Details

sample363.0ms

Algorithm

intervals

Results

122.0ms	101×	body	1280	valid
40.0ms	39×	body	10240	exit
31.0ms	37×	body	640	valid
29.0ms	11×	body	320	nan
25.0ms	43×	body	320	valid
25.0ms	162×	body	80	valid
22.0ms	18×	body	1280	nan
20.0ms	168×	body	80	nan
15.0ms	20×	body	640	nan
5.0ms	14×	body	160	valid
2.0ms	5×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2681
5	735
4	218
3	82
2	34
1	17
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1) (/ 1 n))
0.0b	(pow x (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite71.0ms

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:

9.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))
57.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series477.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(pow (+ x 1) (/ 1 n))
72.0ms	(pow x (/ 1 n))
308.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.5s

Counts

91 → 91

Iterations

Iter	Nodes
3	3504
2	1179
1	462
0	176

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1 n))
0.0b	(pow x (/ 1 n))
0.0b	(* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))
3.6b	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
54×	`sqrt-prod`
32×	`*-un-lft-identity` `add-cube-cbrt`
27×	`unpow-prod-down`
26×	`pow-unpow`
18×	`times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
13×	`pow1`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
8×	`add-exp-log`
6×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `pow-sqr` `pow-prod-up` `difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 144

Calls

4 calls:

3.0ms	(pow x (/ 1 n))
3.0ms	(pow x (/ 1 n))
16.0ms	(* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))
62.0ms	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow x (/ 1 n))
71.0ms	(pow x (/ 1 n))
73.0ms	(* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))
247.0ms	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))

simplify4.4s

Counts

156 → 156

Iterations

Iter	Nodes
3	3570
2	1141
1	475
0	199

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.4b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow (* x x) (/ (/ 1 n) 2)))
16.3b	(pow (* x x) (/ (/ 1 n) 2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
56×	`pow-unpow`
55×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
12×	`pow1`
11×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
7×	`pow-pow` `add-exp-log`
5×	`div-inv` `add-log-exp`
3×	`add-cbrt-cube` `pow-exp` `insert-posit16`
2×	`pow-to-exp`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 114

Calls

3 calls:

8.0ms	(pow (+ x 1) (/ 1 n))
55.0ms	(- (pow (+ x 1) (/ 1 n)) (pow (* x x) (/ (/ 1 n) 2)))
14.0ms	(pow (* x x) (/ (/ 1 n) 2))

series324.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(pow (+ x 1) (/ 1 n))
178.0ms	(- (pow (+ x 1) (/ 1 n)) (pow (* x x) (/ (/ 1 n) 2)))
52.0ms	(pow (* x x) (/ (/ 1 n) 2))

simplify5.2s

Counts

123 → 123

Iterations

Iter	Nodes
3	5604
2	1884
1	731
0	246

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (log x) n)
0.5b	(/ 1/2 (* (* x x) n))
2.3b	(- (/ (/ 1 n) x) (- (* (/ (/ 1 n) x) (/ (log x) n))))
9.3b	(* (* x x) n)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`times-frac` `add-cbrt-cube` `add-exp-log`
19×	`*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`pow1`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r*` `div-exp` `log-pow` `insert-posit16` `distribute-neg-frac` `difference-of-squares`
3×	`associate-r` `pow-prod-down` `frac-sub`
2×	`clear-num` `frac-2neg` `diff-log` `associate-*l/` `div-inv`
1×	`neg-sub0` `frac-times` `sub-neg` `flip3--` `associate-l` `neg-log` `associate-r/` `-commutative` `flip--` `distribute-lft-out--` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

14.0ms	(/ (log x) n)
28.0ms	(/ 1/2 (* (* x x) n))
37.0ms	(- (/ (/ 1 n) x) (- (* (/ (/ 1 n) x) (/ (log x) n))))
30.0ms	(* (* x x) n)

series231.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (log x) n)
28.0ms	(/ 1/2 (* (* x x) n))
81.0ms	(- (/ (/ 1 n) x) (- (* (/ (/ 1 n) x) (/ (log x) n))))
33.0ms	(* (* x x) n)

simplify12.0s

Counts

112 → 112

Iterations

Iter	Nodes
3	7638
2	1682
1	506
0	203

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

regimes361.0ms

Accuracy

91.1% (1.4b remaining)

Error of 21.7b against oracle of 20.2b and baseline of 36.5b

bsearch254.0ms

Steps

Iters	Range		Point
9	2267696953.837344	7.908444725616567e+17	4227328813.442648
6	-680.9862580031221	-89.78068905705634	-669.2773459285388

simplify14.0ms

Iterations

Iter	Nodes
4	48
3	48
2	45
1	39
0	29

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.2s	3199×	body	1280	valid
1.4s	1180×	body	10240	exit
1.2s	4775×	body	80	valid
1.1s	637×	body	1280	nan
1.1s	1542×	body	640	valid
496.0ms	4878×	body	80	nan
487.0ms	613×	body	640	nan
396.0ms	827×	body	320	valid
173.0ms	333×	body	320	nan
130.0ms	438×	body	160	valid
52.0ms	193×	body	160	nan