Details

analyze264.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample84.0ms

Algorithm

intervals

Results

44.0ms	85×	body	1280	valid
16.0ms	52×	body	640	valid
10.0ms	30×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	59×	body	80	valid
0.0ms	4×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

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: 53.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.5b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 45

Calls

3 calls:

8.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.1s

Counts

3 → 9

Calls

3 calls:

325.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
433.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
350.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	687	688
1	687	688
0	687	688
1	687	688
0	5153	12
0	1900	1095
1	1900	1095
0	1900	1095
1	1900	1095
0	5122	8
0	1373	630
1	1373	630
0	1373	630
1	1373	630
0	5163	15

simplify122.0ms

Counts

54 → 54

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5006	759

prune54.0ms

Filtered

41 candidates to 54 candidates (-31.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 13.3b

Counts

55 → 4

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify21.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 13.3b

Counts

4 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

2.5b	(log.f64 (+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))))
8.0b	(+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-prod_binary64`
5×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
3×	`log-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `log-div_binary64`
1×	`rem-log-exp_binary64` `log-pow_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

3.0ms	(log.f64 (+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))))
4.0ms	(+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.6s

Counts

4 → 12

Calls

4 calls:

500.0ms	(log.f64 (+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))))
403.0ms	(+.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
339.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
336.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	687	688
1	687	688
0	687	688
1	687	688
0	5153	12
0	687	688
1	687	688
0	687	688
1	687	688
0	5153	12
0	1650	1103
1	1650	1103
0	1650	1103
1	1650	1103
0	5083	15
0	2274	1533
1	2274	1533
0	2274	1533
1	2274	1533
0	5123	8

simplify145.0ms

Counts

71 → 71

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	5465	941

prune59.0ms

Filtered

57 candidates to 71 candidates (-24.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Merged error: 13.3b

Counts

75 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.3b	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.8b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
24×	`log-prod_binary64`
16×	`difference-of-squares_binary64`
11×	`sqrt-prod_binary64`
9×	`add-exp-log_binary64`
8×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r/_binary64` `insert-posit16`
3×	`flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
10.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
10.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.6s

Counts

4 → 12

Calls

4 calls:

424.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
324.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
489.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
337.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	687	688
1	687	688
0	687	688
1	687	688
0	5153	12
0	2270	1459
1	2270	1459
0	2270	1459
1	2270	1459
0	64	45
1	64	45
0	1403	632
1	1403	632
0	1403	632
1	1403	632
0	5543	15
0	2050	1220
1	2050	1220
0	2050	1220
1	2050	1220
0	4888	18
1	4888	18

simplify118.0ms

Counts

121 → 121

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4953	2679
1	4953	2679

prune89.0ms

Filtered

85 candidates to 121 candidates (-42.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	120	5	125

Merged error: 10.5b

Counts

125 → 5

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 11.1b against oracle of 11.1b and baseline of 30.9b

bsearch94.0ms

Steps

Iters	Range		Point
8	4.685512529426347e+149	2.5842072098636875e+154	1.3218907971973426e+154
9	1.45069025105974e-07	0.6814830664350081	1.119329551643299e-05
9	-3.996062453584732	-1.8155029574833036e-07	-7.433249191736301e-06
9	-1.327565426163676e+160	-4.4865653202028787e+151	-1.3376046051696085e+154

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	85
1	45	85

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2349×	body	1280	valid
438.0ms	1552×	body	640	valid
281.0ms	821×	body	2560	valid
142.0ms	811×	body	320	valid
94.0ms	2093×	body	80	valid
38.0ms	374×	body	160	valid

Details

analyze264.0ms

sample84.0ms

simplify21.0ms

prune2.0ms

localize7.0ms

rewrite22.0ms

series1.1s

simplify122.0ms

prune54.0ms

localize3.0ms

rewrite0.0ms

series0.0ms

simplify21.0ms

prune3.0ms

localize9.0ms

rewrite21.0ms

series1.6s

simplify145.0ms

prune59.0ms

localize8.0ms

rewrite42.0ms

series1.6s

simplify118.0ms

prune89.0ms

regimes35.0ms

bsearch94.0ms

simplify8.0ms

end0.0ms

sample2.2s

Profiling