Details

sample225.0ms

Algorithm

intervals

Results

64.0ms	100×	body	1280	valid
37.0ms	43×	body	10240	exit
34.0ms	170×	body	80	valid
25.0ms	51×	body	640	valid
10.0ms	171×	body	80	nan
10.0ms	14×	body	1280	nan
9.0ms	29×	body	320	valid
8.0ms	15×	body	640	nan
4.0ms	12×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify2.6s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize31.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1) (/ 1 n))
1.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `div-inv` `flip--`

Counts

2 → 122

Calls

2 calls:

10.0ms	(pow (+ x 1) (/ 1 n))
160.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series334.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(pow (+ x 1) (/ 1 n))
247.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.5s

Counts

128 → 128

Iterations

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

prune580.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)))
0.7b	(pow (+ x 1) (/ (/ 1 n) 2))
0.7b	(pow (+ x 1) (/ (/ 1 n) 2))
2.0b	(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ 1 n)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
104×	`*-un-lft-identity`
100×	`add-sqr-sqrt`
86×	`pow-unpow` `add-cube-cbrt`
38×	`unpow-prod-down`
18×	`add-exp-log`
14×	`sqr-pow`
10×	`swap-sqr`
9×	`prod-exp` `unswap-sqr`
8×	`pow-to-exp` `associate-r` `associate-l` `pow-exp` `div-inv` `distribute-lft-out`
7×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow-pow`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--`

Counts

4 → 208

Calls

4 calls:

100.0ms	(* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)))
26.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
30.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
48.0ms	(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ 1 n)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)))
147.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
106.0ms	(pow (+ x 1) (/ (/ 1 n) 2))
357.0ms	(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow x (/ 1 n)))

simplify2.4s

Counts

220 → 220

Iterations

Iter	Nodes
done	5006
2	2236
1	820
0	290

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.6b

localize56.0ms

Local error

Found 3 expressions with local error:

0.4b	(posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n))))
0.7b	(pow (+ 1 x) (/ 1 n))
1.3b	(- (posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n)))) (pow x (/ 1 n)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
25×	`add-cube-cbrt`
21×	`prod-diff`
14×	`unpow-prod-down`
13×	`pow-unpow`
9×	`times-frac`
5×	`add-log-exp` `sqr-pow`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `div-inv` `remove-posit16` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 85

Calls

3 calls:

0.0ms	(posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n))))
13.0ms	(pow (+ 1 x) (/ 1 n))
17.0ms	(- (posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n)))) (pow x (/ 1 n)))

series504.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n))))
130.0ms	(pow (+ 1 x) (/ 1 n))
256.0ms	(- (posit16->real (real->posit16 (pow (+ 1 x) (/ 1 n)))) (pow x (/ 1 n)))

simplify2.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
3	4141
2	1199
1	473
0	192

prune860.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.7b	(pow (+ x 1) (/ 1 n))
1.7b	(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))))
2.0b	(- (pow (+ x 1) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
12×	`unpow-prod-down`
9×	`times-frac`
8×	`fma-neg` `prod-diff`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `pow1/3` `diff-log` `pow-exp` `fma-udef` `div-inv` `flip--`

Counts

4 → 87

Calls

4 calls:

1.0ms	(cbrt x)
10.0ms	(pow (+ 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))))
170.0ms	(- (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:

223.0ms	(cbrt x)
97.0ms	(pow (+ x 1) (/ 1 n))
450.0ms	(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))))
494.0ms	(- (pow (+ x 1) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

simplify2.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1857
1	565
0	218

prune758.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.2b

regimes476.0ms

Accuracy

88.4% (1.4b remaining)

Error of 18.8b against oracle of 17.4b and baseline of 29.4b

bsearch4.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	42
1	42
0	36

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.0s	3175×	body	1280	valid
1.0s	1569×	body	640	valid
996.0ms	626×	body	1280	nan
968.0ms	1179×	body	10240	exit
535.0ms	4651×	body	80	valid
477.0ms	631×	body	640	nan
436.0ms	5178×	body	80	nan
315.0ms	846×	body	320	valid
116.0ms	354×	body	320	nan
102.0ms	443×	body	160	valid
33.0ms	166×	body	160	nan