Details

sample384.0ms

Algorithm

intervals

Results

115.0ms	99×	body	1280	valid
61.0ms	28×	body	1280	nan
55.0ms	62×	body	640	valid
32.0ms	26×	body	10240	exit
27.0ms	161×	body	80	valid
22.0ms	153×	body	80	nan
19.0ms	22×	body	640	nan
15.0ms	23×	body	320	valid
10.0ms	18×	body	320	nan
5.0ms	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize16.0ms

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))

rewrite131.0ms

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:

4.0ms	(pow x (/ 1 n))
112.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms	(pow (+ x 1) (/ 1 n))

series443.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(pow x (/ 1 n))
239.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
107.0ms	(pow (+ x 1) (/ 1 n))

simplify2.7s

Counts

91 → 91

Iterations

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

prune496.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.8b

localize19.0ms

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))

rewrite416.0ms

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` `add-exp-log`
6×	`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` `rem-log-exp` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `flip--`

Counts

4 → 114

Calls

4 calls:

4.0ms	(pow x (/ 1 n))
229.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
161.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
18.0ms	(pow (+ x 1) (/ 1 n))

series625.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(pow x (/ 1 n))
227.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
225.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
89.0ms	(pow (+ x 1) (/ 1 n))

simplify3.3s

Counts

126 → 126

Iterations

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

prune679.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.7b

localize66.0ms

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))

rewrite182.0ms

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:

140.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
16.0ms	(pow (+ x 1) (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))

series564.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
112.0ms	(pow (+ x 1) (/ 1 n))
134.0ms	(pow (+ x 1) (/ 1 n))
91.0ms	(pow (+ x 1) (/ 1 n))

simplify1.8s

Counts

124 → 124

Iterations

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

prune914.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.7b

localize57.0ms

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))))

rewrite136.0ms

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:

14.0ms	(pow (+ x 1) (/ 1 n))
10.0ms	(pow (+ x 1) (/ 1 n))
10.0ms	(pow (+ x 1) (/ 1 n))
94.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(pow (+ x 1) (/ 1 n))
120.0ms	(pow (+ x 1) (/ 1 n))
105.0ms	(pow (+ x 1) (/ 1 n))
323.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

simplify2.2s

Counts

132 → 132

Iterations

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

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.7b

regimes372.0ms

Accuracy

86.4% (1.2b remaining)

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

bsearch359.0ms

Steps

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

simplify17.0ms

Iterations

Iter	Nodes
done	47
1	47
0	36

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.6s	3099×	body	1280	valid
1.3s	1627×	body	640	valid
1.2s	1113×	body	10240	exit
915.0ms	844×	body	320	valid
786.0ms	670×	body	1280	nan
738.0ms	4806×	body	80	valid
647.0ms	4975×	body	80	nan
555.0ms	635×	body	640	nan
218.0ms	460×	body	160	valid
197.0ms	359×	body	320	nan
53.0ms	190×	body	160	nan