Details

sample222.0ms

Algorithm

intervals

Results

62.0ms	116×	body	1280	valid
31.0ms	63×	body	640	valid
30.0ms	29×	body	1280	nan
19.0ms	30×	body	640	nan
17.0ms	122×	body	80	overflowed
9.0ms	97×	body	80	valid
8.0ms	169×	body	80	nan
7.0ms	21×	body	320	valid
4.0ms	10×	body	320	nan
3.0ms	15×	body	160	valid
1.0ms	6×	body	160	nan

simplify1.2s

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	216	13
5	737	13
6	3385	13
done	5000	13

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.8b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

11.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify748.0ms

Counts

27 → 27

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	117	719
1	283	686
2	826	646
3	2772	642
done	5000	640

prune77.0ms

Filtered

23 candidates to 27 candidates (-17.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 25.0b

Counts

28 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 0.5 (* (pow x 2) n))
0.7b	(/ (neg (log x)) (pow n 2))
2.8b	(* (/ 1.0 x) (- (/ 1 n) (/ (neg (log x)) (pow n 2))))
9.9b	(* (pow x 2) n)

rewrite112.0ms

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:

6.0ms	(/ 0.5 (* (pow x 2) n))
9.0ms	(/ (neg (log x)) (pow n 2))
79.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (neg (log x)) (pow n 2))))
6.0ms	(* (pow x 2) n)

series55.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.5 (* (pow x 2) n))
15.0ms	(/ (neg (log x)) (pow n 2))
32.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (neg (log x)) (pow n 2))))
4.0ms	(* (pow x 2) n)

simplify878.0ms

Counts

258 → 258

Iterations

Useful iterations: done (871.0ms)

Iter	Nodes	Cost
0	413	3756
1	1020	3447
2	4193	2998
done	5000	2980

prune415.0ms

Filtered

165 candidates to 258 candidates (-56.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	251	7	258
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	252	8	260

Merged error: 24.8b

Counts

260 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 0.5 (* (pow x 2) n))
0.7b	(/ (log x) (* n n))
2.8b	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
9.9b	(* (pow x 2) n)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-exp-log`
22×	`times-frac`
21×	`add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`associate-/l*`
8×	`associate-l` `distribute-lft-out`
7×	`div-exp` `prod-exp` `div-inv`
6×	`pow1`
5×	`cbrt-undiv` `associate-/r*`
4×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
3×	`frac-2neg` `associate-r` `clear-num` `cbrt-unprod` `associate-/l/`
2×	`pow-to-exp` `pow-exp` `log-pow` `unpow2` `sqr-pow`
1×	`flip3-+` `frac-add` `*-commutative` `flip-+`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ 0.5 (* (pow x 2) n))
6.0ms	(/ (log x) (* n n))
16.0ms	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
8.0ms	(* (pow x 2) n)

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.5 (* (pow x 2) n))
13.0ms	(/ (log x) (* n n))
22.0ms	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
4.0ms	(* (pow x 2) n)

simplify538.0ms

Counts

123 → 123

Iterations

Useful iterations: done (535.0ms)

Iter	Nodes	Cost
0	192	1541
1	448	1486
2	1647	1329
done	5001	1297

prune185.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	122	9	131

Merged error: 24.8b

Counts

131 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (* 1.0 (/ (+ (/ (log x) (* n n)) (/ 1 n)) x)) (/ 0.5 (log (exp (* (pow x 2) n)))))
2.4b	(log (exp (* (pow x 2) n)))
2.8b	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
9.9b	(* (pow x 2) n)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
11×	`add-exp-log`
8×	`associate-l` `add-cbrt-cube` `distribute-lft-out`
7×	`add-log-exp`
5×	`pow1` `div-inv` `associate-/l*`
4×	`unpow-prod-down` `unswap-sqr`
3×	`log-prod` `associate-r` `prod-exp` `associate-/r*` `log-pow` `associate-/l/`
2×	`unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `frac-2neg` `flip3-+` `diff-log` `associate-r/` `div-exp` `rem-log-exp` `frac-add` `pow-exp` `clear-num` `-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+`

Counts

4 → 92

Calls

4 calls:

20.0ms	(- (* 1.0 (/ (+ (/ (log x) (* n n)) (/ 1 n)) x)) (/ 0.5 (log (exp (* (pow x 2) n)))))
2.0ms	(log (exp (* (pow x 2) n)))
17.0ms	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
6.0ms	(* (pow x 2) n)

series54.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (* 1.0 (/ (+ (/ (log x) (* n n)) (/ 1 n)) x)) (/ 0.5 (log (exp (* (pow x 2) n)))))
4.0ms	(log (exp (* (pow x 2) n)))
26.0ms	(/ (+ (/ (log x) (* n n)) (/ 1 n)) x)
4.0ms	(* (pow x 2) n)

simplify473.0ms

Counts

104 → 104

Iterations

Useful iterations: done (470.0ms)

Iter	Nodes	Cost
0	189	1816
1	470	1683
2	1596	1504
done	5000	1490

prune184.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	98	15	113

Merged error: 24.8b

Counts

113 → 15

regimes442.0ms

Accuracy

80.8% (2.1b remaining)

Error of 24.0b against oracle of 21.9b and baseline of 32.7b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	66
1	41	54
done	41	54

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.0s	3937×	body	1280	valid
1.3s	1072×	body	1280	nan
840.0ms	1767×	body	640	valid
592.0ms	888×	body	640	nan
582.0ms	3907×	body	80	overflowed
301.0ms	3002×	body	80	valid
292.0ms	5963×	body	80	nan
266.0ms	873×	body	320	valid
192.0ms	446×	body	320	nan
80.0ms	419×	body	160	valid
40.0ms	187×	body	160	nan

Details

sample222.0ms

simplify1.2s

prune3.0ms

localize8.0ms

rewrite12.0ms

series49.0ms

simplify748.0ms

prune77.0ms

localize17.0ms

rewrite112.0ms

series55.0ms

simplify878.0ms

prune415.0ms

localize16.0ms

rewrite41.0ms

series43.0ms

simplify538.0ms

prune185.0ms

localize20.0ms

rewrite48.0ms

series54.0ms

simplify473.0ms

prune184.0ms

regimes442.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample7.3s

Profiling