Details

analyze1.4s (15%)

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)

sample57.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
15.0ms	159×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4891	29
1	4891	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 (0.1%)

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))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite72.0ms (0.8%)

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:

20.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
19.0ms	(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))))))

series571.0ms (6%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
162.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
55.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
28.0ms	(pow.f64 (/.f64 t l) 2)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4941	6661
1	4941	6661

prune762.0ms (8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	9	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Merged error: 8.7b

Counts

186 → 10

Compiler

Compiled 13480 to 10775 computations (20.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.7b	(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))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
10×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `asin-acos_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(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))))))

series179.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
55.0ms	(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))))))
25.0ms	(pow.f64 (/.f64 t l) 2)
25.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4920	1431
1	4920	1431

prune207.0ms (2.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Merged error: 3.1b

Counts

103 → 11

Compiler

Compiled 3850 to 2968 computations (22.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.4b	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))
7.6b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))

rewrite140.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64`
412×	`*-un-lft-identity_binary64`
404×	`add-sqr-sqrt_binary64`
182×	`add-cube-cbrt_binary64`
125×	`sqrt-prod_binary64`
108×	`difference-of-squares_binary64`
61×	`distribute-lft-out_binary64`
30×	`associate-/r*_binary64`
27×	`distribute-lft-out--_binary64`
20×	`associate-/r/_binary64`
13×	`unpow-prod-down_binary64`
12×	`add-exp-log_binary64` `div-inv_binary64`
9×	`flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64`
2×	`associate-/l/_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `asin-acos_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 346

Calls

4 calls:

36.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))
25.0ms	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
5.0ms	(pow.f64 (/.f64 t l) 2)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))

series604.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

344.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc)))))
173.0ms	(/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))
60.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (/.f64 Om Omc))))))
26.0ms	(pow.f64 (/.f64 t l) 2)

simplify211.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4955	19290
1	4955	19290

prune1.1s (12%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	357	1	358
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	358	11	369

Merged error: 3.1b

Counts

369 → 11

Compiler

Compiled 15900 to 10135 computations (36.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.6b	(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)))))))
28.5b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
28.5b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
28.5b	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64`
54×	`cbrt-prod_binary64`
51×	`unpow-prod-down_binary64`
48×	`sqrt-prod_binary64`
46×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64`
9×	`unpow2_binary64` `sqr-pow_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64`
3×	`pow1/3_binary64` `distribute-lft-out--_binary64`
2×	`associate-/r/_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 138

Calls

4 calls:

19.0ms	(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)))))))
7.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

series791.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(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)))))))
187.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
145.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))
126.0ms	(cbrt.f64 (pow.f64 (/.f64 t l) 2))

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4927	4188
1	4927	4188

prune294.0ms (3.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	150	11	161

Merged error: 3.1b

Counts

161 → 11

Compiler

Compiled 5616 to 3612 computations (35.7% saved)

regimes563.0ms (5.9%)

Compiler: Compiled 6274 to 5614 computations (10.5% saved)

bsearch2.0ms (0%)

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

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	63
1	39	63

end0.0ms (0%)

sample2.0s (20.9%)

Algorithm

1×

intervals

Results

768.0ms	8000×	body	128	valid
460.0ms	4774×	body	128	nan

Compiler

Compiled 399 to 353 computations (11.5% saved)

Details

analyze1.4s (15%)

sample57.0ms (0.6%)

simplify55.0ms (0.6%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite72.0ms (0.8%)

series571.0ms (6%)

simplify103.0ms (1.1%)

prune762.0ms (8%)

localize15.0ms (0.2%)

rewrite22.0ms (0.2%)

series179.0ms (1.9%)

simplify72.0ms (0.8%)

prune207.0ms (2.2%)

localize15.0ms (0.2%)

rewrite140.0ms (1.5%)

series604.0ms (6.4%)

simplify211.0ms (2.2%)

prune1.1s (12%)

localize18.0ms (0.2%)

rewrite61.0ms (0.6%)

series791.0ms (8.3%)

simplify120.0ms (1.3%)

prune294.0ms (3.1%)

regimes563.0ms (5.9%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (20.9%)

Profiling