Details

sample353.0ms

Algorithm

intervals

Results

107.0ms	103×	body	1280	valid
49.0ms	32×	body	10240	exit
40.0ms	51×	body	640	valid
38.0ms	30×	body	640	nan
27.0ms	24×	body	1280	nan
20.0ms	136×	body	80	valid
19.0ms	37×	body	320	valid
18.0ms	156×	body	80	nan
5.0ms	12×	body	320	nan
3.0ms	9×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	2679
5	667
4	231
3	87
2	35
1	17
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize16.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite75.0ms

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:

3.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
60.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series440.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(pow x (/ 1 n))
113.0ms	(pow (+ x 1) (/ 1 n))
245.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify6.5s

Counts

161 → 161

Iterations

Iter	Nodes
3	5080
2	1635
1	651
0	257

prune700.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.2b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1 n))
1.3b	(pow (+ x 1) (/ 1 n))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.4b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 241

Calls

4 calls:

3.0ms	(pow x (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
73.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
178.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(pow x (/ 1 n))
116.0ms	(pow (+ x 1) (/ 1 n))
267.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
255.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))

simplify6.2s

Counts

253 → 253

Iterations

Iter	Nodes
3	5683
2	1949
1	839
0	417

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize64.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (+ x 1) (/ 1 n))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite322.0ms

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:

14.0ms	(pow (+ x 1) (/ 1 n))
67.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
117.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
112.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series893.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (+ x 1) (/ 1 n))
250.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
282.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
252.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.9s

Counts

316 → 316

Iterations

Iter	Nodes
3	3813
2	1275
1	541
0	221

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize122.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.7b	(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))))
3.1b	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite161.0ms

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:

62.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
92.0ms	(- (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 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

248.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
275.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
374.0ms	(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))))
866.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

simplify6.3s

Counts

216 → 216

Iterations

Iter	Nodes
3	6805
2	1802
1	641
0	277

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

regimes350.0ms

Accuracy

85% (1.8b remaining)

Error of 18.8b against oracle of 17.0b and baseline of 28.9b

bsearch473.0ms

Steps

Iters	Range		Point
8	0.00249723671336719	0.9376093183107279	0.9292141684675859
6	-3.314279583631801e-301	-3.0744577275576913e-302	-3.1374879532667245e-302
9	-6472449387759.926	-7016528.6044858415	-29869477.165418986

simplify18.0ms

Iterations

Iter	Nodes
3	66
2	66
1	64
0	54

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.8s	3133×	body	1280	valid
1.7s	1119×	body	10240	exit
1.4s	1597×	body	640	valid
724.0ms	660×	body	1280	nan
687.0ms	4634×	body	80	valid
586.0ms	4942×	body	80	nan
532.0ms	886×	body	320	valid
498.0ms	633×	body	640	nan
195.0ms	346×	body	320	nan
140.0ms	442×	body	160	valid
51.0ms	183×	body	160	nan