Details

sample314.0ms

Algorithm

intervals

Results

102.0ms	113×	body	1280	valid
48.0ms	161×	body	80	valid
40.0ms	37×	body	10240	exit
32.0ms	49×	body	640	valid
20.0ms	28×	body	1280	nan
15.0ms	157×	body	80	nan
14.0ms	19×	body	640	nan
11.0ms	27×	body	320	valid
4.0ms	13×	body	160	valid
3.0ms	7×	body	320	nan
1.0ms	5×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	2506
5	667
4	220
3	84
2	36
1	19
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize25.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1 n))
1.7b	(pow (+ x 1) (/ 1 n))
2.0b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 82

Calls

3 calls:

5.0ms	(pow x (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
85.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series512.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(pow x (/ 1 n))
137.0ms	(pow (+ x 1) (/ 1 n))
293.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.1s

Counts

91 → 91

Iterations

Iter	Nodes
3	3497
2	1130
1	460
0	176

prune942.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.4b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ (/ 1 n) 2))
1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
129×	`pow-unpow`
124×	`add-sqr-sqrt`
123×	`*-un-lft-identity`
112×	`add-cube-cbrt`
21×	`unpow-prod-down`
12×	`div-inv`
9×	`difference-of-squares` `sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 201

Calls

4 calls:

4.0ms	(pow x (/ (/ 1 n) 2))
13.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
15.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
57.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow x (/ (/ 1 n) 2))
139.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
115.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
267.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

simplify1.3s

Counts

213 → 213

Iterations

Iter	Nodes
2	2198
1	843
0	285

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize77.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
66×	`times-frac`
63×	`*-un-lft-identity`
43×	`pow-unpow`
40×	`add-cube-cbrt`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
10×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `div-inv` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp`

Counts

4 → 134

Calls

4 calls:

8.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
49.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
63.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
99.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
238.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
297.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
281.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

simplify4.0s

Counts

146 → 146

Iterations

Iter	Nodes
3	5042
2	1639
1	627
0	215

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize116.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
2.6b	(- (sqrt (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ (/ (/ 1 n) 2) 2)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
66×	`times-frac`
58×	`*-un-lft-identity`
43×	`pow-unpow`
40×	`add-cube-cbrt`
31×	`unpow-prod-down`
30×	`difference-of-squares`
20×	`sqr-pow`
10×	`add-log-exp`
9×	`sqrt-prod`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `div-inv`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp`

Counts

4 → 135

Calls

4 calls:

8.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
60.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
55.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
96.0ms	(- (sqrt (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ (/ (/ 1 n) 2) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

125.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
301.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
322.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
342.0ms	(- (sqrt (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ (/ (/ 1 n) 2) 2)))

simplify4.6s

Counts

147 → 147

Iterations

Iter	Nodes
3	5910
2	1910
1	779
0	276

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

regimes397.0ms

Accuracy

85.6% (1.3b remaining)

Error of 21.8b against oracle of 20.5b and baseline of 29.3b

bsearch313.0ms

Steps

Iters	Range		Point
6	6143511848.122867	97383972881.30028	7615007254.767728
11	-41824574.29247571	-2.6799709080204617e-24	-21135787.307639804

simplify14.0ms

Iterations

Iter	Nodes
2	43
1	43
0	31

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.8s	3197×	body	1280	valid
1.4s	1583×	body	640	valid
1.3s	1168×	body	10240	exit
1.1s	4642×	body	80	valid
729.0ms	652×	body	1280	nan
584.0ms	5062×	body	80	nan
571.0ms	666×	body	640	nan
506.0ms	883×	body	320	valid
174.0ms	371×	body	320	nan
164.0ms	428×	body	160	valid
79.0ms	170×	body	160	nan