Details

sample158.0ms

Algorithm

intervals

Results

56.0ms	118×	body	1280	valid
26.0ms	50×	body	10240	exit
17.0ms	50×	body	640	valid
8.0ms	149×	body	80	valid
8.0ms	25×	body	640	nan
6.0ms	157×	body	80	nan
5.0ms	28×	body	320	valid
5.0ms	12×	body	1280	nan
2.0ms	12×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
14×	`unpow-prod-down`
13×	`pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
86.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series412.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify34.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	359	490
1	1141	475
2	5002	466
done	5002	466

prune163.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
1.1b	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
1.6b	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`unpow-prod-down`
15×	`difference-of-squares`
14×	`*-un-lft-identity`
12×	`sqr-pow`
10×	`add-cube-cbrt` `pow-unpow`
6×	`cbrt-prod` `times-frac` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
14.0ms	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
166.0ms	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt n)
175.0ms	(cbrt n)
323.0ms	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
725.0ms	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

simplify67.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	728	1392
1	2935	1332
2	5001	1327
done	5001	1327

prune355.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 1.0 (log x)) (* x (pow n 2)))
2.3b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
10.4b	(/ (/ 0.5 n) (pow x 2))
10.9b	(* x (pow n 2))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

17.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
268.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
15.0ms	(/ (/ 0.5 n) (pow x 2))
12.0ms	(* x (pow n 2))

series208.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
65.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
30.0ms	(/ (/ 0.5 n) (pow x 2))
30.0ms	(* x (pow n 2))

simplify43.0ms

Counts

232 → 232

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1111	2050
1	5001	1858
done	5001	1858

prune591.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 1.0 (log x)) (* x (pow n 2)))
2.3b	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
10.4b	(/ (/ 0.5 n) (pow x 2))
10.9b	(* x (pow n 2))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

265×	`times-frac`
211×	`add-sqr-sqrt`
119×	`*-un-lft-identity`
100×	`add-cube-cbrt`
52×	`unpow-prod-down`
46×	`add-exp-log`
27×	`difference-of-squares`
23×	`add-cbrt-cube` `unpow2`
22×	`sqr-pow`
17×	`div-exp`
14×	`associate-/l*`
13×	`prod-exp` `div-inv`
9×	`associate-/r*`
8×	`associate-r`
7×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`pow1` `unswap-sqr`
3×	`associate-l`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `*-commutative` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 242

Calls

4 calls:

18.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
221.0ms	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
15.0ms	(/ (/ 0.5 n) (pow x 2))
17.0ms	(* x (pow n 2))

series224.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
76.0ms	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
29.0ms	(/ (/ 0.5 n) (pow x 2))
35.0ms	(* x (pow n 2))

simplify114.0ms

Counts

254 → 254

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1081	2200
1	4917	1971
2	5001	1971
done	5001	1971

prune648.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.8b

regimes164.0ms

Accuracy

80.3% (1.7b remaining)

Error of 22.4b against oracle of 20.7b and baseline of 29.4b

bsearch281.0ms

Steps

Iters	Range		Point
11	2.142008608447194e-19	60.065953071798994	59.53547333114815
9	-1.3392188720065574e+27	-9.230054167364397e+20	-9.348333424414554e+20

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	53
1	57	53
2	57	53
done	57	53

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3183×	body	1280	valid
513.0ms	1514×	body	640	valid
507.0ms	1188×	body	10240	exit
281.0ms	620×	body	1280	nan
238.0ms	4681×	body	80	valid
203.0ms	655×	body	640	nan
200.0ms	914×	body	320	valid
178.0ms	4913×	body	80	nan
66.0ms	360×	body	320	nan
59.0ms	435×	body	160	valid
22.0ms	194×	body	160	nan