Details

sample300.0ms

Algorithm

intervals

Results

83.0ms	91×	body	1280	valid
43.0ms	34×	body	10240	exit
43.0ms	68×	body	640	valid
27.0ms	22×	body	1280	nan
21.0ms	32×	body	640	nan
18.0ms	166×	body	80	valid
16.0ms	187×	body	80	nan
10.0ms	26×	body	320	valid
6.0ms	14×	body	320	nan
4.0ms	16×	body	160	valid
3.0ms	10×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1 n))
0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite93.0ms

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:

3.0ms	(pow x (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
76.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series404.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(pow x (/ 1 n))
97.0ms	(pow (+ x 1) (/ 1 n))
233.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.7s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	1649
1	651
0	257

prune749.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (+ x 1) (/ 1 n))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 304

Calls

4 calls:

8.0ms	(pow (+ x 1) (/ 1 n))
105.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
123.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
127.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(pow (+ x 1) (/ 1 n))
245.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
284.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
280.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.6s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
3	4376
2	1287
1	543
0	221

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize77.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.9b	(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))))
3.6b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
114×	`*-un-lft-identity`
112×	`prod-diff`
92×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
44×	`sqr-pow`
18×	`distribute-lft-out` `difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--`

Counts

4 → 204

Calls

4 calls:

108.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
65.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 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 (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

229.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
241.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
373.0ms	(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))))
591.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify2.8s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
2	1820
1	638
0	277

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize119.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.9b	(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))))
3.6b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
114×	`*-un-lft-identity`
112×	`prod-diff`
92×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
44×	`sqr-pow`
18×	`distribute-lft-out` `difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--`

Counts

4 → 204

Calls

4 calls:

76.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
68.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 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 (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

272.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
236.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
424.0ms	(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))))
542.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify2.9s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
2	1820
1	638
0	277

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.5b

regimes621.0ms

Accuracy

90% (1.2b remaining)

Error of 19.0b against oracle of 17.9b and baseline of 29.4b

bsearch3.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	67
2	67
1	65
0	50

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.3s	3141×	body	1280	valid
1.0s	1145×	body	10240	exit
1.0s	1578×	body	640	valid
615.0ms	648×	body	1280	nan
532.0ms	4744×	body	80	valid
394.0ms	863×	body	320	valid
389.0ms	5032×	body	80	nan
389.0ms	634×	body	640	nan
119.0ms	368×	body	320	nan
103.0ms	440×	body	160	valid
35.0ms	185×	body	160	nan