Details

sample492.0ms

Algorithm

intervals

Results

308.0ms	101×	body	2560	valid
116.0ms	89×	body	1280	valid
27.0ms	34×	body	640	valid
13.0ms	20×	body	320	valid
11.0ms	256×	pre	80	true
3.0ms	11×	body	160	valid
0.0ms	1×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
2.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite54.0ms

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:

6.0ms	(/ 1 (tan x))
32.0ms	(- (/ 1 x) (/ 1 (tan x)))

series179.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ 1 (tan x))
116.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify938.0ms

Counts

268 → 268

Iterations

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

prune2.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow x 5) 2/945)
0.2b	(* x 1/45)
0.3b	(fma 1/3 x (* (pow x 5) 2/945))

rewrite17.0ms

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:

8.0ms	(* (pow x 5) 2/945)
7.0ms	(* x 1/45)
1.0ms	(fma 1/3 x (* (pow x 5) 2/945))

series291.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* (pow x 5) 2/945)
35.0ms	(* x 1/45)
163.0ms	(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

prune736.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize47.0ms

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)))

rewrite21.0ms

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:

15.0ms	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (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)))
1.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

series3.3s

Counts

4 → 12

Calls

4 calls:

756.0ms	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
768.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
897.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
878.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

simplify1.0s

Counts

97 → 97

Iterations

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

prune930.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize71.0ms

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

rewrite5.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

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

series3.5s

Counts

4 → 12

Calls

4 calls:

768.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
807.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1.1s	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
819.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

simplify981.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	2002
4	2002
3	938
2	350
1	147
0	69

prune806.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.2b

regimes93.0ms

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	13
1	13
0	11

end0.0ms

sample14.6s

Algorithm

intervals

Results

8.7s	3190×	body	2560	valid
3.8s	2568×	body	1280	valid
1.1s	1249×	body	640	valid
416.0ms	628×	body	320	valid
307.0ms	8000×	pre	80	true
112.0ms	322×	body	160	valid
7.0ms	43×	body	80	valid