Details

sample301.0ms

Algorithm

intervals

Results

98.0ms	113×	body	1280	valid
53.0ms	37×	body	10240	exit
36.0ms	49×	body	640	valid
24.0ms	161×	body	80	valid
21.0ms	28×	body	1280	nan
16.0ms	157×	body	80	nan
14.0ms	19×	body	640	nan
11.0ms	27×	body	320	valid
4.0ms	13×	body	160	valid
3.0ms	7×	body	320	nan
1.0ms	5×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	2654
5	661
4	233
3	89
2	37
1	19
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize33.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1 n))
1.7b	(pow (+ x 1) (/ 1 n))
2.0b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 152

Calls

3 calls:

6.0ms	(pow x (/ 1 n))
8.0ms	(pow (+ x 1) (/ 1 n))
104.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series468.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(pow x (/ 1 n))
126.0ms	(pow (+ x 1) (/ 1 n))
246.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.2s

Counts

161 → 161

Iterations

Iter	Nodes
3	5158
2	1593
1	651
0	257

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

localize75.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (cbrt x) (/ 1 n))
1.7b	(pow (cbrt (+ x 1)) (/ 1 n))
2.9b	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
3.2b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
13×	`unpow-prod-down`
7×	`cbrt-prod`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow1/3` `pow-exp` `fma-udef` `div-inv` `sqr-pow`
1×	`distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

3.0ms	(pow (cbrt x) (/ 1 n))
13.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
0.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
0.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

156.0ms	(pow (cbrt x) (/ 1 n))
200.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
360.0ms	(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
838.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify1.6s

Counts

103 → 103

Iterations

Iter	Nodes
2	2106
1	677
0	247

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.9b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ (/ 1 n) 2))
1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 273

Calls

4 calls:

7.0ms	(pow x (/ (/ 1 n) 2))
16.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
8.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
64.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow x (/ (/ 1 n) 2))
125.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
121.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
308.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

simplify1.7s

Counts

285 → 285

Iterations

Iter	Nodes
2	2645
1	1036
0	366

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.9b

localize35.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
1.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
2.0b	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

190×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
140×	`unpow-prod-down` `add-cube-cbrt`
132×	`times-frac`
112×	`prod-diff`
86×	`pow-unpow`
46×	`sqr-pow`
20×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`div-inv` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

4 → 304

Calls

4 calls:

10.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
8.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
109.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
116.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

series784.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
126.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
252.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
279.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))

simplify1.2s

Counts

316 → 316

Iterations

Iter	Nodes
2	2048
1	827
0	300

prune5.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.9b

regimes363.0ms

Accuracy

89.3% (1.3b remaining)

Error of 18.6b against oracle of 17.3b and baseline of 29.3b

bsearch809.0ms

Steps

Iters	Range		Point
6	6143511848.122867	97383972881.30028	6277284157.817854
9	-7.31485499214668e-305	1.445416933309411e-307	-1.1961188537549e-310
11	-41824574.29247571	-2.6799709080204617e-24	-233718.83379744613

simplify13.0ms

Iterations

Iter	Nodes
3	57
2	57
1	55
0	46

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.3s	3197×	body	1280	valid
1.7s	1583×	body	640	valid
1.3s	1168×	body	10240	exit
1.1s	4642×	body	80	valid
681.0ms	5062×	body	80	nan
636.0ms	652×	body	1280	nan
526.0ms	883×	body	320	valid
518.0ms	666×	body	640	nan
206.0ms	371×	body	320	nan
129.0ms	428×	body	160	valid
45.0ms	170×	body	160	nan