Details

sample485.0ms

Algorithm

intervals

Results

321.0ms	111×	body	2560	valid
89.0ms	69×	body	1280	valid
39.0ms	53×	body	640	valid
11.0ms	256×	pre	80	true
8.0ms	15×	body	320	valid
3.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
2.1b	(- (/ 1 x) (/ 1 (tan x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
33×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 262

Calls

2 calls:

13.0ms	(/ 1 (tan x))
70.0ms	(- (/ 1 x) (/ 1 (tan x)))

series140.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ 1 (tan x))
95.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.2s

Counts

268 → 268

Iterations

Iter	Nodes
done	2001
3	2001
2	1356
1	762
0	342

prune786.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow x 5) 2/945)
0.3b	(* x 1/45)
0.3b	(fma 1/3 x (* (pow x 5) 2/945))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`associate-l` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`add-cbrt-cube`
6×	`associate-r`
5×	`pow1`
4×	`unpow-prod-down` `prod-exp` `unswap-sqr`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `cbrt-unprod` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `fma-udef`

Counts

3 → 60

Calls

3 calls:

9.0ms	(* (pow x 5) 2/945)
12.0ms	(* x 1/45)
1.0ms	(fma 1/3 x (* (pow x 5) 2/945))

series329.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(* (pow x 5) 2/945)
25.0ms	(* x 1/45)
208.0ms	(fma 1/3 x (* (pow x 5) 2/945))

simplify1.3s

Counts

69 → 69

Iterations

Iter	Nodes
done	2003
4	2003
3	1470
2	463
1	190
0	94

prune381.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

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` `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:

16.0ms	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
2.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
2.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
2.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

series3.8s

Counts

4 → 12

Calls

4 calls:

920.0ms	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
941.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
984.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1000.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
3	2000
2	789
1	308
0	137

prune520.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.7b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.7b	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`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 → 54

Calls

4 calls:

1.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
7.0ms	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))

series3.7s

Counts

4 → 12

Calls

4 calls:

817.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1.1s	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
821.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
946.0ms	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))

simplify1.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	2012
4	2012
3	1659
2	633
1	255
0	118

prune483.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes92.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample17.6s

Algorithm

intervals

Results

10.6s	3272×	body	2560	valid
4.3s	2466×	body	1280	valid
1.2s	1279×	body	640	valid
545.0ms	305×	body	160	valid
461.0ms	634×	body	320	valid
325.0ms	8000×	pre	80	true
9.0ms	44×	body	80	valid