Details

sample384.0ms

Algorithm

intervals

Results

197.0ms	89×	body	2560	valid
130.0ms	93×	body	1280	valid
22.0ms	45×	body	640	valid
7.0ms	19×	body	320	valid
6.0ms	256×	pre	80	true
2.0ms	9×	body	160	valid
0.0ms	1×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	8
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite105.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`

Counts

2 → 249

Calls

2 calls:

24.0ms	(/ 1.0 (tan x))
62.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series205.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ 1.0 (tan x))
156.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.8s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	2774
1	843
0	369

prune744.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 0.0021164021164021165 (pow x 5) (fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

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

simplify2.8s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
4	3671
3	460
2	109
1	48
0	24

prune115.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b

(expm1 (log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165)))))

0.0b

(log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165))))

0.1b

(* (pow x 5) 0.0021164021164021165)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms

(expm1 (log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165)))))

1.0ms

(log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165))))

19.0ms

(* (pow x 5) 0.0021164021164021165)

series783.0ms

Counts

3 → 9

Calls

3 calls:

479.0ms

(expm1 (log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165)))))

218.0ms

(log1p (fma 0.022222222222222223 (pow x 3) (fma 0.3333333333333333 x (* (pow x 5) 0.0021164021164021165))))

85.0ms

(* (pow x 5) 0.0021164021164021165)

simplify828.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
2	1399
1	354
0	150

prune453.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))) (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))))
0.6b	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
0.6b	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
0.6b	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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:

17.0ms	(* (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))) (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))))
1.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
1.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
1.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))

series1.6s

Counts

4 → 12

Calls

4 calls:

398.0ms	(* (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))) (cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333)))))
407.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
363.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))
415.0ms	(cbrt (fma (pow x 3) 0.022222222222222223 (fma (pow x 5) 0.0021164021164021165 (* x 0.3333333333333333))))

simplify845.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1674
1	441
0	173

prune799.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes128.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.7s	3293×	body	2560	valid
3.0s	2475×	body	1280	valid
1.3s	1259×	body	640	valid
321.0ms	642×	body	320	valid
295.0ms	8000×	pre	80	true
65.0ms	296×	body	160	valid
4.0ms	35×	body	80	valid