Details

sample322.0ms

Algorithm

intervals

Results

95.0ms	99×	body	1280	valid
51.0ms	62×	body	640	valid
31.0ms	26×	body	10240	exit
28.0ms	28×	body	1280	nan
24.0ms	23×	body	320	valid
22.0ms	161×	body	80	valid
17.0ms	22×	body	640	nan
17.0ms	153×	body	80	nan
9.0ms	18×	body	320	nan
3.0ms	12×	body	160	valid
1.0ms	2×	body	160	nan

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1169
4	263
3	84
2	36
1	19
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize36.0ms

Local error

Found 3 expressions with local error:

1.2b	(pow x (/ 1 n))
1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0b	(pow (+ x 1) (/ 1 n))

rewrite104.0ms

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` `insert-posit16` `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 → 82

Calls

3 calls:

3.0ms	(pow x (/ 1 n))
82.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
17.0ms	(pow (+ x 1) (/ 1 n))

series452.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(pow x (/ 1 n))
247.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
133.0ms	(pow (+ x 1) (/ 1 n))

simplify2.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	4298
2	1233
1	473
0	176

prune463.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.8b

localize43.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ 1 n))
1.8b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0b	(pow (+ x 1) (/ 1 n))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube` `insert-posit16`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 113

Calls

4 calls:

5.0ms	(pow x (/ 1 n))
157.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
55.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
20.0ms	(pow (+ x 1) (/ 1 n))

series767.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow x (/ 1 n))
290.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
275.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
113.0ms	(pow (+ x 1) (/ 1 n))

simplify3.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	5013
3	4548
2	1360
1	551
0	222

prune750.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.7b

localize51.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0b	(pow (+ x 1) (/ 1 n))
2.0b	(pow (+ x 1) (/ 1 n))
2.0b	(pow (+ x 1) (/ 1 n))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
39×	`pow-unpow`
28×	`add-cube-cbrt`
27×	`times-frac`
22×	`unpow-prod-down`
9×	`difference-of-squares` `sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 112

Calls

4 calls:

85.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))

series575.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
112.0ms	(pow (+ x 1) (/ 1 n))
107.0ms	(pow (+ x 1) (/ 1 n))
112.0ms	(pow (+ x 1) (/ 1 n))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
3	2775
2	867
1	349
0	136

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.7b

localize95.0ms

Local error

Found 4 expressions with local error:

2.0b	(pow (+ x 1) (/ 1 n))
2.0b	(pow (+ x 1) (/ 1 n))
2.0b	(pow (+ x 1) (/ 1 n))
2.0b	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
39×	`pow-unpow`
30×	`sqrt-prod`
28×	`add-cube-cbrt`
27×	`times-frac`
24×	`unpow-prod-down`
16×	`difference-of-squares`
11×	`sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 120

Calls

4 calls:

15.0ms	(pow (+ x 1) (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
16.0ms	(pow (+ x 1) (/ 1 n))
100.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow (+ x 1) (/ 1 n))
124.0ms	(pow (+ x 1) (/ 1 n))
143.0ms	(pow (+ x 1) (/ 1 n))
330.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

simplify2.0s

Counts

132 → 132

Iterations

Iter	Nodes
done	5045
3	3209
2	993
1	382
0	150

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.7b

regimes366.0ms

Accuracy

86.4% (1.2b remaining)

Error of 22.0b against oracle of 20.8b and baseline of 29.5b

bsearch332.0ms

Steps

Iters	Range		Point
9	13.66253041814236	2484744.5477507794	55908.36668550803
6	-93704170.82885565	-8916862.296519369	-48075474.504670314

simplify20.0ms

Iterations

Iter	Nodes
done	47
1	47
0	36

end0.0ms

sample11.1s

Algorithm

intervals

Results

3.4s	3099×	body	1280	valid
1.4s	1627×	body	640	valid
1.3s	1113×	body	10240	exit
1.2s	4806×	body	80	valid
1.1s	4975×	body	80	nan
732.0ms	670×	body	1280	nan
527.0ms	635×	body	640	nan
518.0ms	844×	body	320	valid
206.0ms	359×	body	320	nan
144.0ms	460×	body	160	valid
60.0ms	190×	body	160	nan