Details

sample177.0ms

Algorithm

intervals

Results

52.0ms	90×	body	1280	valid
25.0ms	31×	body	10240	exit
18.0ms	43×	body	640	valid
11.0ms	169×	body	80	valid
10.0ms	24×	body	640	nan
9.0ms	16×	body	1280	nan
9.0ms	29×	body	320	valid
9.0ms	170×	body	80	nan
3.0ms	10×	body	320	nan
2.0ms	15×	body	160	valid
1.0ms	6×	body	160	nan

simplify953.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1231
4	238
3	81
2	34
1	17
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite95.0ms

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:

6.0ms	(pow x (/ 1.0 n))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))
71.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series743.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(pow x (/ 1.0 n))
233.0ms	(pow (+ x 1.0) (/ 1.0 n))
431.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2073
1	544
0	189

prune468.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ 1.0 x) (/ 1.0 n))
0.7b	(pow (+ 1.0 x) (/ 1.0 n))
3.4b	(- (* (sqrt (pow (+ 1.0 x) (/ 1.0 n))) (sqrt (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(pow x (/ 1.0 n))
16.0ms	(pow (+ 1.0 x) (/ 1.0 n))
13.0ms	(pow (+ 1.0 x) (/ 1.0 n))
36.0ms	(- (* (sqrt (pow (+ 1.0 x) (/ 1.0 n))) (sqrt (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow x (/ 1.0 n))
202.0ms	(pow (+ 1.0 x) (/ 1.0 n))
183.0ms	(pow (+ 1.0 x) (/ 1.0 n))
779.0ms	(- (* (sqrt (pow (+ 1.0 x) (/ 1.0 n))) (sqrt (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify1.0s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	2103
1	538
0	180

prune632.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* 1.0 (log x)) (* x (* n n)))
2.0b	(+ (/ (/ 1.0 x) n) (/ (* 1.0 (log x)) (* x (* n n))))
9.1b	(* x (* n n))
10.6b	(/ (/ 0.5 n) (* x x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-cbrt-cube` `add-exp-log`
33×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod` `associate-/l*`
12×	`cbrt-undiv` `div-exp`
9×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
3×	`associate-l` `pow-prod-down`
2×	`clear-num` `associate-/r*` `frac-2neg` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `associate-r` `frac-add` `*-commutative` `flip-+` `unswap-sqr` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

19.0ms	(/ (* 1.0 (log x)) (* x (* n n)))
44.0ms	(+ (/ (/ 1.0 x) n) (/ (* 1.0 (log x)) (* x (* n n))))
13.0ms	(* x (* n n))
11.0ms	(/ (/ 0.5 n) (* x x))

series416.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (* 1.0 (log x)) (* x (* n n)))
202.0ms	(+ (/ (/ 1.0 x) n) (/ (* 1.0 (log x)) (* x (* n n))))
35.0ms	(* x (* n n))
32.0ms	(/ (/ 0.5 n) (* x x))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	4916
1	674
0	227

prune566.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (- (log x)) (* x (* n n)))
2.0b	(- (/ (/ 1 n) x) (/ (- (log x)) (* x (* n n))))
9.1b	(* x (* n n))
10.6b	(/ (/ 0.5 n) (* x x))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
38×	`add-sqr-sqrt`
30×	`add-cbrt-cube` `add-exp-log`
28×	`*-un-lft-identity`
25×	`add-cube-cbrt` `associate-/l*`
13×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`log-pow` `div-inv` `difference-of-squares`
3×	`associate-l` `pow-prod-down`
2×	`neg-sub0` `clear-num` `associate-/r*` `neg-mul-1` `frac-2neg` `div-sub`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `distribute-frac-neg` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `associate--r-` `unswap-sqr` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

25.0ms	(/ (- (log x)) (* x (* n n)))
117.0ms	(- (/ (/ 1 n) x) (/ (- (log x)) (* x (* n n))))
34.0ms	(* x (* n n))
22.0ms	(/ (/ 0.5 n) (* x x))

series272.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (- (log x)) (* x (* n n)))
68.0ms	(- (/ (/ 1 n) x) (/ (- (log x)) (* x (* n n))))
52.0ms	(* x (* n n))
38.0ms	(/ (/ 0.5 n) (* x x))

simplify2.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	3984
1	693
0	251

prune852.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.6b

regimes510.0ms

Accuracy

83.2% (1.5b remaining)

Error of 21.9b against oracle of 20.4b and baseline of 29.4b

bsearch315.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	61777.909360781356	61241.106988453445
9	-220115457164908.94	-531429590.62988466	-594192892.165202

simplify3.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.0s	3137×	body	1280	valid
1.3s	1151×	body	10240	exit
1.1s	1624×	body	640	valid
546.0ms	672×	body	1280	nan
541.0ms	5096×	body	80	nan
432.0ms	4706×	body	80	valid
388.0ms	633×	body	640	nan
346.0ms	848×	body	320	valid
147.0ms	441×	body	160	valid
105.0ms	316×	body	320	nan
35.0ms	182×	body	160	nan