Details

sample348.0ms

Algorithm

intervals

Results

226.0ms	93×	body	2560	valid
69.0ms	81×	body	1280	valid
22.0ms	44×	body	640	valid
9.0ms	25×	body	320	valid
8.0ms	256×	pre	80	true
3.0ms	13×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
4.1b	(- (/ 1 x) (/ 1 (tan x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
33×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 262

Calls

2 calls:

9.0ms	(/ 1 (tan x))
85.0ms	(- (/ 1 x) (/ 1 (tan x)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ 1 (tan x))
86.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify2.3s

Counts

268 → 268

Iterations

Iter	Nodes
done	5024
3	3081
2	1356
1	762
0	342

prune516.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))
0.0b	(fma 1/45 (* x x) 1/3)
0.4b	(* x (fma 1/45 (* x x) 1/3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`fma-udef`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))
0.0ms	(fma 1/45 (* x x) 1/3)
12.0ms	(* x (fma 1/45 (* x x) 1/3))

series319.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))
87.0ms	(fma 1/45 (* x x) 1/3)
156.0ms	(* x (fma 1/45 (* x x) 1/3))

simplify2.2s

Counts

54 → 54

Iterations

Iter	Nodes
done	5012
3	1849
2	391
1	147
0	70

prune331.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))))
0.6b	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
0.6b	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
0.6b	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

28.0ms	(* (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))))
1.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
2.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
2.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))

series920.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))))
193.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
198.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))
267.0ms	(cbrt (fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3))))

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
3	2063
2	730
1	316
0	142

prune530.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series977.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt x)
269.0ms	(cbrt x)
235.0ms	(cbrt x)
199.0ms	(cbrt x)

simplify4.3s

Counts

68 → 68

Iterations

Iter	Nodes
done	5011
6	4856
5	1192
4	406
3	186
2	97
1	47
0	27

prune543.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 0.1b

regimes109.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample11.4s

Algorithm

intervals

Results

7.0s	3245×	body	2560	valid
3.0s	2537×	body	1280	valid
675.0ms	1242×	body	640	valid
254.0ms	612×	body	320	valid
227.0ms	8000×	pre	80	true
64.0ms	313×	body	160	valid
6.0ms	51×	body	80	valid