Details

sample258.0ms

Algorithm

intervals

Results

87.0ms	99×	body	1280	valid
39.0ms	49×	body	640	valid
22.0ms	21×	body	1280	nan
20.0ms	146×	body	80	valid
17.0ms	171×	body	80	nan
15.0ms	21×	body	640	nan
15.0ms	21×	body	10240	exit
9.0ms	22×	body	320	valid
5.0ms	12×	body	320	nan
4.0ms	16×	body	160	valid
4.0ms	12×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2099
6	2099
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: 27.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1 n))
1.0b	(pow (+ x 1) (/ 1 n))
1.7b	(- (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))
15.0ms	(pow (+ x 1) (/ 1 n))
96.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series434.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(pow x (/ 1 n))
102.0ms	(pow (+ x 1) (/ 1 n))
243.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.3s

Counts

161 → 161

Iterations

Iter	Nodes
done	2000
3	2000
2	1649
1	651
0	257

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b	(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)))

rewrite278.0ms

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:

7.0ms	(pow (+ x 1) (/ 1 n))
94.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
73.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
98.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow (+ x 1) (/ 1 n))
279.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
241.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
262.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.2s

Counts

316 → 316

Iterations

Iter	Nodes
done	2001
3	2001
2	1287
1	543
0	221

prune5.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize100.0ms

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)))
2.4b	(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))))
2.6b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite197.0ms

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:

70.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
123.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0ms	(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 1 (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:

283.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
275.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
442.0ms	(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))))
454.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify1.7s

Counts

216 → 216

Iterations

Iter	Nodes
done	2006
3	2006
2	1828
1	642
0	277

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize116.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
2.4b	(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))))
2.6b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

128×	`unpow-prod-down`
112×	`*-un-lft-identity` `prod-diff`
92×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
43×	`sqr-pow`
18×	`difference-of-squares`
17×	`distribute-lft-out`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `fma-udef`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 202

Calls

4 calls:

69.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
137.0ms	(log (exp (- (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 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

220.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
243.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
379.0ms	(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))))
447.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify1.4s

Counts

214 → 214

Iterations

Iter	Nodes
done	2001
2	2001
1	823
0	435

prune4.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

regimes385.0ms

Accuracy

86.5% (1.5b remaining)

Error of 19.3b against oracle of 17.8b and baseline of 29.2b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	42
2	42
1	40
0	33

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.6s	3153×	body	1280	valid
1.2s	1569×	body	640	valid
1.2s	1164×	body	10240	exit
1.0s	5168×	body	80	nan
905.0ms	659×	body	1280	nan
667.0ms	4795×	body	80	valid
593.0ms	675×	body	640	nan
432.0ms	869×	body	320	valid
160.0ms	347×	body	320	nan
128.0ms	436×	body	160	valid
48.0ms	180×	body	160	nan