Details

sample294.0ms

Algorithm

intervals

Results

92.0ms	102×	body	1280	valid
49.0ms	45×	body	10240	exit
40.0ms	55×	body	640	valid
23.0ms	19×	body	1280	nan
17.0ms	144×	body	80	valid
15.0ms	183×	body	80	nan
14.0ms	24×	body	640	nan
13.0ms	29×	body	320	valid
5.0ms	11×	body	320	nan
4.0ms	13×	body	160	valid
1.0ms	4×	body	160	nan

simplify2.2s

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: 31.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite126.0ms

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:

7.0ms	(pow x (/ 1 n))
17.0ms	(pow (+ x 1) (/ 1 n))
98.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series507.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(pow x (/ 1 n))
140.0ms	(pow (+ x 1) (/ 1 n))
289.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.6s

Counts

91 → 91

Iterations

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

prune495.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite328.0ms

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:

10.0ms	(pow (+ x 1) (/ 1 n))
119.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
84.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
112.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series895.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow (+ x 1) (/ 1 n))
239.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
284.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
273.0ms	(- (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

prune933.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.0b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

rewrite331.0ms

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:

11.0ms	(pow (+ x 1) (/ 1 n))
106.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
109.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
102.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

127.0ms	(pow (+ x 1) (/ 1 n))
272.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
267.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
372.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))

simplify2.5s

Counts

117 → 117

Iterations

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

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.0b

localize143.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b	(- (sqrt (sqrt (pow (+ x 1) (/ 1 n)))) (pow x (/ (/ (/ 1 n) 2) 2)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
33×	`difference-of-squares`
32×	`unpow-prod-down`
30×	`*-un-lft-identity`
21×	`sqrt-prod` `sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
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 → 108

Calls

4 calls:

20.0ms	(pow (+ x 1) (/ 1 n))
78.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
98.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
117.0ms	(- (sqrt (sqrt (pow (+ x 1) (/ 1 n)))) (pow x (/ (/ (/ 1 n) 2) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

140.0ms	(pow (+ x 1) (/ 1 n))
325.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
277.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
314.0ms	(- (sqrt (sqrt (pow (+ x 1) (/ 1 n)))) (pow x (/ (/ (/ 1 n) 2) 2)))

simplify2.3s

Counts

120 → 120

Iterations

Iter	Nodes
done	5008
3	3608
2	1205
1	504
0	205

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.0b

regimes380.0ms

Accuracy

83.8% (1.3b remaining)

Error of 22.7b against oracle of 21.4b and baseline of 29.6b

bsearch339.0ms

Steps

Iters	Range		Point
8	1.159988114222822e+18	7.228602892249866e+20	1.180746203929133e+18
8	-4607476146472.435	-225049136.96346036	-490576324.36488575

simplify23.0ms

Iterations

Iter	Nodes
done	58
1	58
0	45

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.7s	3060×	body	1280	valid
1.3s	1135×	body	10240	exit
1.1s	1584×	body	640	valid
872.0ms	5008×	body	80	nan
661.0ms	685×	body	1280	nan
540.0ms	640×	body	640	nan
513.0ms	4768×	body	80	valid
410.0ms	920×	body	320	valid
189.0ms	376×	body	320	nan
117.0ms	452×	body	160	valid
41.0ms	187×	body	160	nan