Details

analyze1.5s (15.4%)

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)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
13.0ms	131×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify221.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4891	29
1	4891	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: 8.1b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.2%)

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 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))))))
7.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite74.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_101`
108×	`times-frac_binary64_85`
98×	`*-un-lft-identity_binary64_79`
70×	`difference-of-squares_binary64_48`
49×	`add-cube-cbrt_binary64_114`
48×	`sqrt-prod_binary64_95`
41×	`unpow-prod-down_binary64_158`
15×	`unpow2_binary64_144` `sqr-pow_binary64_51`
14×	`associate-/l*_binary64_24`
9×	`add-exp-log_binary64_117`
7×	`distribute-lft-out--_binary64_31`
6×	`add-cbrt-cube_binary64_115` `pow1_binary64_140`
4×	`associate-/r/_binary64_25` `add-log-exp_binary64_118`
3×	`associate-/r*_binary64_23` `pow-unpow_binary64_156` `div-inv_binary64_76`
2×	`pow-exp_binary64_147` `div-exp_binary64_130` `flip-+_binary64_53` `rem-sqrt-square_binary64_92` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `asin-acos_binary64_259` `div-sub_binary64_84` `pow-pow_binary64_151` `flip--_binary64_54` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90`

Counts

4 → 173

Calls

4 calls:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
21.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (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))))))

series563.0ms (6%)

Counts

4 → 12

Calls

4 calls:

328.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
154.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
56.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4927	6661
1	4927	6661

prune420.0ms (4.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	180	6	186

Merged error: 8.0b

Counts

186 → 6

Compiler

Compiled 7744 to 5656 computations (27% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 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))))))
7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64_95` `add-sqr-sqrt_binary64_101`
125×	`times-frac_binary64_85`
112×	`*-un-lft-identity_binary64_79`
70×	`difference-of-squares_binary64_48`
63×	`add-cube-cbrt_binary64_114`
41×	`unpow-prod-down_binary64_158`
17×	`associate-/l*_binary64_24`
15×	`unpow2_binary64_144` `sqr-pow_binary64_51`
9×	`add-exp-log_binary64_117`
7×	`distribute-lft-out--_binary64_31`
6×	`associate-/r*_binary64_23` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96` `pow1_binary64_140`
4×	`add-log-exp_binary64_118`
3×	`pow-unpow_binary64_156`
2×	`pow-exp_binary64_147` `div-exp_binary64_130` `flip-+_binary64_53` `div-inv_binary64_76` `associate-/r/_binary64_25` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `asin-acos_binary64_259` `pow-pow_binary64_151` `flip--_binary64_54` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3--_binary64_83` `frac-2neg_binary64_90` `sqrt-undiv_binary64_100`

Counts

4 → 194

Calls

4 calls:

22.0ms	(/.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 Om Omc) 2)
4.0ms	(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))))))

series463.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
67.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
54.0ms	(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))))))
25.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5022	8052

prune486.0ms (5.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	206	6	212

Merged error: 3.6b

Counts

212 → 6

Compiler

Compiled 8120 to 5934 computations (26.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_95`
16×	`add-sqr-sqrt_binary64_101`
12×	`sqrt-div_binary64_96`
10×	`add-cube-cbrt_binary64_114` `sqrt-pow1_binary64_97` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
6×	`rem-sqrt-square_binary64_92` `pow1/2_binary64_159`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip-+_binary64_53` `add-log-exp_binary64_118` `flip3-+_binary64_82`

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series485.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
177.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
67.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
63.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4875	1536
1	4875	1536

prune175.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	6	90

Merged error: 3.6b

Counts

90 → 6

Compiler

Compiled 3543 to 2661 computations (24.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.1b	(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)))))))
8.1b	(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)))))))
8.1b	(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)))))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_101`
49×	`times-frac_binary64_85`
48×	`sqrt-prod_binary64_95`
46×	`*-un-lft-identity_binary64_79`
30×	`difference-of-squares_binary64_48`
25×	`add-cube-cbrt_binary64_114`
12×	`unpow-prod-down_binary64_158`
9×	`cbrt-prod_binary64_110`
6×	`unpow2_binary64_144` `sqr-pow_binary64_51`
5×	`pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`distribute-lft-out--_binary64_31` `pow1/3_binary64_161`
2×	`associate-/r/_binary64_25` `rem-sqrt-square_binary64_92`
1×	`flip-+_binary64_53` `div-inv_binary64_76` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `pow1/2_binary64_159` `flip3-+_binary64_82`

Counts

4 → 93

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

series1.1s (11.9%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
277.0ms	(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)))))))
274.0ms	(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)))))))
270.0ms	(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)))))))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4954	4317
1	4954	4317

prune618.0ms (6.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	102	9	111

Merged error: 3.6b

Counts

111 → 9

Compiler

Compiled 10950 to 8155 computations (25.5% saved)

regimes626.0ms (6.6%)

Compiler: Compiled 8450 to 7098 computations (16% saved)

bsearch26.0ms (0.3%)

Steps

Iters	Range		Point
4	5.828892761156686e+58	9.44574430147431e+58	6.394025814331313e+58

Compiler

Compiled 3 to 5 computations (-66.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms (0%)

sample2.1s (22.1%)

Algorithm

1×

intervals

Results

788.0ms	8000×	body	128	valid
473.0ms	4697×	body	128	nan

Compiler

Compiled 502 to 422 computations (15.9% saved)

Details

analyze1.5s (15.4%)

sample52.0ms (0.6%)

simplify221.0ms (2.3%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite74.0ms (0.8%)

series563.0ms (6%)

simplify99.0ms (1.1%)

prune420.0ms (4.5%)

localize15.0ms (0.2%)

rewrite64.0ms (0.7%)

series463.0ms (4.9%)

simplify105.0ms (1.1%)

prune486.0ms (5.2%)

localize19.0ms (0.2%)

rewrite25.0ms (0.3%)

series485.0ms (5.1%)

simplify76.0ms (0.8%)

prune175.0ms (1.9%)

localize23.0ms (0.2%)

rewrite44.0ms (0.5%)

series1.1s (11.9%)

simplify65.0ms (0.7%)

prune618.0ms (6.6%)

regimes626.0ms (6.6%)

bsearch26.0ms (0.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (22.1%)

Profiling