Details

analyze1.5s (13.5%)

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)

sample65.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms	116×	body	160	valid
13.0ms	140×	body	80	valid
12.0ms	126×	body	80	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4894	29
1	4894	29

prune6.0ms (0.1%)

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: 9.8b

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 Om Omc) 2)
0.4b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 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))))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
98×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
49×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
41×	`unpow-prod-down_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
14×	`associate-/l*_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`

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))))
16.0ms	(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)
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))))))

series133.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
39.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
19.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5051	6460

prune269.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Merged error: 9.8b

Counts

186 → 5

Compiler

Compiled 5714 to 3906 computations (31.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.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))))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
125×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
63×	`add-cube-cbrt_binary64`
41×	`unpow-prod-down_binary64`
17×	`associate-/l*_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 194

Calls

4 calls:

19.0ms	(/.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))))))

series101.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.0ms	(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))))))
11.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5351	7842

prune314.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	205	6	211

Merged error: 5.6b

Counts

211 → 6

Compiler

Compiled 6692 to 4699 computations (29.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.2b	(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)))))))
8.2b	(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)))))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64`
102×	`sqrt-prod_binary64`
98×	`times-frac_binary64`
84×	`*-un-lft-identity_binary64`
60×	`difference-of-squares_binary64`
42×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
12×	`unpow2_binary64` `sqr-pow_binary64`
8×	`pow1_binary64`
6×	`rem-sqrt-square_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

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)))))
16.0ms	(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)))))))

series211.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

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

simplify287.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4930	6552
1	4930	6552

prune412.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	156	8	164

Merged error: 5.6b

Counts

164 → 8

Compiler

Compiled 8732 to 6192 computations (29.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite87.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`add-sqr-sqrt_binary64`
196×	`times-frac_binary64`
192×	`sqrt-prod_binary64`
160×	`*-un-lft-identity_binary64`
120×	`difference-of-squares_binary64`
76×	`add-cube-cbrt_binary64`
48×	`unpow-prod-down_binary64`
24×	`unpow2_binary64` `sqr-pow_binary64`
12×	`distribute-lft-out--_binary64`
8×	`pow1_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 240

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)))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series303.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
71.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
70.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
69.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5397	11340

prune2.2s (20.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	250	10	260

Merged error: 5.6b

Counts

260 → 10

Compiler

Compiled 25212 to 18010 computations (28.6% saved)

regimes1.3s (12%)

Compiler: Compiled 11819 to 9651 computations (18.3% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
9	2.4253858307594573e+135	3.0268798238994306e+140	1.916588774785655e+137

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	40	65
1	40	65

end0.0ms (0%)

sample3.2s (28.7%)

Algorithm

1×

intervals

Results

741.0ms	3793×	body	160	valid
448.0ms	4662×	body	80	nan
409.0ms	4207×	body	80	valid

Compiler

Compiled 701 to 573 computations (18.3% saved)

Details

analyze1.5s (13.5%)

sample65.0ms (0.6%)

simplify68.0ms (0.6%)

prune6.0ms (0.1%)

localize14.0ms (0.1%)

rewrite48.0ms (0.4%)

series133.0ms (1.2%)

simplify117.0ms (1.1%)

prune269.0ms (2.4%)

localize15.0ms (0.1%)

rewrite38.0ms (0.3%)

series101.0ms (0.9%)

simplify117.0ms (1.1%)

prune314.0ms (2.8%)

localize17.0ms (0.2%)

rewrite46.0ms (0.4%)

series211.0ms (1.9%)

simplify287.0ms (2.6%)

prune412.0ms (3.7%)

localize24.0ms (0.2%)

rewrite87.0ms (0.8%)

series303.0ms (2.7%)

simplify126.0ms (1.1%)

prune2.2s (20.1%)

regimes1.3s (12%)

bsearch42.0ms (0.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (28.7%)

Profiling