Details

sample351.0ms

Algorithm

intervals

Results

90.0ms	91×	body	1280	valid
47.0ms	68×	body	640	valid
44.0ms	34×	body	10240	exit
33.0ms	26×	body	320	valid
29.0ms	22×	body	1280	nan
25.0ms	32×	body	640	nan
24.0ms	166×	body	80	valid
20.0ms	187×	body	80	nan
7.0ms	14×	body	320	nan
5.0ms	16×	body	160	valid
3.0ms	10×	body	160	nan

simplify2.4s

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize14.0ms

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)))

rewrite142.0ms

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:

4.0ms	(pow x (/ 1 n))
13.0ms	(pow (+ x 1) (/ 1 n))
123.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series419.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(pow x (/ 1 n))
103.0ms	(pow (+ x 1) (/ 1 n))
223.0ms	(- (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

prune783.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize65.0ms

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)))

rewrite333.0ms

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:

13.0ms	(pow (+ x 1) (/ 1 n))
91.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
95.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
123.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(pow (+ x 1) (/ 1 n))
262.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
272.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
265.0ms	(- (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

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize83.0ms

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)))))

rewrite189.0ms

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:

82.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
98.0ms	(- (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 (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:

285.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
259.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
405.0ms	(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))))
533.0ms	(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)))))

simplify3.3s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
2	1820
1	638
0	277

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize118.0ms

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)))))

rewrite127.0ms

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:

60.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
62.0ms	(- (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:

242.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
250.0ms	(- (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))))
603.0ms	(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)))))

simplify3.0s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
2	1820
1	638
0	277

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.5b

regimes699.0ms

Accuracy

90% (1.2b remaining)

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

bsearch4.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	63
2	63
1	61
0	47

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.8s	3141×	body	1280	valid
1.4s	1145×	body	10240	exit
1.3s	1578×	body	640	valid
1.0s	4744×	body	80	valid
708.0ms	648×	body	1280	nan
614.0ms	634×	body	640	nan
560.0ms	5032×	body	80	nan
522.0ms	863×	body	320	valid
176.0ms	440×	body	160	valid
174.0ms	368×	body	320	nan
52.0ms	185×	body	160	nan