Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

sample31.0ms

Algorithm

intervals

Results

14.0ms	70×	body	1280	valid
7.0ms	55×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	85×	body	80	valid
1.0ms	20×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	167	9
1	167	9

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: 40.8b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

4.6b	(-.f64 (exp.f64 x) 1)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `insert-posit16` `flip--_binary64`

Counts

1 → 16

Calls

1 calls:

5.0ms

(-.f64 (exp.f64 x) 1)

series257.0ms

Counts

1 → 3

Calls

1 calls:

257.0ms

(-.f64 (exp.f64 x) 1)

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	238	216
1	238	216
0	238	216
1	238	216
0	5116	12

simplify115.0ms

Counts

19 → 19

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5640	188

prune18.0ms

Filtered

14 candidates to 19 candidates (-35.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	2	20

Merged error: 0.1b

Counts

20 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 x x) 2))
10.3b	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) x)

rewrite17.0ms

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×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_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:

6.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
9.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) x)

series819.0ms

Counts

2 → 6

Calls

2 calls:

255.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
564.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) x)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	3990	299
1	3990	299
0	3990	299
1	3990	299
0	1	3
1	1	3
0	28	99
1	28	99
0	28	99
1	28	99
0	1	3
1	1	3

simplify86.0ms

Counts

53 → 53

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5417	896

prune35.0ms

Filtered

38 candidates to 53 candidates (-39.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0.1b

Counts

55 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
2.0b	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
8.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
63×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
51×	`add-exp-log_binary64`
40×	`add-cube-cbrt_binary64`
36×	`cbrt-prod_binary64`
28×	`associate-r_binary64`
20×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
16×	`div-exp_binary64`
13×	`distribute-lft-out_binary64`
9×	`unswap-sqr_binary64`
8×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
7×	`associate-l_binary64`
6×	`associate-/r*_binary64` `pow1_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 150

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
10.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
27.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x)))

series2.2s

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt.f64 x)
214.0ms	(cbrt.f64 x)
774.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
1.0s	(.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x)))

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4347	1902
1	4347	1902
0	4347	1902
1	4347	1902
0	4878	3
1	4878	3
0	28	216
1	28	216
0	28	216
1	28	216
0	5133	3
0	41	1602
1	41	1602
0	41	1602
1	41	1602
0	5408	14
0	41	1602
1	41	1602
0	41	1602
1	41	1602
0	5408	14

simplify143.0ms

Counts

162 → 162

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5020	3537

prune133.0ms

Filtered

116 candidates to 162 candidates (-39.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	162	4	166

Merged error: 0.1b

Counts

166 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))
2.0b	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
2.0b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))))
6.7b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
54×	`cbrt-prod_binary64`
41×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
29×	`associate-l_binary64`
27×	`cbrt-div_binary64`
18×	`pow1_binary64` `frac-times_binary64`
16×	`add-cbrt-cube_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`distribute-lft-out_binary64`
12×	`associate-r/_binary64` `unswap-sqr_binary64` `associate-l/_binary64`
11×	`associate-r_binary64`
9×	`pow-prod-down_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 175

Calls

4 calls:

10.0ms	(cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))
10.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
21.0ms	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))))
27.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))

series3.1s

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))
766.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 x x) 2)) (cbrt.f64 x))
961.0ms	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))))
1.1s	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) 2)) (cbrt.f64 x)) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4335	2112
1	4335	2112
0	4335	2112
1	4335	2112
0	5184	3
0	4232	1920
1	4232	1920
0	4232	1920
1	4232	1920
0	4952	3
1	4952	3
0	28	216
1	28	216
0	28	216
1	28	216
0	5133	3
0	73	1692
1	73	1692
0	73	1692
1	73	1692
0	4973	22
1	4973	22

simplify125.0ms

Counts

187 → 187

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5092	5595

prune222.0ms

Filtered

130 candidates to 187 candidates (-43.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	187	4	191

Merged error: 0.1b

Counts

191 → 4

regimes18.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.9b

bsearch13.0ms

Steps

Iters	Range		Point
7	-4.365103781118071e-05	-2.9327265540848124e-07	-6.4930921653586126e-06

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	40
1	32	40

end0.0ms

sample908.0ms

Algorithm

intervals

Results

425.0ms	2233×	body	1280	valid
210.0ms	1689×	body	640	valid
71.0ms	2850×	body	80	valid
70.0ms	821×	body	320	valid
22.0ms	407×	body	160	valid

Details

analyze4.0ms

sample31.0ms

simplify34.0ms

prune1.0ms

localize4.0ms

rewrite6.0ms

series257.0ms

simplify115.0ms

prune18.0ms

localize5.0ms

rewrite17.0ms

series819.0ms

simplify86.0ms

prune35.0ms

localize10.0ms

rewrite47.0ms

series2.2s

simplify143.0ms

prune133.0ms

localize16.0ms

rewrite78.0ms

series3.1s

simplify125.0ms

prune222.0ms

regimes18.0ms

bsearch13.0ms

simplify7.0ms

end0.0ms

sample908.0ms

Profiling