Details

sample129.0ms

Algorithm

intervals

Results

68.0ms	172×	body	1280	valid
27.0ms	118×	body	640	valid
7.0ms	44×	body	320	valid
6.0ms	148×	body	80	valid
2.0ms	20×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	21	12
2	44	12
3	99	12
4	183	12
5	266	12
6	403	12
7	448	12
8	695	12
9	1360	12
10	1826	12
11	1864	12
12	1902	12
done	1902	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
7.1b	(- (exp (- 0.0 im)) (exp im))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`add-cube-cbrt` `sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 40

Calls

2 calls:

113.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
55.0ms	(- (exp (- 0.0 im)) (exp im))

series121.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
37.0ms	(- (exp (- 0.0 im)) (exp im))

simplify2.0s

Counts

46 → 46

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	103	679
1	266	661
2	921	568
3	3533	565
done	5002	563

prune111.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`associate-l`
13×	`associate-r` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `associate-*r/` `pow-exp`
1×	`+-commutative` `cube-mult` `flip3--` `flip3-+` `unpow3` `sum-log` `flip--` `flip-+`

Counts

4 → 91

Calls

4 calls:

9.0ms	(+ (* 1/60 (pow im 5)) (* 2 im))
11.0ms	(* 1/60 (pow im 5))
66.0ms	(* (* 0.5 (cos re)) (- (* (pow im 3) -1/3) (+ (* 1/60 (pow im 5)) (* 2 im))))
13.0ms	(* (pow im 3) -1/3)

series398.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (* 1/60 (pow im 5)) (* 2 im))
51.0ms	(* 1/60 (pow im 5))
174.0ms	(* (* 0.5 (cos re)) (- (* (pow im 3) -1/3) (+ (* 1/60 (pow im 5)) (* 2 im))))
36.0ms	(* (pow im 3) -1/3)

simplify1.1s

Counts

103 → 103

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	183	1415
1	476	1298
2	1702	1166
done	5000	1158

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
27×	`prod-exp`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-l`
14×	`pow1`
13×	`cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in` `associate-r`
7×	`unswap-sqr`
6×	`pow-prod-down`
4×	`pow-to-exp` `sub-neg` `cube-prod` `associate-r/` `pow-exp` `-commutative` `add-log-exp` `sqr-pow`
1×	`cube-mult` `flip3--` `unpow3` `flip--`

Counts

4 → 108

Calls

4 calls:

12.0ms	(* (pow im 5) -1/60)
33.0ms	(* (* 0.5 (cos re)) (* (pow im 3) -1/3))
56.0ms	(* (cos re) (* 0.5 (- (* (pow im 5) -1/60) (* 2 im))))
13.0ms	(* (pow im 3) -1/3)

series455.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (pow im 5) -1/60)
93.0ms	(* (* 0.5 (cos re)) (* (pow im 3) -1/3))
272.0ms	(* (cos re) (* 0.5 (- (* (pow im 5) -1/60) (* 2 im))))
36.0ms	(* (pow im 3) -1/3)

simplify1.0s

Counts

120 → 120

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	200	1470
1	506	1336
2	1957	1174
done	5000	1166

prune317.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

13.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))
1.0ms	(cbrt (cos re))

series455.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cbrt (cos re)) (cbrt (cos re)))
98.0ms	(cbrt (cos re))
98.0ms	(cbrt (cos re))
99.0ms	(cbrt (cos re))

simplify3.8s

Counts

85 → 85

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	64	686
1	122	615
2	336	521
3	1145	499
4	4976	492
done	5001	492

prune295.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	25
1	28	25
done	28	25

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.3s	5766×	body	1280	valid
824.0ms	3498×	body	640	valid
215.0ms	1448×	body	320	valid
195.0ms	4456×	body	80	valid
64.0ms	678×	body	160	valid