Details

sample156.0ms

Algorithm

intervals

Results

52.0ms	115×	body	1280	valid
19.0ms	36×	body	10240	exit
18.0ms	53×	body	640	valid
13.0ms	23×	body	1280	nan
9.0ms	151×	body	80	valid
7.0ms	210×	body	80	nan
7.0ms	20×	body	640	nan
5.0ms	22×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	13×	body	160	nan
1.0ms	9×	body	160	valid

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: 31.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite94.0ms

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))
78.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series481.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify43.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune237.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
110.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (+ x 1.0) (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify39.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	332	872
1	1120	760
2	5002	718
done	5002	718

prune367.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (log x) (/ 1.0 n)))
0.3b	(* (log x) (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
1.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
13×	`pow-unpow` `associate-r`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`add-log-exp`
5×	`unpow-prod-down`
4×	`associate-l`
3×	`difference-of-squares`
2×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `pow-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `log-pow` `-commutative` `flip--` `rem-exp-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

3.0ms	(exp (* (log x) (/ 1.0 n)))
14.0ms	(* (log x) (/ 1.0 n))
73.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series560.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (* (log x) (/ 1.0 n)))
58.0ms	(* (log x) (/ 1.0 n))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify56.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	534	693
1	2241	647
2	5001	645
done	5001	645

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 21.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* 1.0 (log x)) (* x (pow n 2)))
2.0b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
10.5b	(/ (/ 0.5 n) (pow x 2))
10.9b	(* x (pow n 2))

rewrite293.0ms

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	(/ (* 1.0 (log x)) (* x (pow n 2)))
238.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* 1.0 (log x)) (* x (pow n 2)))))
17.0ms	(/ (/ 0.5 n) (pow x 2))
12.0ms	(* x (pow n 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
72.0ms	(- (/ (/ 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))
34.0ms	(* x (pow n 2))

simplify52.0ms

Counts

232 → 232

Iterations

Useful iterations: 1 (26.0ms)

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

prune593.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.7b

regimes225.0ms

Accuracy

78.8% (1.8b remaining)

Error of 22.7b against oracle of 20.9b and baseline of 29.4b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	33
1	40	33
done	40	33

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3162×	body	1280	valid
521.0ms	1550×	body	640	valid
446.0ms	1100×	body	10240	exit
276.0ms	611×	body	1280	nan
247.0ms	4773×	body	80	valid
222.0ms	696×	body	640	nan
188.0ms	835×	body	320	valid
179.0ms	5097×	body	80	nan
71.0ms	358×	body	320	nan
61.0ms	461×	body	160	valid
22.0ms	197×	body	160	nan