Details

sample323.0ms

Algorithm

intervals

Results

95.0ms	102×	body	1280	valid
52.0ms	42×	body	10240	exit
47.0ms	166×	body	80	valid
31.0ms	41×	body	640	valid
20.0ms	17×	body	1280	nan
16.0ms	22×	body	640	nan
15.0ms	161×	body	80	nan
13.0ms	26×	body	320	valid
8.0ms	18×	body	320	nan
3.0ms	9×	body	160	valid
2.0ms	8×	body	160	nan

simplify1.8s

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.3b	(pow (+ x 1) (/ 1 n))
0.3b	(pow x (/ 1 n))

rewrite104.0ms

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:

Slowest

81.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms	(pow (+ x 1) (/ 1 n))
6.0ms	(pow x (/ 1 n))

series361.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

206.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
90.0ms	(pow (+ x 1) (/ 1 n))
65.0ms	(pow x (/ 1 n))

simplify672.0ms

Counts: 161 → 161

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.3b	(pow (+ x 1) (/ 1 n))

rewrite264.0ms

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:

Slowest

94.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
82.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
74.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
9.0ms	(pow (+ x 1) (/ 1 n))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

603.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
266.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
229.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
111.0ms	(pow (+ x 1) (/ 1 n))

simplify1.8s

Counts: 316 → 316

prune5.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.0b

localize109.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.3b	(pow (+ x 1) (/ 1 n))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

136×	`unpow-prod-down`
124×	`*-un-lft-identity`
112×	`prod-diff`
100×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv`

Counts

4 → 224

Calls

4 calls:

Slowest

95.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
75.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 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)))))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

269.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
258.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
226.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
116.0ms	(pow (+ x 1) (/ 1 n))

simplify2.0s

Counts: 236 → 236

prune4.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.0b

localize73.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
2.1b	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
0.3b	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.3b	(cbrt (+ x 1))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
28×	`cbrt-prod`
21×	`add-sqr-sqrt`
14×	`cbrt-div`
13×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
7×	`flip3-+` `pow1/3` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

Slowest

47.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms	(cbrt (+ x 1))
1.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
1.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series809.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

517.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
184.0ms	(fma (- (pow x (/ (/ 1 n) 2))) (pow x (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
69.0ms	(cbrt (+ x 1))
40.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))

simplify864.0ms

Counts: 107 → 107

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

regimes453.0ms

Accuracy

88.1% (1.4b remaining)

Error of 18.9b against oracle of 17.5b and baseline of 29.5b

bsearch956.0ms

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.7s	3184×	body	1280	valid
1.7s	1574×	body	640	valid
1.3s	1138×	body	10240	exit
788.0ms	632×	body	1280	nan
737.0ms	4704×	body	80	valid
714.0ms	5065×	body	80	nan
532.0ms	668×	body	640	nan
496.0ms	862×	body	320	valid
161.0ms	349×	body	320	nan
143.0ms	446×	body	160	valid
51.0ms	171×	body	160	nan