Details

sample323.0ms

Algorithm

intervals

Results

103.0ms	104×	body	1280	valid
46.0ms	36×	body	10240	exit
38.0ms	50×	body	640	valid
35.0ms	140×	body	80	valid
24.0ms	22×	body	1280	nan
17.0ms	34×	body	320	valid
15.0ms	150×	body	80	nan
12.0ms	17×	body	640	nan
5.0ms	10×	body	320	nan
4.0ms	9×	body	160	valid
2.0ms	8×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
2.1b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite92.0ms

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))
10.0ms	(pow (+ x 1) (/ 1 n))
72.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series434.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(pow x (/ 1 n))
117.0ms	(pow (+ x 1) (/ 1 n))
237.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.3s

Counts

161 → 161

Iterations

Iter	Nodes
3	5158
2	1593
1	651
0	257

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
2.2b	(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
4.2b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

3.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
0.0ms	(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
0.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))

series841.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow x (/ 1 n))
116.0ms	(pow (+ x 1) (/ 1 n))
421.0ms	(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
239.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))

simplify1.5s

Counts

95 → 95

Iterations

Iter	Nodes
3	3671
2	1198
1	454
0	177

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.6b

localize134.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
4.2b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
4.2b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
4.2b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

349.0ms	(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
241.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
262.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
223.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))

simplify1.4s

Counts

56 → 56

Iterations

Iter	Nodes
4	2775
3	793
2	296
1	150
0	72

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.6b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (log1p x) n)
0.3b	(pow x (/ 1 n))
2.1b	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
21×	`prod-diff`
18×	`times-frac`
13×	`pow-unpow` `unpow-prod-down`
6×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp` `sqr-pow`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `fma-neg` `insert-posit16` `log1p-expm1-u` `associate-/l` `difference-of-squares`
2×	`div-inv`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `flip3--` `diff-log` `div-exp` `pow-exp` `flip--` `distribute-lft-out--`

Counts

3 → 103

Calls

3 calls:

6.0ms	(/ (log1p x) n)
6.0ms	(pow x (/ 1 n))
48.0ms	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (log1p x) n)
99.0ms	(pow x (/ 1 n))
211.0ms	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))

simplify2.4s

Counts

112 → 112

Iterations

Iter	Nodes
3	4721
2	1518
1	578
0	242

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.5b

regimes382.0ms

Accuracy

80.3% (2.4b remaining)

Error of 19.7b against oracle of 17.3b and baseline of 29.7b

bsearch3.0ms

simplify24.0ms

Iterations

Iter	Nodes
3	58
2	58
1	54
0	44

end0.0ms

sample10.9s

Algorithm

intervals

Results

3.5s	3156×	body	1280	valid
1.5s	4662×	body	80	valid
1.4s	1580×	body	640	valid
1.2s	1129×	body	10240	exit
746.0ms	627×	body	1280	nan
675.0ms	4869×	body	80	nan
537.0ms	929×	body	320	valid
473.0ms	582×	body	640	nan
217.0ms	318×	body	320	nan
181.0ms	449×	body	160	valid
49.0ms	172×	body	160	nan