Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample26.0ms

Algorithm

intervals

Results

8.0ms	58×	body	640	valid
7.0ms	39×	body	1280	valid
5.0ms	137×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	4×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.7b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
1.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64` `times-frac_binary64`
64×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
4×	`div-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 166

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
38.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series1.7s

Counts

4 → 12

Calls

4 calls:

352.0ms	(sqrt.f64 (+.f64 x 1))
405.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
84.0ms	(/.f64 1 (sqrt.f64 x))
866.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	7165	9
1	7165	9
0	7165	9
1	7165	9
0	1	3
1	1	3
0	671	9
1	671	9
0	671	9
1	671	9
0	1	3
1	1	3
0	4553	9
1	4553	9
0	4553	9
1	4553	9
0	1	3
1	1	3
0	4445	9
1	4445	9
0	4445	9
1	4445	9
0	1	3
1	1	3

simplify193.0ms

Counts

178 → 178

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4841	2966
1	4841	2966

prune121.0ms

Filtered

91 candidates to 178 candidates (-95.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	9	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	9	179

Merged error: 18.2b

Counts

179 → 9

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
1.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `sqrt-div_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series1.6s

Counts

4 → 12

Calls

4 calls:

341.0ms	(sqrt.f64 (+.f64 1 x))
448.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
382.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
388.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	4493	9
1	4493	9
0	4493	9
1	4493	9
0	1	3
1	1	3
0	4490	9
1	4490	9
0	4490	9
1	4490	9
0	1	3
1	1	3
0	4780	9
1	4780	9
0	4780	9
1	4780	9
0	1	3
1	1	3
0	4439	9
1	4439	9
0	4439	9
1	4439	9
0	1	3
1	1	3

simplify154.0ms

Counts

123 → 123

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5410	2003

prune92.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 0.3b

Counts

132 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
45×	`distribute-lft-out_binary64`
39×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
27×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
9×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `associate-l_binary64` `flip-+_binary64`
5×	`prod-exp_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

series1.8s

Counts

4 → 12

Calls

4 calls:

381.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
434.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
384.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
575.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	5473	9
1	5473	9
0	5473	9
1	5473	9
0	1	3
1	1	3
0	4490	9
1	4490	9
0	4490	9
1	4490	9
0	1	3
1	1	3
0	4681	9
1	4681	9
0	4681	9
1	4681	9
0	1	3
1	1	3
0	4469	9
1	4469	9
0	4469	9
1	4469	9
0	1	3
1	1	3

simplify110.0ms

Counts

182 → 182

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5141	3707

prune160.0ms

Filtered

101 candidates to 182 candidates (-80.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	173	9	182
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Merged error: 0.0b

Counts

185 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 1 (+.f64 x (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
0.3b	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt_binary64`
82×	`times-frac_binary64`
80×	`*-un-lft-identity_binary64`
54×	`add-exp-log_binary64`
53×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`
29×	`associate-l_binary64`
24×	`associate-r_binary64`
22×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`unswap-sqr_binary64`
17×	`prod-exp_binary64`
15×	`pow1_binary64`
10×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64`
8×	`distribute-lft-out_binary64`
6×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `inv-pow_binary64` `div-inv_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `sqrt-unprod_binary64` `un-div-inv_binary64` `frac-times_binary64`

Counts

4 → 209

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
25.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 1 (+.f64 x (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
11.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))

series3.3s

Counts

4 → 12

Calls

4 calls:

1.4s	(/.f64 1 (+.f64 1 (+.f64 x (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
1.4s	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 1 (+.f64 x (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
390.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
85.0ms	(/.f64 1 (sqrt.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	671	9
1	671	9
0	671	9
1	671	9
0	1	3
1	1	3
0	4490	9
1	4490	9
0	4490	9
1	4490	9
0	1	3
1	1	3
0	16937	9
1	16937	9
0	16937	9
1	16937	9
0	1	3
1	1	3
0	18524	9
1	18524	9
0	18524	9
1	18524	9
0	1	3
1	1	3

simplify199.0ms

Counts

221 → 221

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4923	4662
1	4923	4662

prune157.0ms

Filtered

122 candidates to 221 candidates (-81.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	223	8	231

Merged error: 0b

Counts

231 → 8

regimes22.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	26
1	20	26

end0.0ms

sample749.0ms

Algorithm

intervals

Results

236.0ms	1787×	body	640	valid
203.0ms	1198×	body	1280	valid
147.0ms	4094×	body	80	valid
59.0ms	616×	body	320	valid
20.0ms	305×	body	160	valid

Details

analyze2.0ms

sample26.0ms

simplify24.0ms

prune7.0ms

localize7.0ms

rewrite64.0ms

series1.7s

simplify193.0ms

prune121.0ms

localize7.0ms

rewrite51.0ms

series1.6s

simplify154.0ms

prune92.0ms

localize9.0ms

rewrite67.0ms

series1.8s

simplify110.0ms

prune160.0ms

localize13.0ms

rewrite60.0ms

series3.3s

simplify199.0ms

prune157.0ms

regimes22.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample749.0ms

Profiling