0ms (0.6%)

series235.0ms (2.8%)

simplify75.0ms (0.9%)

prune222.0ms (2.7%)

localize15.0ms (0.2%)

rewrite57.0ms (0.7%)

series260.0ms (3.1%)

simplify121.0ms (1.5%)

prune378.0ms (4.5%)

localize19.0ms (0.2%)

rewrite70.0ms (0.8%)

series427.0ms (5.1%)

simplify107.0ms (1.3%)

prune584.0ms (7%)

localize21.0ms (0.3%)

rewrite23.0ms (0.3%)

series274.0ms (3.3%)

simplify78.0ms (0.9%)

prune169.0ms (2%)

regimes1.0s (12.5%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (27.9%)

Profiling