Details

analyze1.0ms

Algorithm

Search

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

sample33.0ms

Algorithm

intervals

Results

14.0ms	64×	body	640	valid
7.0ms	41×	body	1280	valid
4.0ms	124×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	7×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune2.0ms

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: 19.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 149

Calls

3 calls:

8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series1.8s

Counts

3 → 9

Calls

3 calls:

369.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
361.0ms	(/.f64 1 (sqrt.f64 x))
1.0s	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	2712	1509
1	2712	1509
0	2712	1509
1	2712	1509
0	5969	20
0	627	1010
1	627	1010
0	627	1010
1	627	1010
0	4961	14
1	4961	14
0	711	1072
1	711	1072
0	711	1072
1	711	1072
0	5326	9

simplify163.0ms

Counts

158 → 158

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4867	2839
1	4867	2839

prune111.0ms

Filtered

79 candidates to 158 candidates (-100.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	11	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	11	159

Merged error: 19.3b

Counts

159 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.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)))
2.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series1.4s

Counts

3 → 9

Calls

3 calls:

595.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
412.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
435.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	757	888
1	757	888
0	757	888
1	757	888
0	4932	17
1	4932	17
0	835	1093
1	835	1093
0	835	1093
1	835	1093
0	5408	14
0	1145	1929
1	1145	1929
0	1145	1929
1	1145	1929
0	5030	20

simplify191.0ms

Counts

103 → 103

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	4994	1884
1	4994	1884

prune121.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 0.3b

Counts

114 → 2

localize12.0ms

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 (/.f64 1 (+.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)))

rewrite73.0ms

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))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
26.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
15.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series1.9s

Counts

4 → 12

Calls

4 calls:

305.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
469.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
709.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
408.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	835	1093
1	835	1093
0	835	1093
1	835	1093
0	5408	14
0	1698	1913
1	1698	1913
0	1698	1913
1	1698	1913
0	5168	14
0	986	1443
1	986	1443
0	986	1443
1	986	1443
0	4963	17
1	4963	17
0	757	888
1	757	888
0	757	888
1	757	888
0	5030	17

simplify141.0ms

Counts

182 → 182

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5062	3757

prune158.0ms

Filtered

108 candidates to 182 candidates (-68.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	178	6	184

Merged error: 0.0b

Counts

184 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`associate-*r/_binary64`
18×	`add-cube-cbrt_binary64`
12×	`flip3-+_binary64` `add-exp-log_binary64` `flip-+_binary64`
11×	`associate-r_binary64`
10×	`add-cbrt-cube_binary64` `sqrt-div_binary64`
9×	`pow1_binary64` `associate-l_binary64` `times-frac_binary64` `sqrt-prod_binary64`
8×	`frac-add_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`unswap-sqr_binary64` `insert-posit16`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(+.f64 (.f64 (sqrt.f64 x) (+.f64 x 1)) (.f64 x (sqrt.f64 (+.f64 x 1))))
9.0ms	(*.f64 (sqrt.f64 x) (+.f64 x 1))
9.0ms	(*.f64 x (sqrt.f64 (+.f64 x 1)))
13.0ms	(/.f64 1 (+.f64 (.f64 (sqrt.f64 x) (+.f64 x 1)) (.f64 x (sqrt.f64 (+.f64 x 1)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

395.0ms	(+.f64 (.f64 (sqrt.f64 x) (+.f64 x 1)) (.f64 x (sqrt.f64 (+.f64 x 1))))
314.0ms	(*.f64 (sqrt.f64 x) (+.f64 x 1))
350.0ms	(*.f64 x (sqrt.f64 (+.f64 x 1)))
486.0ms	(/.f64 1 (+.f64 (.f64 (sqrt.f64 x) (+.f64 x 1)) (.f64 x (sqrt.f64 (+.f64 x 1)))))

Iterations

Useful iterations: 0 (183.0ms)

Iter	Nodes	Cost
0	1187	1714
1	1187	1714
0	1187	1714
1	1187	1714
0	4961	14
1	4961	14
0	590	795
1	590	795
0	590	795
1	590	795
0	5105	9
0	609	849
1	609	849
0	609	849
1	609	849
0	5408	14
0	958	1240
1	958	1240
0	958	1240
1	958	1240
0	5408	14

simplify119.0ms

Counts

122 → 122

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5096	2471

prune106.0ms

Filtered

92 candidates to 122 candidates (-32.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Merged error: 0b

Counts

128 → 7

regimes17.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	23
1	16	23

end0.0ms

sample767.0ms

Algorithm

intervals

Results

253.0ms	1862×	body	640	valid
204.0ms	1191×	body	1280	valid
141.0ms	4019×	body	80	valid
62.0ms	616×	body	320	valid
20.0ms	312×	body	160	valid

Details

analyze1.0ms

sample33.0ms

simplify25.0ms

prune2.0ms

localize7.0ms

rewrite64.0ms

series1.8s

simplify163.0ms

prune111.0ms

localize10.0ms

rewrite47.0ms

series1.4s

simplify191.0ms

prune121.0ms

localize12.0ms

rewrite73.0ms

series1.9s

simplify141.0ms

prune158.0ms

localize8.0ms

rewrite45.0ms

series1.5s

simplify119.0ms

prune106.0ms

regimes17.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample767.0ms

Profiling