Details

analyze1.8s (6.7%)

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)

sample63.0ms (0.2%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
15.0ms	164×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

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

9.2b

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	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (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))))
8.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite615.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

9.1b

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` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `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 → 173

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(/.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))))))

Compiler

Compiled 6194 to 4303 computations (30.5% saved)

series1.8s (6.6%)

Error

1.3b

Counts

4 → 58

Calls

4 calls:

749.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
669.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
127.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
117.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5402 to 4829 computations (10.6% saved)

simplify151.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4986	8023
1	4986	8023

prune485.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	9	232

Error

0.4b

Counts

232 → 9

Compiler

Compiled 6934 to 4727 computations (31.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.3b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.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)))))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite410.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

44×	`sqrt-prod_binary64_94`
26×	`add-sqr-sqrt_binary64_100`
21×	`times-frac_binary64_84`
18×	`cbrt-div_binary64_110`
17×	`*-un-lft-identity_binary64_78`
10×	`add-cube-cbrt_binary64_113` `difference-of-squares_binary64_47`
9×	`flip3-+_binary64_81` `flip-+_binary64_52` `cbrt-prod_binary64_109`
8×	`associate-/r/_binary64_24`
5×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157` `frac-times_binary64_88`
3×	`pow1/3_binary64_160` `rem-sqrt-square_binary64_91`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `distribute-lft-out--_binary64_30` `div-inv_binary64_75`

Counts

4 → 81

Calls

4 calls:

28.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.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)))))))
3.0ms	(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))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 5605 to 4067 computations (27.4% saved)

series2.0s (7.4%)

Error

0.4b

Counts

4 → 56

Calls

4 calls:

1.1s	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.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)))))))
248.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
244.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
233.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9133 to 7617 computations (16.6% saved)

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4958	4588
1	4958	4588

prune573.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Error

0.4b

Counts

146 → 9

Compiler

Compiled 8187 to 5913 computations (27.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.9b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
13.7b	(cbrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite968.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

194×	`sqrt-prod_binary64_94`
154×	`add-sqr-sqrt_binary64_100`
136×	`times-frac_binary64_84`
109×	`*-un-lft-identity_binary64_78`
71×	`cbrt-prod_binary64_109`
67×	`add-cube-cbrt_binary64_113`
60×	`difference-of-squares_binary64_47`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
8×	`add-exp-log_binary64_116`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114` `associate-/r/_binary64_24` `distribute-lft-out--_binary64_30`
5×	`cbrt-div_binary64_110` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52`
3×	`div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`pow1/3_binary64_160` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `inv-pow_binary64_163` `pow-flip_binary64_152` `1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 193

Calls

4 calls:

38.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.0ms	(cbrt.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))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 10287 to 7654 computations (25.6% saved)

series1.8s (6.7%)

Error

0.4b

Counts

4 → 52

Calls

4 calls:

1.1s	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
247.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
234.0ms	(cbrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
102.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 6187 to 5435 computations (12.2% saved)

simplify187.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4957	9893
1	4957	9893

prune994.0ms (3.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	244	10	254

Error

0.4b

Counts

254 → 10

Compiler

Compiled 11491 to 8480 computations (26.2% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
13.7b	(cbrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite3.1s (11.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

578×	`sqrt-prod_binary64_94`
401×	`cbrt-prod_binary64_109`
399×	`add-sqr-sqrt_binary64_100`
355×	`times-frac_binary64_84`
282×	`*-un-lft-identity_binary64_78`
183×	`unpow-prod-down_binary64_157`
180×	`difference-of-squares_binary64_47`
156×	`add-cube-cbrt_binary64_113`
111×	`cube-prod_binary64_106`
37×	`sqr-pow_binary64_50`
36×	`unpow2_binary64_143`
18×	`distribute-lft-out--_binary64_30`
10×	`cbrt-div_binary64_110`
8×	`associate-/r/_binary64_24`
5×	`pow1_binary64_139` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `div-inv_binary64_75`
3×	`pow1/3_binary64_160`
2×	`sqrt-div_binary64_95`
1×	`cube-div_binary64_107` `unpow3_binary64_144` `cube-mult_binary64_108` `rem-cbrt-cube_binary64_102` `pow1/2_binary64_158` `sqrt-pow1_binary64_96`

Counts

4 → 398

Calls

4 calls:

50.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
40.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
5.0ms	(cbrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 24646 to 18728 computations (24% saved)

series2.5s (9.1%)

Error

0.4b

Counts

4 → 60

Calls

4 calls:

1.0s	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
838.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
242.0ms	(cbrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
224.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 8097 to 7178 computations (11.3% saved)

simplify318.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

458 → 458

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4985	23834
1	4985	23834

prune2.6s (9.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	458	0	458
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	458	10	468

Error

0.4b

Counts

468 → 10

Compiler

Compiled 23473 to 17329 computations (26.2% saved)

regimes2.5s (9.4%)

Accuracy

Total 0.1b remaining (13.6%)

Threshold costs 0.1b (13.6%)

Compiler

Compiled 28592 to 25030 computations (12.5% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	126
1	128	126

end0.0ms (0%)

sample3.9s (14.3%)

Algorithm

1×

intervals

Results

923.0ms	8000×	body	128	valid
516.0ms	4696×	body	128	nan

Compiler

Compiled 1650 to 1437 computations (12.9% saved)

Details

analyze1.8s (6.7%)

sample63.0ms (0.2%)

simplify64.0ms (0.2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite615.0ms (2.3%)

series1.8s (6.6%)

simplify151.0ms (0.6%)

prune485.0ms (1.8%)

localize22.0ms (0.1%)

rewrite410.0ms (1.5%)

series2.0s (7.4%)

simplify105.0ms (0.4%)

prune573.0ms (2.1%)

localize22.0ms (0.1%)

rewrite968.0ms (3.6%)

series1.8s (6.7%)

simplify187.0ms (0.7%)

prune994.0ms (3.7%)

localize35.0ms (0.1%)

rewrite3.1s (11.5%)

series2.5s (9.1%)

simplify318.0ms (1.2%)

prune2.6s (9.6%)

regimes2.5s (9.4%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.9s (14.3%)

Profiling