Details

analyze2.2s (18.8%)

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 (0.5%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
15.0ms	156×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify177.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

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

Error

7.2b

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)
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
6.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite44.0ms (0.4%)

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:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.0ms	(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))))))

series324.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(sqrt.f64 (/.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))))))
25.0ms	(pow.f64 (/.f64 Om Omc) 2)
18.0ms	(pow.f64 (/.f64 t l) 2)

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5089	3793

prune254.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	130	9	139

Error

7.1b

Counts

139 → 9

Compiler

Compiled 4043 to 2775 computations (31.4% saved)

localize15.0ms (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)
0.5b	(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))))))
6.6b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64_157`
22×	`add-sqr-sqrt_binary64_100`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
18×	`times-frac_binary64_84`
10×	`add-exp-log_binary64_116`
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×	`sqrt-prod_binary64_94`
2×	`pow-to-exp_binary64_147` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `asin-acos_binary64_258` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 81

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 Om Omc) 2)
5.0ms	(pow.f64 (/.f64 t l) 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))))))

series321.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(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))))))
70.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0ms	(pow.f64 (/.f64 Om Omc) 2)
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4946	1375
1	4946	1375

prune182.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Error

3.2b

Counts

102 → 9

Compiler

Compiled 2495 to 1749 computations (29.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 l)
0.5b	(cbrt.f64 l)
0.7b	(pow.f64 (cbrt.f64 l) 3)
6.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (/.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 3)) (cbrt.f64 l)) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))))))

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64_100`
50×	`*-un-lft-identity_binary64_78`
49×	`times-frac_binary64_84`
48×	`sqrt-prod_binary64_94`
30×	`difference-of-squares_binary64_47`
29×	`add-cube-cbrt_binary64_113`
18×	`unpow-prod-down_binary64_157`
12×	`cbrt-prod_binary64_109`
7×	`sqr-pow_binary64_50`
6×	`unpow2_binary64_143` `cube-prod_binary64_106` `pow1_binary64_139`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `pow1/3_binary64_160` `pow-unpow_binary64_155`
2×	`rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `associate-/r/_binary64_24`
1×	`rem-cube-cbrt_binary64_101` `cube-mult_binary64_108` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `pow1/2_binary64_158` `unpow3_binary64_144` `flip3-+_binary64_81`

Counts

4 → 112

Calls

4 calls:

36.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (/.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 3)) (cbrt.f64 l)) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))))))
6.0ms	(pow.f64 (cbrt.f64 l) 3)
2.0ms	(cbrt.f64 l)
2.0ms	(cbrt.f64 l)

series794.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (/.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 3)) (cbrt.f64 l)) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))))))
173.0ms	(pow.f64 (cbrt.f64 l) 3)
114.0ms	(cbrt.f64 l)
110.0ms	(cbrt.f64 l)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5536	3467

prune278.0ms (2.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	124	9	133

Error

3.2b

Counts

133 → 9

Compiler

Compiled 4565 to 2487 computations (45.5% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.5b	(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 (asin.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 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

rewrite82.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-sqr-sqrt_binary64_100`
102×	`sqrt-prod_binary64_94`
98×	`times-frac_binary64_84`
84×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
42×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
8×	`pow1_binary64_139`
6×	`rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `add-exp-log_binary64_116` `associate-/r/_binary64_24` `pow1/2_binary64_158`
2×	`flip-+_binary64_52` `div-inv_binary64_75` `sqrt-div_binary64_95` `flip3-+_binary64_81`

Counts

4 → 146

Calls

4 calls:

24.0ms	(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)))))
2.0ms	(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)))))))
2.0ms	(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)))))))

series672.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
230.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
103.0ms	(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)))))))
94.0ms	(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)))))))

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5138	6552

prune628.0ms (5.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	157	10	167

Error

3.2b

Counts

167 → 10

Compiler

Compiled 8412 to 5929 computations (29.5% saved)

regimes1.5s (12.7%)

Accuracy

Total 0.1b remaining (1.7%)

Threshold costs 0.1b (1.7%)

Compiler

Compiled 15075 to 13123 computations (12.9% saved)

bsearch3.0ms (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%)

sample3.5s (30.3%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
631.0ms	4874×	body	128	nan

Compiler

Compiled 938 to 810 computations (13.6% saved)

Details

analyze2.2s (18.8%)

sample57.0ms (0.5%)

simplify177.0ms (1.5%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite44.0ms (0.4%)

series324.0ms (2.8%)

simplify107.0ms (0.9%)

prune254.0ms (2.2%)

localize15.0ms (0.1%)

rewrite24.0ms (0.2%)

series321.0ms (2.8%)

simplify101.0ms (0.9%)

prune182.0ms (1.6%)

localize21.0ms (0.2%)

rewrite67.0ms (0.6%)

series794.0ms (6.9%)

simplify87.0ms (0.8%)

prune278.0ms (2.4%)

localize35.0ms (0.3%)

rewrite82.0ms (0.7%)

series672.0ms (5.8%)

simplify113.0ms (1%)

prune628.0ms (5.4%)

regimes1.5s (12.7%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (30.3%)

Profiling