Details

sample206.0ms

Algorithm

intervals

Results

130.0ms	105×	body	2560	valid
49.0ms	81×	body	1280	valid
8.0ms	34×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4
done	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite65.0ms

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))
42.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series150.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1.0 (tan x))
109.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify79.0ms

Counts

255 → 255

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	811	5920
1	2193	4160
2	5001	3667
done	5001	3667

prune267.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

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:

0.0ms

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

series137.0ms

Counts

1 → 3

Calls

1 calls:

137.0ms

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

simplify47.0ms

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	59
1	65	52
2	228	52
3	978	52
4	5001	52
done	5001	52

prune52.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.0021164021164021165 (pow x 5))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
3×	`associate-l` `prod-exp` `add-cbrt-cube` `unswap-sqr`
2×	`sqr-pow`
1×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

11.0ms

(* 0.0021164021164021165 (pow x 5))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(* 0.0021164021164021165 (pow x 5))

simplify50.0ms

Counts

30 → 30

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	101	106
1	366	98
2	1419	98
3	5001	98
done	5001	98

prune83.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (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:

14.0ms	(* (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)))

series4.1s

Counts

4 → 12

Calls

4 calls:

997.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.1s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
960.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
949.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify46.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	396	1201
1	1377	1116
2	5001	949
done	5001	949

prune333.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes66.0ms

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	12	5
1	12	5
done	12	5

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.4s	3196×	body	2560	valid
1.4s	2474×	body	1280	valid
365.0ms	1343×	body	640	valid
129.0ms	8000×	pre	80	true
119.0ms	624×	body	320	valid
40.0ms	325×	body	160	valid
2.0ms	38×	body	80	valid