Details

sample481.0ms

Algorithm

intervals

Results

303.0ms	102×	body	2560	valid
93.0ms	69×	body	1280	valid
46.0ms	51×	body	640	valid
11.0ms	19×	body	320	valid
10.0ms	256×	pre	80	true
5.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.5b	(- (/ 1 x) (/ 1 (tan x)))

rewrite75.0ms

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:

10.0ms	(/ 1 (tan x))
58.0ms	(- (/ 1 x) (/ 1 (tan x)))

series157.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ 1 (tan x))
105.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify806.0ms

Counts

268 → 268

Iterations

Iter	Nodes
done	2001
2	1356
1	762
0	342

prune639.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

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))

rewrite28.0ms

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:

16.0ms	(* (pow x 5) 2/945)
10.0ms	(* x 1/45)
0.0ms	(fma 1/3 x (* (pow x 5) 2/945))

series304.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (pow x 5) 2/945)
15.0ms	(* x 1/45)
217.0ms	(fma 1/3 x (* (pow x 5) 2/945))

simplify876.0ms

Counts

69 → 69

Iterations

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

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize40.0ms

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))))
0.6b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.6b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.6b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

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` `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:

10.0ms	(* (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)))

series3.5s

Counts

4 → 12

Calls

4 calls:

922.0ms	(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
796.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
849.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
932.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

simplify607.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
2	789
1	308
0	137

prune471.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.6b	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
0.6b	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))
0.7b	(cbrt (cbrt (fma 1/3 x (* (pow x 5) 2/945))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

16×	`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 → 57

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)))
4.0ms	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))
1.0ms	(cbrt (cbrt (fma 1/3 x (* (pow x 5) 2/945))))

series3.5s

Counts

4 → 12

Calls

4 calls:

846.0ms	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1.1s	(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
848.0ms	(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))
758.0ms	(cbrt (cbrt (fma 1/3 x (* (pow x 5) 2/945))))

simplify750.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
2	864
1	344
0	159

prune447.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes103.0ms

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

sample15.1s

Algorithm

intervals

Results

9.1s	3245×	body	2560	valid
3.4s	2491×	body	1280	valid
1.6s	1284×	body	640	valid
345.0ms	634×	body	320	valid
320.0ms	8000×	pre	80	true
104.0ms	304×	body	160	valid
8.0ms	42×	body	80	valid