Details

sample149.0ms

Algorithm

intervals

Results

47.0ms	104×	body	1280	valid
22.0ms	34×	body	10240	exit
16.0ms	47×	body	640	valid
11.0ms	19×	body	1280	nan
8.0ms	153×	body	80	valid
8.0ms	139×	body	80	nan
6.0ms	28×	body	320	valid
4.0ms	17×	body	640	nan
3.0ms	18×	body	320	nan
2.0ms	16×	body	160	valid
1.0ms	7×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize9.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite97.0ms

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` `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 → 79

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
78.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series494.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609
done	5001	609

prune246.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

73.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
77.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series781.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
64.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify59.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	686	1271
1	2625	1268
2	5001	1266
done	5001	1266

prune380.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.8b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.9b	(/ (/ 0.5 n) (pow x 2))
9.4b	(* x (pow n 2))

rewrite291.0ms

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:

15.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
239.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
14.0ms	(/ (/ 0.5 n) (pow x 2))
12.0ms	(* x (pow n 2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
75.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
27.0ms	(/ (/ 0.5 n) (pow x 2))
31.0ms	(* x (pow n 2))

simplify44.0ms

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1857
done	5001	1857

prune646.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (exp (/ 0.5 (* (pow x 2) n))))
2.8b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.7b	(* (pow x 2) n)
9.4b	(* x (pow n 2))

rewrite230.0ms

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:

13.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
187.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
15.0ms	(* (pow x 2) n)
12.0ms	(* x (pow n 2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
72.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
25.0ms	(* (pow x 2) n)
33.0ms	(* x (pow n 2))

simplify72.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	514	973
1	2276	880
2	5001	868
done	5001	868

prune369.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 19.7b

regimes352.0ms

Accuracy

78% (1.9b remaining)

Error of 22.3b against oracle of 20.3b and baseline of 29.1b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26
done	41	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3205×	body	1280	valid
539.0ms	1587×	body	640	valid
427.0ms	1158×	body	10240	exit
282.0ms	635×	body	1280	nan
250.0ms	4609×	body	80	valid
209.0ms	660×	body	640	nan
189.0ms	4864×	body	80	nan
187.0ms	845×	body	320	valid
68.0ms	359×	body	320	nan
61.0ms	421×	body	160	valid
22.0ms	199×	body	160	nan