Details

sample239.0ms

Algorithm

intervals

Results

181.0ms	99×	body	2560	valid
35.0ms	78×	body	1280	valid
7.0ms	49×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite39.0ms

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:

4.0ms	(/ 1.0 (tan x))
19.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ 1.0 (tan x))
100.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (48.0ms)

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

prune250.0ms

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)))

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:

1.0ms	(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)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
58.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

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

prune74.0ms

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 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

rewrite11.0ms

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:

5.0ms	(* (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
267.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
265.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
262.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	406	1479
1	1432	1371
2	5002	1179

prune369.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`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 → 52

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
279.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
265.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
260.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify82.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	212	984
1	668	924
2	2820	800
3	5001	784

prune326.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample6.9s

Algorithm

intervals

Results

5.1s	3226×	body	2560	valid
1.3s	2539×	body	1280	valid
213.0ms	1281×	body	640	valid
97.0ms	8000×	pre	80	true
63.0ms	618×	body	320	valid
20.0ms	285×	body	160	valid
2.0ms	51×	body	80	valid