Details

sample292.0ms

Algorithm

intervals

Results

143.0ms	199×	body	1280	valid
82.0ms	104×	body	640	valid
15.0ms	51×	body	320	valid
14.0ms	165×	body	80	valid
6.0ms	33×	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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.8b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
5.5b	(- (exp (- 0.0 im)) (exp im))

rewrite343.0ms

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:

212.0ms	(* (cos re) (* 0.5 (- (exp (- 0.0 im)) (exp im))))
87.0ms	(- (exp (- 0.0 im)) (exp im))

series201.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(* (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

prune578.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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	(* 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)))))))

rewrite34.0ms

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)))
11.0ms	(* 1/3 (pow im 3))
18.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3))))
83.0ms	(fma 2 im (* 1/3 (pow im 3)))
48.0ms	(* 1/3 (pow im 3))
272.0ms	(* (cos re) (* 0.5 (- (fma 1/60 (pow im 5) (fma 2 im (* 1/3 (pow im 3)))))))

simplify750.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1404
1	380
0	156

prune754.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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))

series668.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
155.0ms	(cbrt (cos re))
135.0ms	(cbrt (cos re))
145.0ms	(cbrt (cos re))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	637
1	152
0	68

prune836.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
33×	`prod-exp`
18×	`add-cbrt-cube`
15×	`cbrt-unprod`
14×	`unpow-prod-down`
13×	`associate-l` `pow-exp`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
7×	`pow-to-exp` `associate-r`
6×	`cbrt-prod`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow1/3` `pow-prod-down` `sqr-pow`
2×	`*-commutative` `unpow2`
1×	`pow-pow` `pow1/3` `distribute-rgt-neg-out`

Counts

4 → 102

Calls

4 calls:

27.0ms	(* (* (- 0.5) (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (cos re)))
71.0ms	(* (pow (pow (cos re) 2) 1/3) (* (* (- 0.5) (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (cos re))))
3.0ms	(pow (cos re) 2)
1.0ms	(cbrt (cos re))

series672.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (* (- 0.5) (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (cos re)))
272.0ms	(* (pow (pow (cos re) 2) 1/3) (* (* (- 0.5) (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))) (cbrt (cos re))))
17.0ms	(pow (cos re) 2)
151.0ms	(cbrt (cos re))

simplify1.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2756
1	533
0	181

prune781.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes587.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

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

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.7s	5684×	body	1280	valid
1.9s	3526×	body	640	valid
916.0ms	1532×	body	320	valid
459.0ms	4370×	body	80	valid
174.0ms	660×	body	160	valid