Details

analyze1.5s (11.9%)

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)

sample63.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	109×	body	160	valid
14.0ms	147×	body	80	valid
14.0ms	145×	body	80	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4909	29
1	4909	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: 10.7b

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)
0.6b	(/.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))))))
9.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite59.0ms (0.5%)

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` `insert-posit16`
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 → 177

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

series613.0ms (5%)

Counts

4 → 12

Calls

4 calls:

344.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
169.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
72.0ms	(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 Om Omc) 2)

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4942	6759
1	4942	6759

prune358.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	7	190

Merged error: 10.7b

Counts

190 → 7

Compiler

Compiled 5987 to 4083 computations (31.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.7b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.7b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite113.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

298×	`sqrt-prod_binary64`
248×	`add-sqr-sqrt_binary64`
196×	`times-frac_binary64`
162×	`*-un-lft-identity_binary64`
120×	`difference-of-squares_binary64`
78×	`add-cube-cbrt_binary64`
48×	`unpow-prod-down_binary64`
24×	`unpow2_binary64` `sqr-pow_binary64`
12×	`distribute-lft-out--_binary64`
10×	`pow1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
8×	`associate-/r/_binary64`
6×	`pow1/2_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`

Counts

4 → 256

Calls

4 calls:

23.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
22.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series1.7s (13.7%)

Counts

4 → 12

Calls

4 calls:

518.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
511.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
331.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
319.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

simplify236.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	5014	12314

prune1.2s (10.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	268	7	275

Merged error: 10.7b

Counts

275 → 7

Compiler

Compiled 14746 to 10303 computations (30.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.3b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
17.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite84.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
162×	`sqrt-prod_binary64`
159×	`add-sqr-sqrt_binary64`
114×	`*-un-lft-identity_binary64`
89×	`cbrt-prod_binary64`
80×	`cbrt-div_binary64`
72×	`add-cube-cbrt_binary64`
60×	`difference-of-squares_binary64`
50×	`associate-/r/_binary64`
40×	`flip3-+_binary64` `flip-+_binary64`
24×	`unpow-prod-down_binary64` `frac-times_binary64`
12×	`unpow2_binary64` `associate-r/_binary64` `sqr-pow_binary64` `associate-l/_binary64`
7×	`div-inv_binary64`
6×	`distribute-lft-out--_binary64`
5×	`pow1_binary64` `rem-sqrt-square_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow1/3_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`

Counts

4 → 220

Calls

4 calls:

49.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series921.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

341.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
197.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
194.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
188.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify218.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4951	18087
1	4951	18087

prune1.2s (9.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	232	7	239

Merged error: 10.7b

Counts

239 → 7

Compiler

Compiled 14309 to 10290 computations (28.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (fabs.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `asin-acos_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (fabs.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))

series661.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
195.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
192.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
74.0ms	(asin.f64 (fabs.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))))

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4869	1657
1	4869	1657

prune137.0ms (1.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	70	7	77

Merged error: 10.7b

Counts

77 → 7

Compiler

Compiled 2642 to 1961 computations (25.8% saved)

regimes317.0ms (2.6%)

Compiler: Compiled 3806 to 3396 computations (10.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	29
1	30	29

end0.0ms (0%)

sample2.4s (20%)

Algorithm

1×

intervals

Results

879.0ms	3771×	body	160	valid
481.0ms	4818×	body	80	nan
411.0ms	4229×	body	80	valid

Compiler

Compiled 297 to 268 computations (9.8% saved)

Details

analyze1.5s (11.9%)

sample63.0ms (0.5%)

simplify144.0ms (1.2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite59.0ms (0.5%)

series613.0ms (5%)

simplify141.0ms (1.1%)

prune358.0ms (2.9%)

localize16.0ms (0.1%)

rewrite113.0ms (0.9%)

series1.7s (13.7%)

simplify236.0ms (1.9%)

prune1.2s (10.1%)

localize19.0ms (0.2%)

rewrite84.0ms (0.7%)

series921.0ms (7.5%)

simplify218.0ms (1.8%)

prune1.2s (9.5%)

localize21.0ms (0.2%)

rewrite15.0ms (0.1%)

series661.0ms (5.4%)

simplify106.0ms (0.9%)

prune137.0ms (1.1%)

regimes317.0ms (2.6%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample2.4s (20%)

Profiling