Details

analyze276.0ms

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

sample72.0ms

Algorithm

intervals

Results

33.0ms	70×	body	1280	valid
13.0ms	47×	body	640	valid
10.0ms	30×	body	2560	valid
5.0ms	29×	body	320	valid
3.0ms	63×	body	80	valid
2.0ms	17×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

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: 55.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
17.7b	(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)))
7.0ms	(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:

358.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
400.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
374.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	296	547
1	296	547
0	12	9
1	12	9
0	296	547
1	296	547
0	12	9
1	12	9
0	4988	42
1	4988	42
0	380	853
1	380	853
0	5888	597
0	380	853
1	380	853
0	5888	597
0	78	45
1	78	45
0	322	583
1	322	583
0	12	9
1	12	9
0	322	583
1	322	583
0	12	9
1	12	9
0	4988	42
1	4988	42

simplify126.0ms

Counts

54 → 54

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5029	847

prune61.0ms

Filtered

43 candidates to 54 candidates (-25.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	5	55

Merged error: 16.3b

Counts

55 → 5

localize7.0ms

Local error

Found 1 expressions with local error:

22.7b

(*.f64 (log.f64 1) (+.f64 1 (pow.f64 x 3)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `insert-posit16` `flip-+_binary64` `*-commutative_binary64`

Counts

1 → 25

Calls

1 calls:

10.0ms

(*.f64 (log.f64 1) (+.f64 1 (pow.f64 x 3)))

series441.0ms

Counts

1 → 3

Calls

1 calls:

441.0ms

(*.f64 (log.f64 1) (+.f64 1 (pow.f64 x 3)))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	484	831
1	484	831
0	10	9
1	10	9
0	484	831
1	484	831
0	10	9
1	10	9
0	5063	42

simplify139.0ms

Counts

28 → 28

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4870	373
1	4870	373

prune26.0ms

Filtered

20 candidates to 28 candidates (-40.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	28	5	33

Merged error: 15.8b

Counts

33 → 5

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify19.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Merged error: 15.8b

Counts

5 → 5

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)))
3.1b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
17.7b	(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:

13.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.0ms	(-.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))

series1.8s

Counts

4 → 12

Calls

4 calls:

549.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
358.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
507.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
369.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	296	547
1	296	547
0	12	9
1	12	9
0	296	547
1	296	547
0	12	9
1	12	9
0	4988	42
1	4988	42
0	533	1045
1	533	1045
0	29	27
1	29	27
0	533	1045
1	533	1045
0	29	27
1	29	27
0	5553	54
0	322	583
1	322	583
0	13	9
1	13	9
0	322	583
1	322	583
0	13	9
1	13	9
0	4988	42
1	4988	42
0	475	983
1	475	983
0	33	9
1	33	9
0	475	983
1	475	983
0	33	9
1	33	9
0	5453	39

simplify255.0ms

Counts

121 → 121

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	4676	2601
1	4676	2601

prune88.0ms

Filtered

88 candidates to 121 candidates (-37.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Merged error: 12.9b

Counts

126 → 6

regimes59.0ms

Accuracy

99.9% (0.0b remaining)

Error of 11.1b against oracle of 11.1b and baseline of 31.3b

bsearch108.0ms

Steps

Iters	Range		Point
12	7.386379393289397e+136	2.9844874321380217e+178	1.3309234847747417e+154
9	1.331223533998654e-09	9.079033223787133e-05	5.3198639586972195e-06
10	-10.722936850014555	-1.2734808308663866e-11	-8.98759362711225e-06
9	-5.75180632944898e+154	-2.7289770523849463e+145	-1.3307054299543536e+154

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	97	120
1	97	120

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2334×	body	1280	valid
453.0ms	1577×	body	640	valid
279.0ms	810×	body	2560	valid
126.0ms	727×	body	320	valid
97.0ms	2173×	body	80	valid
38.0ms	379×	body	160	valid

Details

analyze276.0ms

sample72.0ms

simplify19.0ms

prune1.0ms

localize7.0ms

rewrite22.0ms

series1.1s

simplify126.0ms

prune61.0ms

localize7.0ms

rewrite11.0ms

series441.0ms

simplify139.0ms

prune26.0ms

localize3.0ms

rewrite0.0ms

series0.0ms

simplify19.0ms

prune5.0ms

localize8.0ms

rewrite42.0ms

series1.8s

simplify255.0ms

prune88.0ms

regimes59.0ms

bsearch108.0ms

simplify9.0ms

end0.0ms

sample2.2s

Profiling