Details

sample211.0ms

Algorithm

intervals

Results

136.0ms	102×	body	2560	valid
43.0ms	82×	body	1280	valid
13.0ms	47×	body	640	valid
3.0ms	256×	pre	80	true
3.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
done	11	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
211×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
199×	`add-cube-cbrt`
182×	`prod-diff`
30×	`div-inv`
13×	`tan-quot` `fma-neg` `associate-/r/`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 219

Calls

1 calls:

46.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

series109.0ms

Counts

1 → 3

Calls

1 calls:

109.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify3.2s

Counts

222 → 222

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	346	9367
1	764	8243
2	1605	5865
3	4996	4062
done	5000	4062

prune152.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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)))

series186.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
61.0ms	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify715.0ms

Counts

26 → 26

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	36	358
1	61	349
2	176	307
3	971	307
done	5000	307

prune80.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(fma 0.022222222222222223 (pow x 3) (* 0.0021164021164021165 (pow x 5)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

15.0ms	(* 0.0021164021164021165 (pow x 5))
0.0ms	(fma 0.022222222222222223 (pow x 3) (* 0.0021164021164021165 (pow x 5)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* 0.0021164021164021165 (pow x 5))
123.0ms	(fma 0.022222222222222223 (pow x 3) (* 0.0021164021164021165 (pow x 5)))

simplify3.5s

Counts

43 → 43

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	67	403
1	128	377
2	298	345
3	972	345
4	4830	345
done	5000	345

prune125.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize19.0ms

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)))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

rewrite16.0ms

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 0.022222222222222223 (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:

278.0ms	(* (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)))))
273.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
278.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
274.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	173	3120
1	407	2936
2	1179	2727
3	4456	2183
done	5000	2179

prune359.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

regimes60.0ms

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	11	13
1	12	13
done	12	13

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.6s	3341×	body	2560	valid
1.4s	2485×	body	1280	valid
327.0ms	1227×	body	640	valid
120.0ms	626×	body	320	valid
97.0ms	8000×	pre	80	true
35.0ms	280×	body	160	valid
3.0ms	41×	body	80	valid