Details

analyze77.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

sample14.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	23×	body	80	overflowed

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	8	13
1	8	13

prune1.0ms

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: 1.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
1.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`add-exp-log_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `associate-/r/_binary64` `insert-posit16` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 47

Calls

2 calls:

5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
9.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series630.0ms

Counts

2 → 6

Calls

2 calls:

230.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
400.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	595	961
1	595	961
0	595	961
1	595	961
0	4919	27
1	4919	27
0	2659	232
1	2659	232
0	2659	232
1	2659	232
0	54	9
1	54	9

simplify128.0ms

Counts

53 → 53

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5143	895

prune38.0ms

Filtered

40 candidates to 53 candidates (-32.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0.7b

Counts

54 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
0.0b	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
1.0b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
1.2b	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac_binary64`
306×	`*-un-lft-identity_binary64`
232×	`sqrt-prod_binary64`
192×	`add-sqr-sqrt_binary64`
190×	`add-cube-cbrt_binary64`
58×	`distribute-lft-out_binary64`
30×	`associate-/l*_binary64`
24×	`sqrt-div_binary64`
20×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-cbrt-cube_binary64`
10×	`div-inv_binary64`
9×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 321

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
24.0ms	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
10.0ms	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))

series1.5s

Counts

4 → 12

Calls

4 calls:

294.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
296.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
550.0ms	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
358.0ms	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	670	1425
1	670	1425
0	670	1425
1	670	1425
0	4930	41
1	4930	41
0	1341	1589
1	1341	1589
0	1341	1589
1	1341	1589
0	5256	26
0	391	550
1	391	550
0	391	550
1	391	550
0	5163	25
0	391	550
1	391	550
0	391	550
1	391	550
0	5163	25

simplify233.0ms

Counts

333 → 333

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5145	11826

prune137.0ms

Filtered

148 candidates to 333 candidates (-125.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	333	4	337

Merged error: 0.7b

Counts

337 → 4

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (exp.f64 a) (+.f64 2 (+.f64 a b)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`associate-/r*_binary64`
3×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`add-exp-log_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `insert-posit16` `flip-+_binary64`

Counts

1 → 38

Calls

1 calls:

10.0ms

(/.f64 (exp.f64 a) (+.f64 2 (+.f64 a b)))

series385.0ms

Counts

1 → 3

Calls

1 calls:

385.0ms

(/.f64 (exp.f64 a) (+.f64 2 (+.f64 a b)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1534	158
1	1534	158
0	1534	158
1	1534	158
0	1	3
1	1	3

simplify108.0ms

Counts

41 → 41

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4974	713
1	4974	713

prune24.0ms

Filtered

26 candidates to 41 candidates (-57.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	41	4	45

Merged error: 0.7b

Counts

45 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f32 (/.f64 (-.f64 a (/.f64 a 2)) 2) (/.f32 b 4))
0.0b	(/.f32 b 4)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
10×	`times-frac_binary32` `add-cube-cbrt_binary32`
4×	`add-cbrt-cube_binary32` `add-exp-log_binary32` `add-log-exp_binary32`
3×	`associate-/r_binary32` `associate-/l_binary32`
2×	`pow1_binary32` `difference-of-squares_binary32`
1×	`flip--_binary32` `frac-2neg_binary32` `diff-log_binary32` `sub-neg_binary32` `flip3--_binary32` `div-inv_binary32` `distribute-lft-out--_binary32` `div-exp_binary32` `clear-num_binary32` `cbrt-undiv_binary32`

Counts

2 → 41

Calls

2 calls:

8.0ms	(-.f32 (/.f64 (-.f64 a (/.f64 a 2)) 2) (/.f32 b 4))
5.0ms	(/.f32 b 4)

series553.0ms

Counts

2 → 6

Calls

2 calls:

302.0ms	(-.f32 (/.f64 (-.f64 a (/.f64 a 2)) 2) (/.f32 b 4))
251.0ms	(/.f32 b 4)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	242	218
1	242	218
0	242	218
1	242	218
0	4977	18
1	4977	18
0	30	162
1	30	162
0	30	162
1	30	162
0	1	3
1	1	3

simplify94.0ms

Counts

47 → 47

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4915	623
1	4915	623

prune43.0ms

Filtered

37 candidates to 47 candidates (-27.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	47	4	51

Merged error: 0.6b

Counts

51 → 4

regimes46.0ms

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.6b and baseline of 0.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	13
1	8	13

end0.0ms

sample387.0ms

Algorithm

intervals

Results

220.0ms	8000×	body	80	valid
19.0ms	697×	body	80	overflowed

Details

analyze77.0ms

sample14.0ms

simplify23.0ms

prune1.0ms

localize6.0ms

rewrite16.0ms

series630.0ms

simplify128.0ms

prune38.0ms

localize8.0ms

rewrite74.0ms

series1.5s

simplify233.0ms

prune137.0ms

localize6.0ms

rewrite12.0ms

series385.0ms

simplify108.0ms

prune24.0ms

localize15.0ms

rewrite15.0ms

series553.0ms

simplify94.0ms

prune43.0ms

regimes46.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample387.0ms

Profiling