Details

sample274.0ms

Algorithm

intervals

Results

105.0ms	109×	body	1280	valid
35.0ms	47×	body	640	valid
23.0ms	28×	body	10240	exit
18.0ms	154×	body	80	valid
16.0ms	22×	body	640	nan
15.0ms	31×	body	320	valid
15.0ms	176×	body	80	nan
11.0ms	16×	body	1280	nan
4.0ms	15×	body	160	valid
4.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify2.3s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite67.0ms

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))
13.0ms	(pow (+ x 1) (/ 1 n))
50.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series417.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(pow x (/ 1 n))
105.0ms	(pow (+ x 1) (/ 1 n))
243.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify3.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5007
3	4337
2	1224
1	473
0	176

prune440.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite212.0ms

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` `insert-posit16` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 104

Calls

4 calls:

7.0ms	(pow (+ x 1) (/ 1 n))
61.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
55.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
86.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series901.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (+ x 1) (/ 1 n))
253.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
265.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
286.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	2507
2	827
1	348
0	136

prune858.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.0b

localize79.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.6b	(log (/ (exp (pow (+ x 1) (/ 1 n))) (exp (pow x (/ 1 n)))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`unpow-prod-down`
19×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
13×	`pow-unpow` `log-prod` `sqr-pow`
8×	`add-log-exp`
6×	`pow1` `exp-prod` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `log-pow` `insert-posit16` `distribute-lft-out`
3×	`pow-div`
2×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `div-inv` `flip--`
1×	`pow-to-exp` `log-div` `pow-pow` `div-exp` `pow-exp`

Counts

4 → 107

Calls

4 calls:

7.0ms	(pow (+ x 1) (/ 1 n))
54.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
80.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
46.0ms	(log (/ (exp (pow (+ x 1) (/ 1 n))) (exp (pow x (/ 1 n)))))

series940.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (+ x 1) (/ 1 n))
230.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
253.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
348.0ms	(log (/ (exp (pow (+ x 1) (/ 1 n))) (exp (pow x (/ 1 n)))))

simplify1.9s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
3	3016
2	1061
1	476
0	201

prune934.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.0b

localize65.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.6b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
31×	`unpow-prod-down`
30×	`*-un-lft-identity` `difference-of-squares`
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` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 105

Calls

4 calls:

13.0ms	(pow (+ x 1) (/ 1 n))
98.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
93.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
55.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

series999.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (+ x 1) (/ 1 n))
258.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
284.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
346.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

simplify2.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5004
3	4701
2	1334
1	504
0	196

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.0b

regimes437.0ms

Accuracy

82.8% (1.5b remaining)

Error of 22.8b against oracle of 21.4b and baseline of 29.9b

bsearch159.0ms

Steps

Iters	Range		Point
5	7.43027159421113e+15	23680829915495896.0	7547414330764314.0
3	-3.988943487888535e+21	-3.1098446226995644e+21	-3.1647883017738754e+21

simplify9.0ms

Iterations

Iter	Nodes
done	49
1	49
0	39

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.1s	3267×	body	1280	valid
1.0s	631×	body	1280	nan
942.0ms	1580×	body	640	valid
908.0ms	1141×	body	10240	exit
573.0ms	4594×	body	80	valid
457.0ms	686×	body	640	nan
452.0ms	4931×	body	80	nan
321.0ms	838×	body	320	valid
150.0ms	353×	body	320	nan
110.0ms	444×	body	160	valid
35.0ms	182×	body	160	nan