Details

sample160.0ms

Algorithm

intervals

Results

56.0ms	118×	body	1280	valid
26.0ms	50×	body	10240	exit
17.0ms	50×	body	640	valid
11.0ms	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

simplify32.0ms

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)))

rewrite85.0ms

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:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
74.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series405.0ms

Counts

2 → 6

Calls

2 calls:

142.0ms	(pow (+ x 1.0) (/ 1.0 n))
263.0ms	(- (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

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.9b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
11.0ms	(pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
152.0ms	(- (pow (pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt n)
174.0ms	(cbrt n)
410.0ms	(pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n))))
682.0ms	(- (pow (pow (+ x 1.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

simplify68.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	596	1438
1	2445	1379
2	5001	1375
done	5001	1375

prune335.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.9b

localize21.0ms

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))

rewrite287.0ms

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)))
235.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
14.0ms	(/ (/ 0.5 n) (pow x 2))
11.0ms	(* x (pow n 2))

series212.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
71.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
26.0ms	(/ (/ 0.5 n) (pow x 2))
30.0ms	(* x (pow n 2))

simplify44.0ms

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

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

prune614.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (exp (/ 0.5 (* (pow x 2) n))))
2.3b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* 1.0 (log x)) (* x (pow n 2)))))
10.4b	(* (pow x 2) n)
10.9b	(* x (pow n 2))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt`
11×	`associate-r` `associate-l`
9×	`log-pow`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
7×	`exp-prod`
6×	`pow1` `log-prod` `times-frac` `prod-exp`
5×	`associate--r+` `distribute-lft-out--`
4×	`unpow2` `sqr-pow`
3×	`diff-log` `associate--l+` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`
1×	`rem-log-exp` `div-inv` `associate--r-`

Counts

4 → 100

Calls

4 calls:

12.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
182.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* 1.0 (log x)) (* x (pow n 2)))))
15.0ms	(* (pow x 2) n)
12.0ms	(* x (pow n 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
67.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* 1.0 (log x)) (* x (pow n 2)))))
22.0ms	(* (pow x 2) n)
30.0ms	(* x (pow n 2))

simplify78.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	514	973
1	2274	880
2	5001	868
done	5001	868

prune348.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

regimes149.0ms

Accuracy

78.8% (1.8b remaining)

Error of 22.6b against oracle of 20.7b and baseline of 29.4b

bsearch293.0ms

Steps

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

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	46
1	59	46
done	59	46

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	3183×	body	1280	valid
510.0ms	1514×	body	640	valid
506.0ms	1188×	body	10240	exit
286.0ms	620×	body	1280	nan
256.0ms	4681×	body	80	valid
214.0ms	655×	body	640	nan
202.0ms	914×	body	320	valid
178.0ms	4913×	body	80	nan
68.0ms	360×	body	320	nan
60.0ms	435×	body	160	valid
22.0ms	194×	body	160	nan