Details

sample224.0ms

Algorithm

intervals

Results

110.0ms	175×	body	1280	valid
68.0ms	112×	body	640	valid
12.0ms	53×	body	320	valid
11.0ms	160×	body	80	valid
2.0ms	17×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4670
5	708
4	212
3	104
2	44
1	21
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.2b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
5.0b	(- (exp (- 0.0 im)) (exp im))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

354×	`prod-diff`
187×	`add-sqr-sqrt` `*-un-lft-identity`
185×	`add-cube-cbrt`
176×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
21×	`sub-neg`
14×	`fma-neg`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`associate-*r/` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
1×	`diff-log` `associate-r` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 270

Calls

2 calls:

204.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
124.0ms	(- (exp (- 0.0 im)) (exp im))

series173.0ms

Counts

2 → 6

Calls

2 calls:

122.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
51.0ms	(- (exp (- 0.0 im)) (exp im))

simplify1.2s

Counts

276 → 276

Iterations

Iter	Nodes
done	5001
2	3702
1	1050
0	462

prune533.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
0.0b	(fma 2 im (* 1/3 (pow im 3)))
0.1b	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
0.1b	(* 1/3 (pow im 3))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `prod-exp` `fma-udef`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-neg-in` `unpow-prod-down` `distribute-lft-in` `cube-prod` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`*-commutative` `distribute-rgt-neg-out` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
0.0ms	(fma 2 im (* 1/3 (pow im 3)))
35.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
28.0ms	(* 1/3 (pow im 3))

series567.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
151.0ms	(fma 2 im (* 1/3 (pow im 3)))
246.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
73.0ms	(* 1/3 (pow im 3))

simplify730.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1390
1	380
0	156

prune600.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos re)) (cbrt (cos re)))
0.2b	(cbrt (cos re))
0.2b	(cbrt (cos re))
0.2b	(cbrt (cos re))

rewrite29.0ms

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:

14.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
10.0ms	(cbrt (cos re))
2.0ms	(cbrt (cos re))
2.0ms	(cbrt (cos re))

series786.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
168.0ms	(cbrt (cos re))
160.0ms	(cbrt (cos re))
173.0ms	(cbrt (cos re))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	637
1	152
0	68

prune737.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow im 3) 1/3)
0.2b	(* (pow (pow (cos re) 2) 1/3) (- (* (* (fma (pow im 5) 1/60 (fma 2 im (* (pow im 3) 1/3))) 0.5) (cbrt (cos re)))))
0.2b	(pow (cos re) 2)
0.2b	(cbrt (cos re))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`associate-l`
23×	`unpow-prod-down`
18×	`add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`unswap-sqr`
9×	`add-cbrt-cube` `associate-r`
8×	`prod-exp`
7×	`sqr-pow`
6×	`pow-exp`
5×	`pow1`
4×	`expm1-log1p-u` `pow-to-exp` `cube-prod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `cbrt-unprod` `unpow2`
2×	`*-commutative`
1×	`distribute-lft-neg-in` `cube-mult` `neg-mul-1` `pow-pow` `distribute-rgt-neg-in` `unpow1/3` `pow1/3` `unpow3` `distribute-rgt-neg-out`

Counts

4 → 108

Calls

4 calls:

17.0ms	(* (pow im 3) 1/3)
51.0ms	(* (pow (pow (cos re) 2) 1/3) (- (* (* (fma (pow im 5) 1/60 (fma 2 im (* (pow im 3) 1/3))) 0.5) (cbrt (cos re)))))
4.0ms	(pow (cos re) 2)
2.0ms	(cbrt (cos re))

series475.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (pow im 3) 1/3)
243.0ms	(* (pow (pow (cos re) 2) 1/3) (- (* (* (fma (pow im 5) 1/60 (fma 2 im (* (pow im 3) 1/3))) 0.5) (cbrt (cos re)))))
26.0ms	(pow (cos re) 2)
140.0ms	(cbrt (cos re))

simplify1.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2235
1	505
0	194

prune873.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes431.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	34
3	34
2	30
1	22
0	17

end0.0ms

sample10.1s

Algorithm

intervals

Results

5.6s	5871×	body	1280	valid
1.7s	3597×	body	640	valid
1.0s	702×	body	160	valid
888.0ms	1462×	body	320	valid
415.0ms	4417×	body	80	valid