Details

sample195.0ms

Algorithm

intervals

Results

107.0ms	108×	body	1280	valid
30.0ms	88×	body	640	valid
21.0ms	267×	body	80	valid
10.0ms	37×	body	320	valid
4.0ms	27×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	23	11
2	57	11
3	89	11
4	119	11
5	153	11
6	217	11
7	346	11
8	382	11
9	418	11
10	474	11
done	474	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (exp (- im)) (exp im))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 12

Calls

1 calls:

19.0ms

(+ (exp (- im)) (exp im))

series54.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(+ (exp (- im)) (exp im))

simplify2.1s

Counts

15 → 15

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	39	157
1	100	149
2	249	130
3	516	129
4	2154	129
done	5000	129

prune64.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/12 (pow im 4)) (+ (pow im 2) 2))
0.0b	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ (pow im 2) 2)))
0.1b	(* 1/12 (pow im 4))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

38.0ms	(+ (* 1/12 (pow im 4)) (+ (pow im 2) 2))
143.0ms	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ (pow im 2) 2)))
18.0ms	(* 1/12 (pow im 4))

series300.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(+ (* 1/12 (pow im 4)) (+ (pow im 2) 2))
179.0ms	(* (* 0.5 (cos re)) (+ (* 1/12 (pow im 4)) (+ (pow im 2) 2)))
47.0ms	(* 1/12 (pow im 4))

simplify1.2s

Counts

69 → 69

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1045
1	356	980
2	1464	860
done	5000	849

prune237.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im)))
0.0b	(* (* 0.5 (cos re)) (/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im))))
8.1b	(- (exp (- im)) (exp im))
8.4b	(- (exp (* im -2)) (exp (+ im im)))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
60×	`times-frac`
38×	`difference-of-squares`
36×	`associate-r`
29×	`add-cube-cbrt`
26×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
12×	`exp-sum`
9×	`pow1`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
5×	`flip3--` `associate-/r*` `flip--`
4×	`associate-/r/`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`frac-2neg` `div-sub` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 143

Calls

4 calls:

123.0ms	(/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im)))
147.0ms	(* (* 0.5 (cos re)) (/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im))))
37.0ms	(- (exp (- im)) (exp im))
22.0ms	(- (exp (* im -2)) (exp (+ im im)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im)))
192.0ms	(* (* 0.5 (cos re)) (/ (- (exp (* im -2)) (exp (+ im im))) (- (exp (- im)) (exp im))))
41.0ms	(- (exp (- im)) (exp im))
56.0ms	(- (exp (* im -2)) (exp (+ im im)))

simplify1.7s

Counts

155 → 155

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	236	3552
1	636	3440
2	2300	3061
done	5001	3015

prune660.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	19	16
done	19	16

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.8s	2946×	body	1280	valid
1.5s	8506×	body	80	valid
910.0ms	2497×	body	640	valid
337.0ms	1176×	body	320	valid
91.0ms	597×	body	160	valid