Details

sample278.0ms

Algorithm

intervals

Results

93.0ms	117×	body	1280	valid
45.0ms	36×	body	10240	exit
29.0ms	46×	body	640	valid
18.0ms	33×	body	640	nan
18.0ms	25×	body	1280	nan
13.0ms	143×	body	80	valid
12.0ms	175×	body	80	nan
9.0ms	23×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	8×	body	320	nan
1.0ms	6×	body	160	nan

simplify3.3s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite121.0ms

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))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
91.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series659.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(pow x (/ 1.0 n))
207.0ms	(pow (+ x 1.0) (/ 1.0 n))
364.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.2s)

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

prune370.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

21.0ms	(pow (+ x 1.0) (/ 1.0 n))
121.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
117.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
102.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

223.0ms	(pow (+ x 1.0) (/ 1.0 n))
384.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
423.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
360.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	149	2370
1	358	2257
2	892	2151
3	2475	2130
done	5001	2114

prune669.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
31×	`unpow-prod-down`
30×	`*-un-lft-identity` `difference-of-squares`
20×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `sqrt-prod`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 101

Calls

4 calls:

12.0ms	(pow (+ x 1.0) (/ 1.0 n))
129.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
105.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
112.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

192.0ms	(pow (+ x 1.0) (/ 1.0 n))
440.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
454.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
600.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify2.9s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	209	2570
1	499	2421
2	1286	2311
3	3889	2291
done	5000	2291

prune938.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite449.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
45×	`difference-of-squares`
31×	`unpow-prod-down`
27×	`sqrt-prod` `sqr-pow`
17×	`*-un-lft-identity`
12×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`
1×	`distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

109.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
110.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
107.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
119.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

442.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
550.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
608.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
608.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify2.4s

Counts

111 → 111

Iterations

Useful iterations: 3 (842.0ms)

Iter	Nodes	Cost
0	155	3288
1	364	3076
2	946	2928
3	3162	2907
done	5000	2907

prune960.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

regimes389.0ms

Accuracy

79% (1.7b remaining)

Error of 23.0b against oracle of 21.3b and baseline of 29.5b

bsearch1.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	251
1	73	251
done	73	251

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.5s	3089×	body	1280	valid
1.4s	1088×	body	10240	exit
1.1s	1629×	body	640	valid
886.0ms	4736×	body	80	valid
594.0ms	667×	body	1280	nan
512.0ms	909×	body	320	valid
427.0ms	665×	body	640	nan
318.0ms	4913×	body	80	nan
115.0ms	360×	body	320	nan
96.0ms	433×	body	160	valid
40.0ms	186×	body	160	nan