Details

sample344.0ms

Algorithm

intervals

Results

188.0ms	93×	body	2560	valid
102.0ms	81×	body	1280	valid
21.0ms	44×	body	640	valid
7.0ms	25×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	13×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	8
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
4.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite140.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`

Counts

2 → 251

Calls

2 calls:

13.0ms	(/ 1.0 (tan x))
72.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series384.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(/ 1.0 (tan x))
250.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify4.3s

Counts

257 → 257

Iterations

Iter	Nodes
done	5000
2	1988
1	844
0	371

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

1.0ms	(fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))
21.0ms	(* x (* x 0.022222222222222223))

series137.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))
32.0ms	(* x (* x 0.022222222222222223))

simplify3.5s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
3	1841
2	420
1	136
0	60

prune316.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize81.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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` `insert-posit16` `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 → 85

Calls

4 calls:

26.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))

series1.6s

Counts

4 → 12

Calls

4 calls:

415.0ms	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
408.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
422.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
368.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))

simplify5.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	3788
2	1156
1	444
0	175

prune1.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

localize150.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 65

Calls

4 calls:

2.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
2.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
2.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
3.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

459.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333))))
366.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
347.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
336.0ms	(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* x (+ (* x (* x 0.022222222222222223)) 0.3333333333333333)))))

simplify5.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5064
3	3254
2	938
1	345
0	144

prune1.0s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 0.1b

regimes332.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample12.9s

Algorithm

intervals

Results

9.0s	3245×	body	2560	valid
2.3s	2537×	body	1280	valid
666.0ms	1242×	body	640	valid
246.0ms	612×	body	320	valid
189.0ms	8000×	pre	80	true
69.0ms	313×	body	160	valid
6.0ms	51×	body	80	valid