Details

analyze1.4s

Algorithm

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

sample60.0ms

Algorithm

intervals

Results

23.0ms	124×	body	160	valid
12.0ms	132×	body	80	valid
11.0ms	121×	body	80	nan

simplify145.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4909	29
1	4909	29

prune2.0ms

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: 10.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
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))))))
10.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
48×	`sqrt-prod_binary64`
38×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
30×	`difference-of-squares_binary64`
10×	`add-exp-log_binary64`
8×	`unpow2_binary64` `sqr-pow_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `insert-posit16` `pow-exp_binary64`
3×	`distribute-lft-out--_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `asin-acos_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 130

Calls

4 calls:

6.0ms	(pow.f64 (/.f64 t l) 2)
6.0ms	(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))))))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

222.0ms	(pow.f64 (/.f64 t l) 2)
234.0ms	(pow.f64 (/.f64 Om Omc) 2)
220.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
715.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	930	1601
1	930	1601
0	85	467
1	85	467
0	930	1601
1	930	1601
0	85	467
1	85	467
0	5103	33
0	348	1896
1	348	1896
0	115	1653
1	115	1653
0	348	1896
1	348	1896
0	115	1653
1	115	1653
0	119	35
1	119	35
0	383	441
1	383	441
0	12	9
1	12	9
0	383	441
1	383	441
0	12	9
1	12	9
0	1	3
1	1	3
0	383	441
1	383	441
0	12	9
1	12	9
0	383	441
1	383	441
0	12	9
1	12	9
0	1	3
1	1	3

simplify150.0ms

Counts

142 → 142

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4925	3951
1	4925	3951

prune169.0ms

Filtered

92 candidates to 142 candidates (-54.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 10.6b

Counts

143 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(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))))))
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)))))
10.1b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
125×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64`
70×	`difference-of-squares_binary64`
63×	`add-cube-cbrt_binary64`
41×	`unpow-prod-down_binary64`
17×	`associate-/l*_binary64`
15×	`unpow2_binary64` `sqr-pow_binary64`
9×	`add-exp-log_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `asin-acos_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 198

Calls

4 calls:

6.0ms	(pow.f64 (/.f64 Om Omc) 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))))))
24.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

226.0ms	(pow.f64 (/.f64 Om Omc) 2)
224.0ms	(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))))))
639.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
424.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	572	741
1	572	741
0	24	9
1	24	9
0	572	741
1	572	741
0	24	9
1	24	9
0	5307	12
0	962	1663
1	962	1663
0	135	559
1	135	559
0	962	1663
1	962	1663
0	135	559
1	135	559
0	5049	81
0	360	1914
1	360	1914
0	110	1680
1	110	1680
0	360	1914
1	360	1914
0	110	1680
1	110	1680
0	122	40
1	122	40
0	383	441
1	383	441
0	12	9
1	12	9
0	383	441
1	383	441
0	12	9
1	12	9
0	1	3
1	1	3

simplify175.0ms

Counts

210 → 210

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5044	8141

prune209.0ms

Filtered

111 candidates to 210 candidates (-89.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	207	10	217

Merged error: 10.5b

Counts

217 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.1b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.1b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`

Counts

4 → 76

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.0ms	(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))))

series1.8s

Counts

4 → 12

Calls

4 calls:

457.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
453.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
422.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
423.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	572	741
1	572	741
0	24	9
1	24	9
0	572	741
1	572	741
0	24	9
1	24	9
0	5307	12
0	572	741
1	572	741
0	24	9
1	24	9
0	572	741
1	572	741
0	24	9
1	24	9
0	5307	12
0	638	903
1	638	903
0	24	9
1	24	9
0	638	903
1	638	903
0	24	9
1	24	9
0	5307	12
0	638	903
1	638	903
0	24	9
1	24	9
0	638	903
1	638	903
0	24	9
1	24	9
0	5307	12

simplify112.0ms

Counts

88 → 88

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4955	1564
1	4955	1564

prune139.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	88	10	98

Merged error: 10.5b

Counts

98 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.2b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
16.4b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `asin-acos_binary64`

Counts

4 → 58

Calls

4 calls:

1.0ms	(asin.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
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))))

series1.1s

Counts

4 → 12

Calls

4 calls:

253.0ms	(asin.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
285.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
273.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
272.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	136	1734
1	136	1734
0	94	1629
1	94	1629
0	136	1734
1	136	1734
0	94	1629
1	94	1629
0	5394	40
0	136	1734
1	136	1734
0	94	1629
1	94	1629
0	136	1734
1	136	1734
0	94	1629
1	94	1629
0	5394	40
0	203	1752
1	203	1752
0	114	1647
1	114	1647
0	203	1752
1	203	1752
0	114	1647
1	114	1647
0	5395	48
0	448	2166
1	448	2166
0	142	1780
1	142	1780
0	448	2166
1	448	2166
0	142	1780
1	142	1780
0	138	33
1	138	33

simplify122.0ms

Counts

70 → 70

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4909	1786
1	4909	1786

prune135.0ms

Filtered

62 candidates to 70 candidates (-12.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	70	10	80

Merged error: 10.5b

Counts

80 → 10

regimes377.0ms

Accuracy

0% (0.2b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	29
1	30	29

end0.0ms

sample1.9s

Algorithm

intervals

Results

724.0ms	3830×	body	160	valid
440.0ms	4672×	body	80	nan
393.0ms	4170×	body	80	valid

Details

analyze1.4s

sample60.0ms

simplify145.0ms

prune2.0ms

localize14.0ms

rewrite41.0ms

series1.4s

simplify150.0ms

prune169.0ms

localize15.0ms

rewrite52.0ms

series1.5s

simplify175.0ms

prune209.0ms

localize18.0ms

rewrite23.0ms

series1.8s

simplify112.0ms

prune139.0ms

localize22.0ms

rewrite16.0ms

series1.1s

simplify122.0ms

prune135.0ms

regimes377.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.9s

Profiling