Details

sample214.0ms

Algorithm

intervals

Results

138.0ms	100×	body	2560	valid
51.0ms	90×	body	1280	valid
7.0ms	27×	body	640	valid
3.0ms	20×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	17×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

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: 59.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
4.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite67.0ms

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))
44.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 1.0 (tan x))
103.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify79.0ms

Counts

255 → 255

Iterations

Useful iterations: 2 (48.0ms)

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

prune247.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

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)))

rewrite1.0ms

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

series184.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
56.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify33.0ms

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	61	148
1	185	130
2	1006	130
3	5002	130
done	5002	130

prune72.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

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:

13.0ms	(* (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)))

series3.9s

Counts

4 → 12

Calls

4 calls:

964.0ms	(* (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)))
931.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
917.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify47.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (36.0ms)

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

prune355.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
8×	`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 → 53

Calls

4 calls:

1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
5.0ms	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
1.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

series3.8s

Counts

4 → 12

Calls

4 calls:

943.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
931.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
982.0ms	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
935.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify50.0ms

Counts

65 → 65

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	481	951
1	1547	877
2	5002	764
done	5002	764

prune340.0ms

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 0.2b

regimes95.0ms

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

sample6.8s

Algorithm

intervals

Results

4.6s	3254×	body	2560	valid
1.4s	2479×	body	1280	valid
356.0ms	1261×	body	640	valid
112.0ms	8000×	pre	80	true
110.0ms	635×	body	320	valid
40.0ms	325×	body	160	valid
3.0ms	46×	body	80	valid