Details

sample131.0ms

Algorithm

intervals

Results

48.0ms	108×	body	1280	valid
16.0ms	47×	body	640	valid
11.0ms	144×	body	80	valid
10.0ms	36×	body	10240	exit
10.0ms	24×	body	1280	nan
5.0ms	16×	body	640	nan
5.0ms	147×	body	80	nan
5.0ms	22×	body	320	valid
3.0ms	15×	body	320	nan
2.0ms	15×	body	160	valid
0.0ms	5×	body	160	nan

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	212	13
5	710	13
6	3120	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite49.0ms

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:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series418.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (492.0ms)

Iter	Nodes	Cost
0	149	1026
1	361	965
2	913	927
3	2631	918
done	5000	918

prune176.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
0.0b	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

60×	`unpow-prod-down`
58×	`add-sqr-sqrt`
46×	`cbrt-prod`
34×	`*-un-lft-identity`
27×	`difference-of-squares`
25×	`cube-prod` `sqr-pow`
22×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `div-inv` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 134

Calls

4 calls:

9.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
9.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
100.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series997.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
146.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
338.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify727.0ms

Counts

146 → 146

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	226	3035
1	552	2461
2	1478	2407
done	5000	2395

prune335.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (- (log x)) (pow n 2))
0.8b	(/ 0.5 (* (pow x 2) n))
3.7b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
10.2b	(* (pow x 2) n)

rewrite297.0ms

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:

8.0ms	(/ (- (log x)) (pow n 2))
4.0ms	(/ 0.5 (* (pow x 2) n))
267.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
6.0ms	(* (pow x 2) n)

series246.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (log x)) (pow n 2))
26.0ms	(/ 0.5 (* (pow x 2) n))
127.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
19.0ms	(* (pow x 2) n)

simplify1.8s

Counts

258 → 258

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	405	3726
1	980	3385
2	3600	3025
done	5001	3022

prune703.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (log x) (pow n 2))
0.8b	(/ 0.5 (* (pow x 2) n))
3.7b	(/ (* 1.0 (+ (/ 1 n) (/ (log x) (pow n 2)))) x)
10.2b	(* (pow x 2) n)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

38×	`times-frac`
36×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log`
19×	`unpow-prod-down`
18×	`add-cbrt-cube`
13×	`pow1`
12×	`associate-/r*`
9×	`div-exp` `log-pow`
8×	`associate-l` `associate-/l*`
7×	`prod-exp` `unpow2` `sqr-pow`
5×	`cbrt-undiv`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `frac-2neg` `associate-r/` `associate-r*` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`flip3-+` `frac-add` `*-commutative` `flip-+`

Counts

4 → 132

Calls

4 calls:

4.0ms	(/ (log x) (pow n 2))
4.0ms	(/ 0.5 (* (pow x 2) n))
32.0ms	(/ (* 1.0 (+ (/ 1 n) (/ (log x) (pow n 2)))) x)
6.0ms	(* (pow x 2) n)

series177.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (log x) (pow n 2))
22.0ms	(/ 0.5 (* (pow x 2) n))
72.0ms	(/ (* 1.0 (+ (/ 1 n) (/ (log x) (pow n 2)))) x)
21.0ms	(* (pow x 2) n)

simplify929.0ms

Counts

144 → 144

Iterations

Useful iterations: done (926.0ms)

Iter	Nodes	Cost
0	237	1763
1	546	1643
2	2068	1417
done	5000	1416

prune376.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.7b

regimes213.0ms

Accuracy

83.3% (1.5b remaining)

Error of 21.7b against oracle of 20.2b and baseline of 29.2b

bsearch139.0ms

Steps

Iters	Range		Point
10	1.4157702531433464e-05	78655976.23378988	59709498.11104911
4	-22864655.36927869	-12817321.398305086	-14349362.023440707

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	77
1	50	77
done	50	77

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3221×	body	1280	valid
540.0ms	1563×	body	640	valid
472.0ms	1129×	body	10240	exit
286.0ms	637×	body	1280	nan
253.0ms	4648×	body	80	valid
202.0ms	620×	body	640	nan
182.0ms	4911×	body	80	nan
181.0ms	819×	body	320	valid
66.0ms	346×	body	320	nan
61.0ms	443×	body	160	valid
22.0ms	167×	body	160	nan