Details

analyze1.5s (17.1%)

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 (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
16.0ms	165×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify229.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4908	29
1	4908	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: 10.2b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.5b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.8b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.8b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite68.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_98`
108×	`times-frac_binary64_83`
98×	`*-un-lft-identity_binary64_77`
70×	`difference-of-squares_binary64_46`
49×	`add-cube-cbrt_binary64_109`
48×	`sqrt-prod_binary64_92`
41×	`unpow-prod-down_binary64_153`
15×	`sqr-pow_binary64_49` `unpow2_binary64_139`
14×	`associate-/l*_binary64_24`
9×	`add-exp-log_binary64_112`
7×	`distribute-lft-out--_binary64_31`
6×	`add-cbrt-cube_binary64_110` `pow1_binary64_135`
4×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
3×	`associate-/r*_binary64_23` `pow-unpow_binary64_151` `div-inv_binary64_74`
2×	`rem-sqrt-square_binary64_90` `flip-+_binary64_51` `flip3-+_binary64_80` `pow-exp_binary64_142` `div-exp_binary64_125` `associate-/l/_binary64_26`
1×	`pow-to-exp_binary64_143` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `div-sub_binary64_82` `flip--_binary64_52` `asin-acos_binary64_254` `pow1/2_binary64_154` `clear-num_binary64_76` `flip3--_binary64_81` `frac-2neg_binary64_88` `pow-pow_binary64_146`

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))))
19.0ms	(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)
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))))))

series587.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
162.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
62.0ms	(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)

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4936	6663
1	4936	6663

prune351.0ms (4.1%)

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: 10.1b

Counts

186 → 7

Compiler

Compiled 5935 to 4046 computations (31.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
6.5b	(sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite73.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`sqrt-prod_binary64_92`
146×	`add-sqr-sqrt_binary64_98`
120×	`times-frac_binary64_83`
98×	`*-un-lft-identity_binary64_77`
60×	`difference-of-squares_binary64_46`
54×	`add-cube-cbrt_binary64_109`
24×	`unpow-prod-down_binary64_153`
12×	`sqr-pow_binary64_49` `unpow2_binary64_139`
10×	`rem-sqrt-square_binary64_90` `sqrt-div_binary64_93` `pow1_binary64_135`
9×	`sqrt-pow1_binary64_94`
6×	`distribute-lft-out--_binary64_31`
5×	`pow1/2_binary64_154`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `associate-/r/_binary64_25`
3×	`pow-flip_binary64_148`
2×	`div-inv_binary64_74`
1×	`inv-pow_binary64_159`

Counts

4 → 176

Calls

4 calls:

24.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
11.0ms	(sqrt.f64 (/.f64 1 (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))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series769.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

423.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
209.0ms	(sqrt.f64 (/.f64 1 (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))))
67.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4885	7127
1	4885	7127

prune594.0ms (6.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	189	6	195

Merged error: 10.1b

Counts

195 → 6

Compiler

Compiled 8774 to 6422 computations (26.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.9b	(sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
14.9b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.9b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.9b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_106`
15×	`sqrt-prod_binary64_92`
13×	`pow1_binary64_135`
11×	`sqrt-pow1_binary64_94` `add-sqr-sqrt_binary64_98`
10×	`*-un-lft-identity_binary64_77`
9×	`flip-+_binary64_51` `flip3-+_binary64_80` `cbrt-prod_binary64_105` `add-cube-cbrt_binary64_109` `pow1/3_binary64_156` `pow-flip_binary64_148`
8×	`associate-/r/_binary64_25`
5×	`times-frac_binary64_83`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `frac-times_binary64_87`
3×	`rem-sqrt-square_binary64_90`
2×	`pow-prod-down_binary64_145` `pow-sqr_binary64_50` `pow-prod-up_binary64_144` `associate-l/_binary64_22` `associate-r/_binary64_21`
1×	`pow2_binary64_155` `sqrt-div_binary64_93` `pow-plus_binary64_137` `inv-pow_binary64_159` `pow1/2_binary64_154` `div-inv_binary64_74`

Counts

4 → 77

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (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))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series759.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
187.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
182.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
174.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5457	2258

prune247.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	89	6	95

Merged error: 10.1b

Counts

95 → 6

Compiler

Compiled 4629 to 3435 computations (25.8% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.2b	(cbrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.2b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_92` `add-sqr-sqrt_binary64_98`
9×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
8×	`sqrt-div_binary64_93`
7×	`pow1_binary64_135`
6×	`cbrt-prod_binary64_105`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80`
3×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `pow1/2_binary64_154`
2×	`cbrt-div_binary64_106`
1×	`pow1/3_binary64_156`

Counts

4 → 61

Calls

4 calls:

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

series367.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt.f64 (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))))
64.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
64.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4878	1413
1	4878	1413

prune238.0ms (2.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	73	6	79

Merged error: 10.1b

Counts

79 → 6

Compiler

Compiled 4217 to 3254 computations (22.8% saved)

regimes301.0ms (3.5%)

Compiler: Compiled 3736 to 3326 computations (11% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	29
1	29	29

end0.0ms (0%)

sample2.0s (22.7%)

Algorithm

1×

intervals

Results

811.0ms	8000×	body	128	valid
480.0ms	4786×	body	128	nan

Compiler

Compiled 292 to 263 computations (9.9% saved)

Details

analyze1.5s (17.1%)

sample57.0ms (0.7%)

simplify229.0ms (2.7%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite68.0ms (0.8%)

series587.0ms (6.8%)

simplify102.0ms (1.2%)

prune351.0ms (4.1%)

localize19.0ms (0.2%)

rewrite73.0ms (0.8%)

series769.0ms (8.9%)

simplify135.0ms (1.6%)

prune594.0ms (6.9%)

localize25.0ms (0.3%)

rewrite35.0ms (0.4%)

series759.0ms (8.8%)

simplify85.0ms (1%)

prune247.0ms (2.9%)

localize27.0ms (0.3%)

rewrite25.0ms (0.3%)

series367.0ms (4.3%)

simplify58.0ms (0.7%)

prune238.0ms (2.8%)

regimes301.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (22.7%)

Profiling