Details

analyze230.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample72.0ms

Algorithm

intervals

Results

30.0ms	55×	body	1280	valid
14.0ms	43×	body	640	valid
10.0ms	122×	body	80	valid
6.0ms	27×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	11×	body	80	invalid
1.0ms	8×	body	80	overflowed
1.0ms	1×	body	1280	invalid

simplify126.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4909	41
1	4909	41

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: 31.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
1.8b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
78×	`exp-neg_binary64`
76×	`frac-times_binary64`
59×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-r/_binary64` `associate-l/_binary64`
31×	`flip3--_binary64` `flip--_binary64`
27×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`un-div-inv_binary64`
17×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
12×	`exp-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `times-frac_binary64`
5×	`add-exp-log_binary64`
4×	`rem-exp-log_binary64` `insert-posit16`
3×	`associate-r_binary64` `difference-of-sqr-1_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 168

Calls

4 calls:

20.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
23.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

326.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
305.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
192.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
444.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	801	1196
1	801	1196
0	6	9
1	6	9
0	801	1196
1	801	1196
0	6	9
1	6	9
0	11	21
1	11	21
0	308	263
1	308	263
0	8	9
1	8	9
0	308	263
1	308	263
0	8	9
1	8	9
0	1	3
1	1	3
0	306	263
1	306	263
0	26	25
1	26	25
0	306	263
1	306	263
0	26	25
1	26	25
0	5030	3
0	489	598
1	489	598
0	6	9
1	6	9
0	489	598
1	489	598
0	6	9
1	6	9
0	11	21
1	11	21

simplify169.0ms

Counts

180 → 180

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4981	8576
1	4981	8576

prune284.0ms

Filtered

98 candidates to 180 candidates (-83.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	163	17	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	17	181

Merged error: 30.7b

Counts

181 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 1 eps) x)
0.0b	(exp.f64 (*.f64 x (+.f64 1 eps)))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
2.7b	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
9×	`frac-add_binary64`
7×	`add-cube-cbrt_binary64` `exp-prod_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`exp-neg_binary64`
4×	`flip3-+_binary64` `neg-sub0_binary64` `exp-diff_binary64` `insert-posit16` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64` `rem-exp-log_binary64`
2×	`associate-*r/_binary64` `exp-sum_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-rgt-neg-in_binary64` `div-sub_binary64` `neg-log_binary64` `prod-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `exp-to-pow_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

9.0ms	(*.f64 (-.f64 1 eps) x)
3.0ms	(exp.f64 (*.f64 x (+.f64 1 eps)))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
36.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

273.0ms	(*.f64 (-.f64 1 eps) x)
183.0ms	(exp.f64 (*.f64 x (+.f64 1 eps)))
308.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
491.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	817	1324
1	817	1324
0	24	101
1	24	101
0	817	1324
1	817	1324
0	24	101
1	24	101
0	20	21
1	20	21
0	306	263
1	306	263
0	26	25
1	26	25
0	306	263
1	306	263
0	26	25
1	26	25
0	5030	3
0	278	243
1	278	243
0	8	9
1	8	9
0	278	243
1	278	243
0	8	9
1	8	9
0	1	3
1	1	3
0	220	153
1	220	153
0	15	20
1	15	20
0	220	153
1	220	153
0	15	20
1	15	20
0	4896	3
1	4896	3

simplify187.0ms

Counts

89 → 89

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	4951	1828
1	4951	1828

prune145.0ms

Filtered

62 candidates to 89 candidates (-43.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	88	18	106

Merged error: 30.7b

Counts

106 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))))
0.0b	(exp.f64 (*.f64 x (+.f64 1 eps)))
2.7b	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (.f64 (-.f64 1 eps) x)))))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))
59.6b	(posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`exp-prod_binary64`
10×	`add-log-exp_binary64`
9×	`frac-add_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`exp-neg_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `neg-sub0_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `insert-posit16` `flip-+_binary64` `frac-times_binary64`
3×	`distribute-lft-neg-in_binary64` `rem-exp-log_binary64` `distribute-rgt-neg-in_binary64`
2×	`associate-r/_binary64` `exp-sum_binary64` `associate-l/_binary64`
1×	`associate-+r-_binary64` `neg-mul-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `neg-log_binary64` `remove-posit16` `un-div-inv_binary64` `+-commutative_binary64` `exp-to-pow_binary64` `sum-log_binary64`

Counts

4 → 66

Calls

4 calls:

3.0ms	(exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))))
3.0ms	(exp.f64 (*.f64 x (+.f64 1 eps)))
36.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (.f64 (-.f64 1 eps) x)))))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))
1.0ms	(posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

355.0ms	(exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))))
182.0ms	(exp.f64 (*.f64 x (+.f64 1 eps)))
673.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (posit16->binary64 (binary64->posit16 (.f64 (-.f64 1 eps) x)))))) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (+.f64 1 eps)))))
228.0ms	(posit16->binary64 (binary64->posit16 (*.f64 (-.f64 1 eps) x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	60	2631
1	60	2631
0	11	9
1	11	9
0	60	2631
1	60	2631
0	11	9
1	11	9
0	1	3
1	1	3
0	784	3001
1	784	3001
0	4973	1916
1	4973	1916
0	784	3001
1	784	3001
0	4973	1916
1	4973	1916
0	1	3
1	1	3
0	278	243
1	278	243
0	8	9
1	8	9
0	278	243
1	278	243
0	8	9
1	8	9
0	1	3
1	1	3
0	150	2667
1	150	2667
0	4936	2565
1	4936	2565
0	150	2667
1	150	2667
0	4936	2565
1	4936	2565
0	1	3
1	1	3

simplify133.0ms

Counts

78 → 78

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4975	1728
1	4975	1728

prune132.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	78	18	96

Merged error: 30.7b

Counts

96 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.1b	(/.f64 (/.f64 1 eps) eps)
9.8b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps))))))
23.7b	(/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac_binary64`
107×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
32×	`associate-/l*_binary64`
20×	`difference-of-squares_binary64`
17×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
12×	`div-inv_binary64`
10×	`difference-of-sqr-1_binary64`
9×	`frac-sub_binary64`
8×	`add-log-exp_binary64` `div-exp_binary64`
7×	`pow1_binary64`
6×	`exp-prod_binary64`
5×	`cbrt-undiv_binary64` `exp-neg_binary64`
4×	`flip3-+_binary64` `associate-/r_binary64` `neg-sub0_binary64` `exp-diff_binary64` `insert-posit16` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64`
3×	`associate-/l/_binary64`
2×	`flip3--_binary64` `pow-div_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `rem-exp-log_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `associate--r-_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `inv-pow_binary64` `neg-log_binary64` `prod-exp_binary64` `rec-exp_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 174

Calls

4 calls:

5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
9.0ms	(/.f64 (/.f64 1 eps) eps)
40.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps))))))
38.0ms	(/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

308.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
408.0ms	(/.f64 (/.f64 1 eps) eps)
585.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps))))))
493.0ms	(/.f64 (-.f64 (/.f64 (/.f64 1 eps) eps) 1) (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 x (+.f64 1 eps)))))

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	702	1404
1	702	1404
0	51	437
1	51	437
0	702	1404
1	702	1404
0	51	437
1	51	437
0	55	21
1	55	21
0	1002	1827
1	1002	1827
0	114	818
1	114	818
0	1002	1827
1	1002	1827
0	114	818
1	114	818
0	55	21
1	55	21
0	423	847
1	423	847
0	15	425
1	15	425
0	423	847
1	423	847
0	15	425
1	15	425
0	5859	47
0	306	263
1	306	263
0	26	25
1	26	25
0	306	263
1	306	263
0	26	25
1	26	25
0	5030	3

simplify138.0ms

Counts

186 → 186

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4983	4860
1	4983	4860

prune300.0ms

Filtered

115 candidates to 186 candidates (-61.7%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	4	11	15
Picked	1	0	1
Done	0	2	2
Total	182	22	204

Merged error: 30.6b

Counts

204 → 22

regimes147.0ms

Accuracy

0% (0.9b remaining)

Error of 30.1b against oracle of 29.2b and baseline of 30.1b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	114	41
1	114	41

end0.0ms

sample2.1s

Algorithm

intervals

Results

923.0ms	1707×	body	1280	valid
446.0ms	1305×	body	640	valid
314.0ms	4009×	body	80	valid
149.0ms	655×	body	320	valid
48.0ms	324×	body	160	valid
18.0ms	233×	body	80	invalid
15.0ms	205×	body	80	overflowed
14.0ms	21×	body	1280	invalid
5.0ms	14×	body	640	invalid
1.0ms	3×	body	320	invalid
0.0ms	1×	body	160	invalid

Details

analyze230.0ms

sample72.0ms

simplify126.0ms

prune7.0ms

localize18.0ms

rewrite66.0ms

series1.3s

simplify169.0ms

prune284.0ms

localize16.0ms

rewrite56.0ms

series1.3s

simplify187.0ms

prune145.0ms

localize18.0ms

rewrite48.0ms

series1.4s

simplify133.0ms

prune132.0ms

localize21.0ms

rewrite105.0ms

series1.8s

simplify138.0ms

prune300.0ms

regimes147.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample2.1s

Profiling