Details

sample350.0ms

Algorithm

intervals

Results

237.0ms	111×	body	2560	valid
66.0ms	76×	body	1280	valid
18.0ms	40×	body	640	valid
7.0ms	22×	body	320	valid
5.0ms	256×	pre	80	true
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize10.0ms

Local error

Found 1 expressions with local error:

3.5b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite95.0ms

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:

75.0ms

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

series157.0ms

Counts

1 → 3

Calls

1 calls:

157.0ms

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

simplify4.0s

Counts

222 → 222

Iterations

Useful iterations: 3 (2.3s)

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

prune189.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 0.022222222222222223 (pow x 3) (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:

1.0ms

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

series107.0ms

Counts

1 → 3

Calls

1 calls:

107.0ms

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

simplify1.0s

Counts

13 → 13

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	26	218
1	51	212
2	149	186
3	837	186
done	5001	186

prune61.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

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))))

rewrite24.0ms

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:

19.0ms	(* (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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (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)))))
380.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
348.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
392.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify2.4s

Counts

93 → 93

Iterations

Useful iterations: done (2.4s)

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

prune544.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize41.0ms

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))))

rewrite4.0ms

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))))

series2.0s

Counts

4 → 12

Calls

4 calls:

766.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
385.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
490.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
377.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	90	1912
1	214	1876
2	579	1760
3	2169	1512
done	5000	1416

prune482.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.2b

regimes75.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample13.5s

Algorithm

intervals

Results

9.0s	3221×	body	2560	valid
3.0s	2485×	body	1280	valid
765.0ms	1289×	body	640	valid
223.0ms	631×	body	320	valid
160.0ms	8000×	pre	80	true
84.0ms	329×	body	160	valid
5.0ms	45×	body	80	valid