Details

sample180.0ms

Algorithm

intervals

Results

64.0ms	99×	body	640	valid
56.0ms	92×	body	1280	valid
23.0ms	292×	body	80	valid
10.0ms	42×	body	320	valid
3.0ms	16×	body	160	valid

simplify1.3s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

38.0ms	(+ (exp (- im)) (exp im))
103.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series120.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (exp (- im)) (exp im))
86.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify4.5s

Counts

41 → 41

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	87	548
1	244	530
2	988	441
3	4297	437
done	5000	437

prune150.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (/ (+ (exp (* im -3)) (exp (* 3 im))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
0.0b	(exp (* 3 im))
0.0b	(exp (* im -3))
5.9b	(+ (exp (+ im im)) -1)

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
26×	`associate-r`
20×	`times-frac`
18×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
3×	`pow-prod-down`
2×	`cbrt-undiv` `difference-of-sqr--1` `exp-prod` `exp-to-pow` `flip3-+` `div-exp` `associate-/r/` `flip-+` `rem-exp-log`
1×	`+-commutative` `associate-r/` `associate-l` `exp-sum` `sum-log` `-commutative` `div-inv`

Counts

4 → 80

Calls

4 calls:

525.0ms	(* (* 0.5 (cos re)) (/ (+ (exp (* im -3)) (exp (* 3 im))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
8.0ms	(exp (* 3 im))
9.0ms	(exp (* im -3))
65.0ms	(+ (exp (+ im im)) -1)

series227.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (* 0.5 (cos re)) (/ (+ (exp (* im -3)) (exp (* 3 im))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
7.0ms	(exp (* 3 im))
7.0ms	(exp (* im -3))
28.0ms	(+ (exp (+ im im)) -1)

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	174	1795
1	482	1711
2	1812	1418
done	5000	1401

prune456.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize385.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 3 im))
0.0b	(exp (* im -3))
5.9b	(log (exp (+ (exp (+ im im)) -1)))
5.9b	(+ (exp (+ im im)) -1)

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt` `exp-prod`
7×	`log-pow`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `difference-of-sqr--1` `log-prod` `add-cbrt-cube`
3×	`exp-sum`
2×	`exp-to-pow` `rem-exp-log` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 53

Calls

4 calls:

9.0ms	(exp (* 3 im))
11.0ms	(exp (* im -3))
201.0ms	(log (exp (+ (exp (+ im im)) -1)))
52.0ms	(+ (exp (+ im im)) -1)

series78.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (* 3 im))
11.0ms	(exp (* im -3))
35.0ms	(log (exp (+ (exp (+ im im)) -1)))
21.0ms	(+ (exp (+ im im)) -1)

simplify4.1s

Counts

65 → 65

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	98	560
1	195	500
2	441	438
3	1041	419
4	4353	409
done	5000	407

prune471.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* im -3))
0.2b	(* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im)))))
0.7b	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im))))) (/ (sqrt (+ (exp (* im -3)) (exp (* 3 im)))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
5.9b	(+ (exp (+ im im)) -1)

rewrite802.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
48×	`associate-r`
35×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`distribute-lft-out`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `sqrt-prod`
18×	`pow1`
15×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
8×	`add-log-exp`
7×	`associate-*r/`
6×	`sqrt-div`
5×	`flip3-+` `flip-+`
3×	`cbrt-undiv` `div-exp`
2×	`difference-of-sqr--1` `frac-times` `associate-l` `associate-l/` `associate-/r/` `-commutative`
1×	`+-commutative` `exp-prod` `exp-to-pow` `exp-sum` `sum-log` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

9.0ms	(exp (* im -3))
101.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im)))))
624.0ms	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im))))) (/ (sqrt (+ (exp (* im -3)) (exp (* 3 im)))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
57.0ms	(+ (exp (+ im im)) -1)

series339.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(exp (* im -3))
112.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im)))))
187.0ms	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im))))) (/ (sqrt (+ (exp (* im -3)) (exp (* 3 im)))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
33.0ms	(+ (exp (+ im im)) -1)

simplify2.1s

Counts

130 → 130

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	238	4053
1	671	3363
2	2681	2821
done	5000	2817

prune614.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

Details

sample180.0ms

simplify1.3s

prune3.0ms

localize12.0ms

rewrite142.0ms

series120.0ms

simplify4.5s

prune150.0ms

localize25.0ms

rewrite614.0ms

series227.0ms

simplify1.4s

prune456.0ms

localize385.0ms

rewrite274.0ms

series78.0ms

simplify4.1s

prune471.0ms

localize39.0ms

rewrite802.0ms

series339.0ms

simplify2.1s

prune614.0ms

regimes2.0ms