Details

analyze1.5s (6.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4997	203
1	4997	203
0	4	4
1	4	4

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)

sample53.0ms (0.2%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
11.0ms	137×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

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

6.8b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.3b	(pow.f64 (/.f64 t l) 2)
0.6b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite399.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

143×	`add-sqr-sqrt_binary64_100`
108×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
49×	`add-cube-cbrt_binary64_113`
48×	`sqrt-prod_binary64_94`
41×	`unpow-prod-down_binary64_157`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
14×	`associate-/l*_binary64_23`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `pow-unpow_binary64_155` `associate-/r*_binary64_22`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `pow-exp_binary64_146` `associate-/l/_binary64_25`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53`

Counts

4 → 173

Calls

4 calls:

17.0ms	(/.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 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))))))

Compiler

Compiled 6194 to 4307 computations (30.5% saved)

series1.5s (6.2%)

Error

1.6b

Counts

4 → 60

Calls

4 calls:

614.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
598.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
112.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
68.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 5545 to 4962 computations (10.5% saved)

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4955	7925
1	4955	7925

prune412.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	227	6	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	228	6	234

Error

0.6b

Counts

234 → 6

Compiler

Compiled 6790 to 4636 computations (31.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.6b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.6b	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

rewrite1.2s (4.9%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

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

Counts

4 → 252

Calls

4 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
19.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
18.0ms	(sqrt.f64 (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)))))

Compiler

Compiled 15204 to 10786 computations (29.1% saved)

series4.1s (16.8%)

Error

0.6b

Counts

4 → 86

Calls

4 calls:

1.3s	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
1.2s	(sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
618.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
614.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 17154 to 14536 computations (15.3% saved)

simplify176.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5438	15302

prune1.4s (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	338	0	338
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	338	6	344

Error

0.6b

Counts

344 → 6

Compiler

Compiled 18171 to 12659 computations (30.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.6b	(asin.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 (/.f64 Om Omc) 2)) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
5.9b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite202.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

31×	`add-sqr-sqrt_binary64_100`
29×	`times-frac_binary64_84`
28×	`*-un-lft-identity_binary64_78`
27×	`add-cube-cbrt_binary64_113`
15×	`sqrt-prod_binary64_94`
13×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
8×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`sqrt-pow1_binary64_96` `div-inv_binary64_75` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `associate-/l_binary64_23` `associate-/r_binary64_22` `pow-unpow_binary64_155`
2×	`inv-pow_binary64_163` `pow-flip_binary64_152` `flip3-+_binary64_81` `flip-+_binary64_52` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-div_binary64_95` `asin-acos_binary64_258` `1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 100

Calls

4 calls:

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

Compiler

Compiled 3362 to 2527 computations (24.8% saved)

series411.0ms (1.7%)

Error

0.6b

Counts

4 → 36

Calls

4 calls:

128.0ms	(asin.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 (/.f64 Om Omc) 2)) 1) (sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
84.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
79.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
78.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 2434 to 2271 computations (6.7% saved)

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4927	2712
1	4927	2712

prune220.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Error

0.6b

Counts

142 → 7

Compiler

Compiled 3906 to 2917 computations (25.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.4b	(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)))))))
9.4b	(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)))))))
9.4b	(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)))))))

rewrite486.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

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-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/3_binary64_160` `distribute-lft-out--_binary64_30`
2×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 93

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)))))
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)))))))

Compiler

Compiled 7553 to 5403 computations (28.5% saved)

series3.7s (15.2%)

Error

0.6b

Counts

4 → 57

Calls

4 calls:

938.0ms	(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)))))))
935.0ms	(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)))))))
933.0ms	(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)))))))
640.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 12241 to 10033 computations (18% saved)

simplify93.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5225	5847

prune737.0ms (3.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	147	10	157

Error

0.6b

Counts

157 → 10

Compiler

Compiled 10651 to 7558 computations (29% saved)

regimes3.2s (13.2%)

Accuracy

Total 0.2b remaining (28.3%)

Threshold costs 0.2b (28.3%)

Compiler

Compiled 51499 to 43228 computations (16.1% saved)

bsearch6.0ms (0%)

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	107	120
1	107	120

end0.0ms (0%)

sample4.2s (17.3%)

Algorithm

1×

intervals

Results

918.0ms	8000×	body	128	valid
397.0ms	4668×	body	128	nan

Compiler

Compiled 2796 to 2353 computations (15.8% saved)

Details

analyze1.5s (6.1%)

sample53.0ms (0.2%)

simplify58.0ms (0.2%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite399.0ms (1.7%)

series1.5s (6.2%)

simplify116.0ms (0.5%)

prune412.0ms (1.7%)

localize19.0ms (0.1%)

rewrite1.2s (4.9%)

series4.1s (16.8%)

simplify176.0ms (0.7%)

prune1.4s (5.6%)

localize18.0ms (0.1%)

rewrite202.0ms (0.8%)

series411.0ms (1.7%)

simplify90.0ms (0.4%)

prune220.0ms (0.9%)

localize20.0ms (0.1%)

rewrite486.0ms (2%)

series3.7s (15.2%)

simplify93.0ms (0.4%)

prune737.0ms (3.1%)

regimes3.2s (13.2%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.2s (17.3%)

Profiling