Details

sample274.0ms

Algorithm

intervals

Results

170.0ms	174×	body	1280	valid
49.0ms	116×	body	640	valid
12.0ms	144×	body	80	valid
11.0ms	41×	body	320	valid
3.0ms	19×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.4b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
6.2b	(- (exp (- 0.0 im)) (exp im))

rewrite446.0ms

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:

281.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
126.0ms	(- (exp (- 0.0 im)) (exp im))

series165.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
59.0ms	(- (exp (- 0.0 im)) (exp im))

simplify1.4s

Counts

276 → 276

Iterations

Iter	Nodes
done	5001
2	3702
1	1050
0	462

prune453.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (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)))))))
0.2b	(* 1/3 (pow im 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma 1/60 (pow im 5) (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)))))))
22.0ms	(* 1/3 (pow im 3))

series355.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
234.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
52.0ms	(* 1/3 (pow im 3))

simplify711.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
2	1320
1	367
0	146

prune518.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos re)) (cbrt (cos re)))
0.3b	(cbrt (cos re))
0.3b	(cbrt (cos re))
0.3b	(cbrt (cos re))

rewrite25.0ms

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:

11.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))

series660.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
131.0ms	(cbrt (cos re))
137.0ms	(cbrt (cos re))
168.0ms	(cbrt (cos re))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	637
1	152
0	68

prune759.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (pow (cos re) 2) 1/3) (* (* 0.5 (- (fma im 2 (fma (pow im 5) 1/60 (* (pow im 3) 1/3))))) (cbrt (cos re))))
0.2b	(* (pow im 3) 1/3)
0.3b	(pow (cos re) 2)
0.3b	(cbrt (cos re))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
33×	`prod-exp`
24×	`associate-l`
21×	`add-sqr-sqrt`
18×	`unpow-prod-down`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `pow-exp` `add-cube-cbrt`
13×	`cbrt-unprod`
8×	`pow-to-exp`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `cube-prod` `associate-r` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-prod` `pow-unpow` `unpow1/3`
2×	`*-commutative` `distribute-rgt-neg-out` `unpow2`
1×	`distribute-lft-neg-out` `cube-mult` `pow-pow` `pow1/3` `unpow3`

Counts

4 → 111

Calls

4 calls:

125.0ms	(* (pow (pow (cos re) 2) 1/3) (* (* 0.5 (- (fma im 2 (fma (pow im 5) 1/60 (* (pow im 3) 1/3))))) (cbrt (cos re))))
22.0ms	(* (pow im 3) 1/3)
5.0ms	(pow (cos re) 2)
2.0ms	(cbrt (cos re))

series469.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (pow (pow (cos re) 2) 1/3) (* (* 0.5 (- (fma im 2 (fma (pow im 5) 1/60 (* (pow im 3) 1/3))))) (cbrt (cos re))))
54.0ms	(* (pow im 3) 1/3)
32.0ms	(pow (cos re) 2)
155.0ms	(cbrt (cos re))

simplify1.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	2534
1	567
0	205

prune735.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes360.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify5.0ms

Iterations

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

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.6s	5713×	body	1280	valid
2.6s	3549×	body	640	valid
681.0ms	654×	body	160	valid
674.0ms	1508×	body	320	valid
583.0ms	4355×	body	80	valid