Details

analyze1.5s (13.4%)

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)

sample53.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
13.0ms	139×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify230.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

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: 10.4b

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	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (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))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite75.0ms (0.7%)

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:

20.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
20.0ms	(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 Om Omc) 2)
3.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

series583.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
158.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
61.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
27.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4927	6661
1	4927	6661

prune512.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	179	7	186

Merged error: 10.3b

Counts

186 → 7

Compiler

Compiled 9237 to 7035 computations (23.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.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))))))
9.6b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite68.0ms (0.6%)

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))))))

series487.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
69.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
57.0ms	(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))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5022	8052

prune519.0ms (4.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	205	8	213

Merged error: 5.2b

Counts

213 → 8

Compiler

Compiled 8493 to 6298 computations (25.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
2.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_101` `cbrt-prod_binary64_110`
8×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
6×	`sqrt-prod_binary64_95` `cbrt-div_binary64_111`
5×	`pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`flip-+_binary64_53` `pow1/3_binary64_161` `flip3-+_binary64_82`
2×	`rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96`
1×	`asin-acos_binary64_259` `pow1/2_binary64_159`

Counts

4 → 54

Calls

4 calls:

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

series690.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
188.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
184.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
128.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4858	1747
1	4858	1747

prune155.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 5.2b

Counts

74 → 8

Compiler

Compiled 3034 to 2314 computations (23.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b	(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)))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite119.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`add-sqr-sqrt_binary64_101`
147×	`times-frac_binary64_85`
144×	`sqrt-prod_binary64_95`
122×	`*-un-lft-identity_binary64_79`
90×	`difference-of-squares_binary64_48`
59×	`add-cube-cbrt_binary64_114`
36×	`unpow-prod-down_binary64_158`
18×	`unpow2_binary64_144` `sqr-pow_binary64_51`
9×	`distribute-lft-out--_binary64_31`
7×	`pow1_binary64_140`
6×	`associate-/r/_binary64_25` `rem-sqrt-square_binary64_92`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`flip-+_binary64_53` `div-inv_binary64_76` `sqrt-pow1_binary64_97` `sqrt-div_binary64_96` `cbrt-prod_binary64_110` `pow1/2_binary64_159` `flip3-+_binary64_82`
1×	`pow1/3_binary64_161`

Counts

4 → 191

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

series1.3s (11.4%)

Counts

4 → 12

Calls

4 calls:

331.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
320.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
311.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
294.0ms	(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)))))))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4954	8775
1	4954	8775

prune1.3s (12%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	200	11	211

Merged error: 5.2b

Counts

211 → 11

Compiler

Compiled 20304 to 15049 computations (25.9% saved)

regimes753.0ms (6.8%)

Compiler: Compiled 10212 to 8605 computations (15.7% saved)

bsearch54.0ms (0.5%)

Steps

Iters	Range		Point
9	1.523018861538269e+74	3.492756617328103e+79	1.4817959701473245e+75

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%)

sample2.2s (19.7%)

Algorithm

1×

intervals

Results

795.0ms	8000×	body	128	valid
475.0ms	4868×	body	128	nan

Compiler

Compiled 601 to 506 computations (15.8% saved)

Details

analyze1.5s (13.4%)

sample53.0ms (0.5%)

simplify230.0ms (2.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite75.0ms (0.7%)

series583.0ms (5.3%)

simplify99.0ms (0.9%)

prune512.0ms (4.6%)

localize16.0ms (0.1%)

rewrite68.0ms (0.6%)

series487.0ms (4.4%)

simplify101.0ms (0.9%)

prune519.0ms (4.7%)

localize19.0ms (0.2%)

rewrite20.0ms (0.2%)

series690.0ms (6.3%)

simplify98.0ms (0.9%)

prune155.0ms (1.4%)

localize20.0ms (0.2%)

rewrite119.0ms (1.1%)

series1.3s (11.4%)

simplify102.0ms (0.9%)

prune1.3s (12%)

regimes753.0ms (6.8%)

bsearch54.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (19.7%)

Profiling