Details

sample193.0ms

Algorithm

intervals

Results

70.0ms	107×	body	1280	valid
20.0ms	43×	body	640	valid
20.0ms	36×	body	10240	exit
16.0ms	26×	body	1280	nan
12.0ms	166×	body	80	valid
10.0ms	21×	body	640	nan
8.0ms	157×	body	80	nan
7.0ms	26×	body	320	valid
4.0ms	12×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	7×	body	160	nan

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
6	2902
5	690
4	225
3	81
2	34
1	17
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(pow x (/ 1.0 n))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite118.0ms

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:

15.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow x (/ 1.0 n))
94.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series617.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(pow (+ x 1.0) (/ 1.0 n))
68.0ms	(pow x (/ 1.0 n))
386.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	4858
2	1379
1	520
0	189

prune532.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
0.7b	(pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

4.0ms	(cbrt (/ 1.0 n))
3.0ms	(cbrt (/ 1.0 n))
3.0ms	(pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
99.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt (/ 1.0 n))
269.0ms	(cbrt (/ 1.0 n))
268.0ms	(pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
725.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))))

simplify2.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5030
3	3779
2	1110
1	445
0	204

prune699.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
33×	`unpow-prod-down` `*-un-lft-identity`
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`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
73.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
115.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

93.0ms	(pow x (/ 1.0 n))
360.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
407.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
355.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5007
3	4060
2	1162
1	429
0	162

prune937.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize121.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.3b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
30×	`unpow-prod-down` `difference-of-squares`
28×	`*-un-lft-identity`
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--`
2×	`distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
86.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
81.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
95.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow x (/ 1.0 n))
456.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
391.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
567.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify1.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1636
1	581
0	222

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

regimes375.0ms

Accuracy

85.4% (1.3b remaining)

Error of 21.9b against oracle of 20.6b and baseline of 29.6b

bsearch1.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	51
1	51
0	44

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	3156×	body	1280	valid
1.0s	1567×	body	640	valid
833.0ms	4974×	body	80	nan
828.0ms	1154×	body	10240	exit
817.0ms	848×	body	320	valid
556.0ms	597×	body	1280	nan
493.0ms	4664×	body	80	valid
351.0ms	654×	body	640	nan
136.0ms	450×	body	160	valid
129.0ms	385×	body	320	nan
33.0ms	189×	body	160	nan