Details

sample302.0ms

Algorithm

intervals

Results

189.0ms	103×	body	2560	valid
66.0ms	79×	body	1280	valid
18.0ms	42×	body	640	valid
5.0ms	17×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify47.0ms

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: 59.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite78.0ms

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:

7.0ms	(/ 1.0 (tan x))
41.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 1.0 (tan x))
123.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	2774
1	843
0	369

prune896.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))
0.0b	(fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (* x x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

0.0ms	(fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))
0.0ms	(fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))
20.0ms	(* 0.022222222222222223 (* x x))

series269.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))
95.0ms	(fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))
35.0ms	(* 0.022222222222222223 (* x x))

simplify965.0ms

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
2	820
1	161
0	70

prune205.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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:

9.0ms	(* (cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))) (cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))))
1.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

429.0ms	(* (cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))) (cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x)))))
354.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
293.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
295.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1660
1	437
0	173

prune581.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series1.6s

Counts

4 → 12

Calls

4 calls:

396.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
396.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
422.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))
369.0ms	(cbrt (fma (* 0.022222222222222223 (* x x)) x (fma (pow x 5) 0.0021164021164021165 (* 0.3333333333333333 x))))

simplify2.8s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4642
2	677
1	209
0	90

prune530.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 0.2b

regimes156.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample13.4s

Algorithm

intervals

Results

8.4s	3279×	body	2560	valid
3.0s	2515×	body	1280	valid
1.2s	1225×	body	640	valid
251.0ms	632×	body	320	valid
165.0ms	8000×	pre	80	true
70.0ms	300×	body	160	valid
5.0ms	49×	body	80	valid