Details

sample231.0ms

Algorithm

intervals

Results

153.0ms	106×	body	2560	valid
49.0ms	81×	body	1280	valid
10.0ms	38×	body	640	valid
4.0ms	18×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	12×	body	160	valid
0.0ms	1×	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: 60.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.4b	(- (/ 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)))

series146.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 1.0 (tan x))
105.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify122.0ms

Counts

255 → 255

Iterations

Useful iterations: 2 (75.0ms)

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

prune265.0ms

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)))

series189.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
64.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify40.0ms

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

prune71.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

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)))

series3.8s

Counts

4 → 12

Calls

4 calls:

989.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
950.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
941.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
965.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify54.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

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

prune348.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

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)))
0.6b	(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)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`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 → 50

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 (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
6.0ms	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

series4.0s

Counts

4 → 12

Calls

4 calls:

948.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
939.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
930.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.2s	(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

simplify38.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	356	898
1	1133	830
2	5001	712
done	5001	712

prune326.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes51.0ms

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

sample6.5s

Algorithm

intervals

Results

4.3s	3168×	body	2560	valid
1.4s	2582×	body	1280	valid
335.0ms	1270×	body	640	valid
105.0ms	8000×	pre	80	true
101.0ms	610×	body	320	valid
39.0ms	335×	body	160	valid
2.0ms	35×	body	80	valid