Details

sample318.0ms

Algorithm

intervals

Results

197.0ms	115×	body	2560	valid
77.0ms	73×	body	1280	valid
17.0ms	39×	body	640	valid
5.0ms	256×	pre	80	true
5.0ms	16×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite434.0ms

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:

9.0ms	(/ 1.0 (tan x))
396.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ 1.0 (tan x))
142.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts

255 → 255

Iterations

Useful iterations: done (1.9s)

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

prune404.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

1.0ms

(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

series145.0ms

Counts

1 → 3

Calls

1 calls:

145.0ms

(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

simplify3.6s

Counts

13 → 13

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	18	140
1	30	137
2	86	121
3	346	121
4	1706	121
done	5001	121

prune40.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

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)))

rewrite15.0ms

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

series5.2s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (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)))
1.1s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.2s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: done (1.1s)

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

prune684.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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:

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

series6.3s

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.8s	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.4s	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.6s	(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))

simplify815.0ms

Counts

73 → 73

Iterations

Useful iterations: done (808.0ms)

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

prune705.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

regimes113.0ms

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

sample13.7s

Algorithm

intervals

Results

8.7s	3199×	body	2560	valid
3.3s	2543×	body	1280	valid
717.0ms	1295×	body	640	valid
287.0ms	621×	body	320	valid
255.0ms	8000×	pre	80	true
69.0ms	298×	body	160	valid
5.0ms	44×	body	80	valid