Details

sample201.0ms

Algorithm

intervals

Results

131.0ms	95×	body	2560	valid
42.0ms	84×	body	1280	valid
9.0ms	36×	body	640	valid
5.0ms	29×	body	320	valid
3.0ms	256×	pre	80	true
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: 59.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.6b	(- (/ 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:

5.0ms	(/ 1.0 (tan x))
43.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ 1.0 (tan x))
96.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (51.0ms)

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

prune236.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

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))

series110.0ms

Counts

1 → 3

Calls

1 calls:

110.0ms

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

simplify47.0ms

Algorithm

egg-herbie

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

prune43.0ms

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)))

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:

10.0ms	(* (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)))

series3.7s

Counts

4 → 12

Calls

4 calls:

932.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
917.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
924.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
888.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify245.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

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

prune350.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

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))))
0.7b	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (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)))
1.0ms	(cbrt (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)))))

series3.6s

Counts

4 → 12

Calls

4 calls:

910.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
902.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
890.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
938.0ms	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (35.0ms)

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

prune331.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes82.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.5s	3267×	body	2560	valid
1.4s	2572×	body	1280	valid
331.0ms	1209×	body	640	valid
115.0ms	607×	body	320	valid
99.0ms	8000×	pre	80	true
37.0ms	303×	body	160	valid
3.0ms	42×	body	80	valid