Details

sample177.0ms

Algorithm

intervals

Results

60.0ms	111×	body	1280	valid
26.0ms	67×	body	640	valid
14.0ms	42×	body	10240	exit
10.0ms	141×	body	80	valid
10.0ms	179×	body	80	nan
9.0ms	20×	body	1280	nan
6.0ms	17×	body	640	nan
6.0ms	23×	body	320	valid
4.0ms	27×	body	160	valid
3.0ms	13×	body	320	nan
0.0ms	3×	body	160	nan

simplify3.7s

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: 34.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite108.0ms

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))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
89.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series650.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(pow x (/ 1.0 n))
189.0ms	(pow (+ x 1.0) (/ 1.0 n))
361.0ms	(- (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

prune415.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite405.0ms

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:

22.0ms	(pow (+ x 1.0) (/ 1.0 n))
126.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
118.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
131.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

214.0ms	(pow (+ x 1.0) (/ 1.0 n))
475.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
382.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
446.0ms	(- (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

prune630.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize23.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite642.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
34×	`*-un-lft-identity`
24×	`sqr-pow`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 102

Calls

4 calls:

263.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
124.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
107.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
144.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.7s

Counts

4 → 12

Calls

4 calls:

413.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
417.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
461.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
431.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	141	2650
1	290	2494
2	664	2344
3	1846	2320
done	5001	2304

prune735.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize39.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite746.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
34×	`*-un-lft-identity`
24×	`sqr-pow`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 102

Calls

4 calls:

308.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
132.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
160.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
137.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.6s

Counts

4 → 12

Calls

4 calls:

424.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
427.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
377.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
401.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

114 → 114

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	141	2650
1	290	2494
2	664	2344
3	1846	2320
done	5001	2304

prune915.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

regimes193.0ms

Accuracy

82.1% (1.6b remaining)

Error of 22.4b against oracle of 20.7b and baseline of 29.9b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	38	139
1	49	88
done	49	88

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.6s	3179×	body	1280	valid
1.5s	1691×	body	640	valid
1.0s	1200×	body	10240	exit
689.0ms	842×	body	320	valid
608.0ms	667×	body	1280	nan
555.0ms	4649×	body	80	valid
402.0ms	5048×	body	80	nan
341.0ms	602×	body	640	nan
120.0ms	362×	body	320	nan
105.0ms	455×	body	160	valid
36.0ms	196×	body	160	nan