Details

analyze1.4s (7.3%)

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 (0.3%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
13.0ms	156×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify142.0ms (0.7%)

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: 9.3b

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)
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64_100`
67×	`times-frac_binary64_84`
59×	`*-un-lft-identity_binary64_78`
48×	`sqrt-prod_binary64_94`
38×	`unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113`
30×	`difference-of-squares_binary64_47`
10×	`add-exp-log_binary64_116`
8×	`unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-cbrt-cube_binary64_114` `pow-exp_binary64_146` `add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75`
2×	`pow-to-exp_binary64_147` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `associate-/r/_binary64_24`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `sqrt-div_binary64_95` `asin-acos_binary64_258` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 126

Calls

4 calls:

22.0ms	(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)
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))))))

series820.0ms (4.3%)

Counts

4 → 40

Calls

4 calls:

550.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
115.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
78.0ms	(pow.f64 (/.f64 Om Omc) 2)
76.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 2974 to 2750 computations (7.5% saved)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5278	4915

prune288.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	158	8	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Merged error: 4.8b

Counts

167 → 9

Compiler

Compiled 4858 to 3269 computations (32.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.1b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite68.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`sqrt-prod_binary64_94`
146×	`add-sqr-sqrt_binary64_100`
120×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
54×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
10×	`rem-sqrt-square_binary64_91` `sqrt-div_binary64_95` `pow1_binary64_139`
9×	`sqrt-pow1_binary64_96`
6×	`distribute-lft-out--_binary64_30`
5×	`pow1/2_binary64_158`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `add-exp-log_binary64_116` `associate-/r/_binary64_24` `flip3-+_binary64_81`
3×	`pow-flip_binary64_152`
2×	`div-inv_binary64_75`
1×	`inv-pow_binary64_163`

Counts

4 → 176

Calls

4 calls:

22.0ms	(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))))

series972.0ms (5.1%)

Counts

4 → 59

Calls

4 calls:

496.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
174.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
158.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
144.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 3779 to 3447 computations (8.8% saved)

simplify108.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5158	8133

prune699.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	235	9	244

Merged error: 4.8b

Counts

244 → 9

Compiler

Compiled 10474 to 7667 computations (26.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.4b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.9b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.9b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.9b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_100`
49×	`times-frac_binary64_84`
48×	`sqrt-prod_binary64_94`
46×	`*-un-lft-identity_binary64_78`
30×	`difference-of-squares_binary64_47`
25×	`add-cube-cbrt_binary64_113`
12×	`unpow-prod-down_binary64_157`
9×	`cbrt-prod_binary64_109`
6×	`unpow2_binary64_143` `sqr-pow_binary64_50`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`distribute-lft-out--_binary64_30` `pow1/3_binary64_160`
2×	`rem-sqrt-square_binary64_91` `associate-/r/_binary64_24`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 93

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

series3.5s (18.6%)

Counts

4 → 52

Calls

4 calls:

988.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
985.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
980.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
576.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 7962 to 6738 computations (15.4% saved)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5907	5934

prune681.0ms (3.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	141	13	154

Merged error: 4.8b

Counts

154 → 13

Compiler

Compiled 11167 to 7881 computations (29.4% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.4b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.9b	(cbrt.f64 (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))))))))
8.9b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.9b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_100`
31×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
30×	`sqrt-prod_binary64_94`
19×	`add-cube-cbrt_binary64_113`
12×	`difference-of-squares_binary64_47`
9×	`cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`distribute-lft-out--_binary64_30` `pow1/3_binary64_160`
2×	`rem-sqrt-square_binary64_91` `associate-/r/_binary64_24`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 75

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(cbrt.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	(cbrt.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	(cbrt.f64 (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))))))))

series3.5s (18.5%)

Counts

4 → 53

Calls

4 calls:

1.0s	(cbrt.f64 (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))))))))
1.0s	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
991.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
467.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 8259 to 6633 computations (19.7% saved)

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5284	5045

prune532.0ms (2.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	128	13	141

Merged error: 4.8b

Counts

141 → 13

Compiler

Compiled 9771 to 6665 computations (31.8% saved)

regimes2.3s (12.2%)

Compiler: Compiled 40291 to 32509 computations (19.3% saved)

bsearch4.0ms (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	40	65
1	40	65

end0.0ms (0%)

sample3.4s (18.2%)

Algorithm

1×

intervals

Results

751.0ms	8000×	body	128	valid
399.0ms	4691×	body	128	nan

Compiler

Compiled 2434 to 1959 computations (19.5% saved)

Details

analyze1.4s (7.3%)

sample57.0ms (0.3%)

simplify142.0ms (0.7%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite46.0ms (0.2%)

series820.0ms (4.3%)

simplify74.0ms (0.4%)

prune288.0ms (1.5%)

localize21.0ms (0.1%)

rewrite68.0ms (0.4%)

series972.0ms (5.1%)

simplify108.0ms (0.6%)

prune699.0ms (3.7%)

localize20.0ms (0.1%)

rewrite41.0ms (0.2%)

series3.5s (18.6%)

simplify73.0ms (0.4%)

prune681.0ms (3.6%)

localize31.0ms (0.2%)

rewrite30.0ms (0.2%)

series3.5s (18.5%)

simplify65.0ms (0.3%)

prune532.0ms (2.8%)

regimes2.3s (12.2%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (18.2%)

Profiling