Details

sample377.0ms

Algorithm

intervals

Results

259.0ms	116×	body	2560	valid
70.0ms	71×	body	1280	valid
15.0ms	32×	body	640	valid
7.0ms	24×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	12×	body	160	valid
0.0ms	1×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
done	11	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
220×	`add-sqr-sqrt`
216×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub` `flip--`

Counts

2 → 249

Calls

2 calls:

6.0ms	(/ 1.0 (tan x))
82.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series257.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ 1.0 (tan x))
197.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.2s

Counts

255 → 255

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	369	9638
1	843	8522
2	2774	6348
done	5001	5452

prune438.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
0.0b	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
1.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series242.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
73.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.5s

Counts

26 → 26

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	36	358
1	68	349
2	264	307
3	1651	307
done	5000	307

prune107.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `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 → 81

Calls

4 calls:

11.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series5.6s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.4s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.3s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.4s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	169	2370
1	428	2227
2	1581	2081
done	5000	1720

prune692.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
3.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
13.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
3.0ms	(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))

series6.0s

Counts

4 → 12

Calls

4 calls:

1.4s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.4s	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.5s	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.8s	(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))

simplify554.0ms

Counts

73 → 73

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	161	1807
1	354	1766
2	1091	1658
done	5001	1435

prune483.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes114.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample13.2s

Algorithm

intervals

Results

8.1s	3278×	body	2560	valid
3.4s	2543×	body	1280	valid
802.0ms	1198×	body	640	valid
262.0ms	642×	body	320	valid
161.0ms	8000×	pre	80	true
69.0ms	297×	body	160	valid
4.0ms	42×	body	80	valid