Details

sample123.0ms

Algorithm

intervals

Results

42.0ms	100×	body	1280	valid
14.0ms	42×	body	640	valid
11.0ms	23×	body	10240	exit
8.0ms	166×	body	80	valid
8.0ms	16×	body	1280	nan
6.0ms	19×	body	640	nan
6.0ms	152×	body	80	nan
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	8×	body	320	nan
0.0ms	4×	body	160	nan

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: 26.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite92.0ms

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))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series467.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
267.0ms	(- (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

prune245.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ (/ 1.0 n) 2))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`add-sqr-sqrt`
69×	`pow-unpow`
62×	`*-un-lft-identity`
56×	`add-cube-cbrt`
18×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`sqr-pow`
9×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`div-inv` `add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

7.0ms	(pow x (/ (/ 1.0 n) 2))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
79.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow x (/ (/ 1.0 n) 2))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
381.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify60.0ms

Counts

150 → 150

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	762	1154
1	2857	1117
2	5001	1117
done	5001	1117

prune545.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
1.2b	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
2.4b	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
11.0ms	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
149.0ms	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt n)
176.0ms	(cbrt n)
316.0ms	(pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n))))
732.0ms	(- (pow (pow (+ x 1.0) (/ (sqrt 1.0) (* (cbrt n) (cbrt n)))) (/ (sqrt 1.0) (cbrt n))) (pow x (/ 1.0 n)))

simplify70.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	728	1392
1	2935	1332
2	5001	1327
done	5001	1327

prune384.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
3.0b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
9.3b	(* x (pow n 2))
11.2b	(* (pow x 2) n)

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`associate-*r/`
16×	`add-exp-log` `frac-add`
15×	`associate-r` `associate-l`
14×	`flip3-+` `flip-+`
12×	`add-cube-cbrt` `distribute-neg-frac`
10×	`frac-times` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`unpow-prod-down` `add-log-exp`
7×	`prod-exp`
6×	`pow1`
4×	`unpow2` `sqr-pow`
3×	`*-commutative` `cbrt-unprod` `distribute-lft-out`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-neg-in` `distribute-lft-in` `associate-*l/` `pow-exp` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-prod-down` `neg-log`

Counts

4 → 112

Calls

4 calls:

27.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
274.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
14.0ms	(* x (pow n 2))
11.0ms	(* (pow x 2) n)

series640.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
500.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
34.0ms	(* x (pow n 2))
19.0ms	(* (pow x 2) n)

simplify43.0ms

Counts

124 → 124

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	947	2401
1	5001	2234
done	5001	2234

prune583.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 19.9b

regimes329.0ms

Accuracy

83.5% (1.4b remaining)

Error of 21.5b against oracle of 20.1b and baseline of 28.8b

bsearch210.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	101.51334682654779	100.33463595681178
8	-2051876093.7044864	-1785161.1935403114	-7365720.817789774

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	67
1	82	67
2	88	67
3	88	67
done	88	67

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3166×	body	1280	valid
552.0ms	1599×	body	640	valid
423.0ms	1091×	body	10240	exit
297.0ms	639×	body	1280	nan
244.0ms	4738×	body	80	valid
214.0ms	655×	body	640	nan
183.0ms	5055×	body	80	nan
180.0ms	830×	body	320	valid
66.0ms	457×	body	160	valid
57.0ms	314×	body	320	nan
19.0ms	180×	body	160	nan