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)

sample64.0ms (0.3%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
20.0ms	187×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify53.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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

9.0b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.5b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (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))))))
7.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite673.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

8.9b

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` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `associate-/l/_binary64_25` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 173

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(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 5888 to 4086 computations (30.6% saved)

series2.3s (9.3%)

Error

2.6b

Counts

4 → 61

Calls

4 calls:

1.1s	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
865.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
163.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
114.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 4665 to 4229 computations (9.3% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5656	8219

prune314.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	227	7	234
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	227	8	235

Error

0.7b

Counts

235 → 8

Compiler

Compiled 3969 to 2747 computations (30.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 t l) 2)
0.6b	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
0.7b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite649.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

155×	`add-sqr-sqrt_binary64_100` `sqrt-prod_binary64_94`
125×	`times-frac_binary64_84`
112×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
63×	`add-cube-cbrt_binary64_113`
41×	`unpow-prod-down_binary64_157`
17×	`associate-/l*_binary64_23`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114` `sqrt-div_binary64_95` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `div-inv_binary64_75` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 194

Calls

4 calls:

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

Compiler

Compiled 6240 to 4492 computations (28% saved)

series1.7s (6.7%)

Error

0.6b

Counts

4 → 57

Calls

4 calls:

1.1s	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
228.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
174.0ms	(asin.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
113.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 4701 to 4225 computations (10.1% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5769	9537

prune377.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	250	9	259

Error

0.6b

Counts

259 → 9

Compiler

Compiled 4212 to 3037 computations (27.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.7b	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.7b	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite505.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

110×	`sqrt-prod_binary64_94`
70×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
64×	`times-frac_binary64_84`
40×	`add-cube-cbrt_binary64_113`
12×	`difference-of-squares_binary64_47`
10×	`sqrt-div_binary64_95`
8×	`pow1_binary64_139` `rem-sqrt-square_binary64_91`
6×	`distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24`
2×	`div-inv_binary64_75`

Counts

4 → 128

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.0ms	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (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))))

Compiler

Compiled 5588 to 3668 computations (34.4% saved)

series3.5s (14.2%)

Error

0.6b

Counts

4 → 72

Calls

4 calls:

1.5s	(sqrt.f64 (/.f64 (-.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
1.4s	(sqrt.f64 (/.f64 (+.f64 1 (fabs.f64 (/.f64 Om Omc))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
249.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
241.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7776 to 6128 computations (21.2% saved)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4961	7228
1	4961	7228

prune483.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	201	8	209

Error

0.6b

Counts

209 → 8

Compiler

Compiled 6014 to 3947 computations (34.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.3b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.3b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite359.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

26×	`sqrt-prod_binary64_94`
16×	`add-sqr-sqrt_binary64_100`
12×	`sqrt-div_binary64_95`
10×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `*-un-lft-identity_binary64_78`
6×	`pow1/2_binary64_158` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 72

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(sqrt.f64 (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))))

Compiler

Compiled 4172 to 2935 computations (29.7% saved)

series1.4s (5.7%)

Error

0.6b

Counts

4 → 60

Calls

4 calls:

371.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
368.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
266.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
236.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 8052 to 6460 computations (19.8% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4948	2892
1	4948	2892

prune440.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	132	8	140

Error

0.6b

Counts

140 → 8

Compiler

Compiled 5680 to 3892 computations (31.5% saved)

regimes7.8s (31.7%)

Accuracy

Total 1.3b remaining (68.4%)

Threshold costs 0b (0%)

Compiler

Compiled 93343 to 82717 computations (11.4% saved)

bsearch8.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	166
1	157	166

end6.0ms (0%)

Compiler: Compiled 108 to 79 computations (26.9% saved)

sample2.0s (8.2%)

Algorithm

1×

intervals

Results

743.0ms	8000×	body	128	valid
407.0ms	4726×	body	128	nan

Compiler

Compiled 381 to 340 computations (10.8% saved)

Details

analyze1.5s (6.1%)

sample64.0ms (0.3%)

simplify53.0ms (0.2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite673.0ms (2.7%)

series2.3s (9.3%)

simplify100.0ms (0.4%)

prune314.0ms (1.3%)

localize15.0ms (0.1%)

rewrite649.0ms (2.6%)

series1.7s (6.7%)

simplify107.0ms (0.4%)

prune377.0ms (1.5%)

localize24.0ms (0.1%)

rewrite505.0ms (2.1%)

series3.5s (14.2%)

simplify104.0ms (0.4%)

prune483.0ms (2%)

localize28.0ms (0.1%)

rewrite359.0ms (1.5%)

series1.4s (5.7%)

simplify78.0ms (0.3%)

prune440.0ms (1.8%)

regimes7.8s (31.7%)

bsearch8.0ms (0%)

simplify5.0ms (0%)

end6.0ms (0%)

sample2.0s (8.2%)

Profiling