Details

sample327.0ms

Algorithm

intervals

Results

96.0ms	103×	body	1280	valid
52.0ms	136×	body	80	valid
40.0ms	32×	body	10240	exit
35.0ms	51×	body	640	valid
21.0ms	24×	body	1280	nan
19.0ms	30×	body	640	nan
16.0ms	156×	body	80	nan
16.0ms	37×	body	320	valid
4.0ms	12×	body	320	nan
3.0ms	9×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2068
6	2068
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: 27.2b

localize22.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite75.0ms

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))
12.0ms	(pow (+ x 1) (/ 1 n))
57.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series408.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(pow x (/ 1 n))
89.0ms	(pow (+ x 1) (/ 1 n))
231.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
3	2003
2	1224
1	473
0	176

prune954.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.4b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.4b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite219.0ms

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:

3.0ms	(pow x (/ 1 n))
8.0ms	(pow (+ x 1) (/ 1 n))
56.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
151.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow x (/ 1 n))
130.0ms	(pow (+ x 1) (/ 1 n))
285.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
275.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

simplify1.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	2012
3	2012
2	1386
1	551
0	222

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (+ x 1) (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
3.6b	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

10.0ms	(pow (+ x 1) (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
112.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (+ x 1) (/ 1 n))
111.0ms	(pow (+ x 1) (/ 1 n))
115.0ms	(pow (+ x 1) (/ 1 n))
238.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

simplify1.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	2011
3	2011
2	810
1	318
0	117

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.3b

localize68.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (cbrt (+ x 1)) (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
3.8b	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (* (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n))))) (pow x (/ 1 n)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
35×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
15×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`cbrt-prod` `pow-pow` `add-cbrt-cube` `insert-posit16`
3×	`pow-to-exp` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`

Counts

4 → 104

Calls

4 calls:

7.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
198.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (* (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n))))) (pow x (/ 1 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
142.0ms	(pow (+ x 1) (/ 1 n))
114.0ms	(pow (+ x 1) (/ 1 n))
698.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (* (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n))))) (pow x (/ 1 n)))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2001
2	2001
1	668
0	230

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.2b

regimes485.0ms

Accuracy

82.3% (1.5b remaining)

Error of 21.8b against oracle of 20.3b and baseline of 28.9b

bsearch378.0ms

Steps

Iters	Range		Point
8	0.00249723671336719	0.9376093183107279	0.9292141684675859
9	-6472449387759.926	-7016528.6044858415	-29869477.165418986

simplify24.0ms

Iterations

Iter	Nodes
done	49
1	49
0	36

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.3s	3133×	body	1280	valid
1.3s	1119×	body	10240	exit
1.2s	1597×	body	640	valid
1.1s	4634×	body	80	valid
892.0ms	633×	body	640	nan
674.0ms	660×	body	1280	nan
610.0ms	886×	body	320	valid
603.0ms	4942×	body	80	nan
162.0ms	346×	body	320	nan
134.0ms	442×	body	160	valid
55.0ms	183×	body	160	nan