Details

sample222.0ms

Algorithm

intervals

Results

79.0ms	109×	body	1280	valid
25.0ms	35×	body	10240	exit
25.0ms	47×	body	640	valid
18.0ms	24×	body	1280	nan
11.0ms	129×	body	80	valid
9.0ms	162×	body	80	nan
8.0ms	17×	body	640	nan
7.0ms	19×	body	320	valid
3.0ms	11×	body	320	nan
3.0ms	14×	body	160	valid
2.0ms	8×	body	160	nan

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	231	13
5	694	13
6	3452	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite159.0ms

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:

7.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
130.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series687.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(pow x (/ 1.0 n))
224.0ms	(pow (+ x 1.0) (/ 1.0 n))
378.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.3s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	190	1337
1	473	1246
2	1191	1206
3	3611	1183
done	5001	1183

prune418.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`cbrt-prod`
13×	`pow-unpow`
12×	`pow1`
9×	`times-frac`
7×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-plus` `diff-log` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

2.0ms	(cbrt x)
15.0ms	(* (cbrt x) (cbrt x))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
101.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt x)
302.0ms	(* (cbrt x) (cbrt x))
226.0ms	(pow (+ x 1.0) (/ 1.0 n))
695.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	233	1518
1	594	1299
2	1817	1212
done	5000	1195

prune571.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (cbrt x))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

5.0ms	(cbrt (* (cbrt x) (cbrt x)))
1.0ms	(cbrt (cbrt x))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
111.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series1.8s

Counts

4 → 12

Calls

4 calls:

506.0ms	(cbrt (* (cbrt x) (cbrt x)))
455.0ms	(cbrt (cbrt x))
215.0ms	(pow (+ x 1.0) (/ 1.0 n))
654.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify1.1s

Counts

75 → 75

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	235	1488
1	607	1324
2	1774	1215
done	5001	1200

prune576.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (log x)) (pow n 2))
0.6b	(/ 0.5 (* (pow x 2) n))
1.6b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
7.8b	(* (pow x 2) n)

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

137×	`times-frac`
122×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
70×	`add-cube-cbrt`
46×	`unpow-prod-down`
38×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
29×	`add-exp-log`
26×	`associate-r`
25×	`pow1`
21×	`associate-l`
19×	`log-pow`
18×	`add-cbrt-cube` `unpow2` `sqr-pow`
15×	`associate-/l*` `difference-of-squares`
9×	`neg-mul-1` `associate-/r*`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
5×	`distribute-lft-out--`
4×	`cbrt-undiv` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`neg-sub0` `distribute-rgt-in` `frac-times` `pow-to-exp` `distribute-lft-in` `div-sub` `associate-*r/` `pow-exp`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`distribute-frac-neg` `pow-prod-down` `associate-*l/`

Counts

4 → 246

Calls

4 calls:

28.0ms	(/ (- (log x)) (pow n 2))
19.0ms	(/ 0.5 (* (pow x 2) n))
520.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
12.0ms	(* (pow x 2) n)

series442.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- (log x)) (pow n 2))
53.0ms	(/ 0.5 (* (pow x 2) n))
217.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
35.0ms	(* (pow x 2) n)

simplify2.1s

Counts

258 → 258

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	405	3726
1	957	3385
2	2879	2963
done	5000	2961

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.1b

regimes430.0ms

Accuracy

80.7% (1.7b remaining)

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

bsearch348.0ms

Steps

Iters	Range		Point
8	5.803242851779569e-05	0.9435061171835805	0.9298484945110257
5	-873354922362061.5	-351616126183326.2	-380251775535541.94

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	44	120
1	56	81
done	56	81

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.1s	3122×	body	1280	valid
1.2s	702×	body	1280	nan
1.0s	1620×	body	640	valid
969.0ms	1180×	body	10240	exit
542.0ms	4668×	body	80	valid
445.0ms	661×	body	640	nan
354.0ms	834×	body	320	valid
336.0ms	5103×	body	80	nan
164.0ms	357×	body	320	nan
115.0ms	465×	body	160	valid
36.0ms	179×	body	160	nan