Details

sample367.0ms

Algorithm

intervals

Results

112.0ms	99×	body	1280	valid
55.0ms	62×	body	640	valid
40.0ms	22×	body	640	nan
29.0ms	161×	body	80	valid
28.0ms	28×	body	1280	nan
28.0ms	26×	body	10240	exit
20.0ms	153×	body	80	nan
13.0ms	23×	body	320	valid
10.0ms	18×	body	320	nan
5.0ms	12×	body	160	valid
1.0ms	2×	body	160	nan

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1210
4	275
3	89
2	37
1	19
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize36.0ms

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))

rewrite107.0ms

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:

5.0ms	(pow x (/ 1 n))
92.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
8.0ms	(pow (+ x 1) (/ 1 n))

series399.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(pow x (/ 1 n))
221.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
90.0ms	(pow (+ x 1) (/ 1 n))

simplify1.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	1672
1	653
0	257

prune812.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize50.0ms

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))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 241

Calls

4 calls:

6.0ms	(pow x (/ 1 n))
164.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
80.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
8.0ms	(pow (+ x 1) (/ 1 n))

series691.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow x (/ 1 n))
282.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
234.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
107.0ms	(pow (+ x 1) (/ 1 n))

simplify1.7s

Counts

253 → 253

Iterations

Iter	Nodes
done	5000
2	1988
1	843
0	417

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.1b

localize103.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (cbrt x) (/ 1 n))
2.0b	(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))))
3.0b	(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)))))

rewrite23.0ms

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:

6.0ms	(pow (cbrt x) (/ 1 n))
14.0ms	(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))))
1.0ms	(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)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (cbrt x) (/ 1 n))
152.0ms	(pow (cbrt (+ x 1)) (/ 1 n))
388.0ms	(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))))
1.2s	(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)))))

simplify3.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5008
2	2180
1	678
0	247

prune963.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize55.0ms

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))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
78×	`unpow-prod-down`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
56×	`prod-diff`
39×	`pow-unpow`
27×	`times-frac`
25×	`sqr-pow`
12×	`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` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 184

Calls

4 calls:

91.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
15.0ms	(pow (+ x 1) (/ 1 n))
10.0ms	(pow (+ x 1) (/ 1 n))
8.0ms	(pow (+ x 1) (/ 1 n))

series614.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
119.0ms	(pow (+ x 1) (/ 1 n))
103.0ms	(pow (+ x 1) (/ 1 n))
129.0ms	(pow (+ x 1) (/ 1 n))

simplify2.7s

Counts

196 → 196

Iterations

Iter	Nodes
done	5000
3	4366
2	1286
1	544
0	221

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.1b

regimes306.0ms

Accuracy

90% (1.1b remaining)

Error of 19.2b against oracle of 18.1b and baseline of 29.5b

bsearch3.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	52
1	52
0	42

end0.0ms

sample11.1s

Algorithm

intervals

Results

3.3s	3099×	body	1280	valid
1.4s	1627×	body	640	valid
1.3s	1113×	body	10240	exit
992.0ms	635×	body	640	nan
988.0ms	4975×	body	80	nan
942.0ms	4806×	body	80	valid
700.0ms	670×	body	1280	nan
536.0ms	844×	body	320	valid
216.0ms	359×	body	320	nan
168.0ms	460×	body	160	valid
93.0ms	190×	body	160	nan