Details

sample280.0ms

Algorithm

intervals

Results

167.0ms	194×	body	1280	valid
48.0ms	108×	body	640	valid
12.0ms	39×	body	320	valid
11.0ms	125×	body	80	valid
5.0ms	23×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
6.3b	(- (exp (- 0.0 im)) (exp im))

rewrite362.0ms

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:

232.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
87.0ms	(- (exp (- 0.0 im)) (exp im))

series216.0ms

Counts

2 → 6

Calls

2 calls:

139.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
77.0ms	(- (exp (- 0.0 im)) (exp im))

simplify1.4s

Counts

276 → 276

Iterations

Iter	Nodes
done	5001
2	3702
1	1050
0	462

prune445.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

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)))))))
0.1b	(* 1/3 (pow im 3))

rewrite32.0ms

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))))
19.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
11.0ms	(* 1/3 (pow im 3))

series785.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
261.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))
444.0ms	(* 1/3 (pow im 3))

simplify704.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
2	1320
1	367
0	146

prune457.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

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))

rewrite18.0ms

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:

12.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))

series730.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
167.0ms	(cbrt (cos re))
171.0ms	(cbrt (cos re))
153.0ms	(cbrt (cos re))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	637
1	152
0	68

prune798.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (cos re) 2) 1/3)
0.2b	(* (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 (cos re) 2)
0.3b	(cbrt (cos re))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
30×	`prod-exp`
25×	`unpow-prod-down`
17×	`pow-exp`
15×	`add-cbrt-cube`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`associate-l` `cbrt-unprod`
9×	`pow-to-exp`
6×	`pow-unpow`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `unpow1/3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `unpow2`
2×	`pow-pow` `distribute-rgt-neg-out`
1×	`distribute-lft-neg-out` `pow1/3` `associate-r` `*-commutative`

Counts

4 → 105

Calls

4 calls:

6.0ms	(pow (pow (cos re) 2) 1/3)
99.0ms	(* (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))))
6.0ms	(pow (cos re) 2)
3.0ms	(cbrt (cos re))

series615.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(pow (pow (cos re) 2) 1/3)
236.0ms	(* (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))))
23.0ms	(pow (cos re) 2)
118.0ms	(cbrt (cos re))

simplify1.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	2272
1	520
0	181

prune878.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes361.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

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

end0.0ms

sample9.8s

Algorithm

intervals

Results

5.3s	5706×	body	1280	valid
2.7s	3622×	body	640	valid
469.0ms	4375×	body	80	valid
461.0ms	1417×	body	320	valid
163.0ms	697×	body	160	valid