Details

sample153.0ms

Algorithm

intervals

Results

52.0ms	92×	body	1280	valid
33.0ms	99×	body	640	valid
32.0ms	292×	body	80	valid
9.0ms	42×	body	320	valid
3.0ms	16×	body	160	valid

simplify1.4s

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)))

rewrite113.0ms

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:

21.0ms	(+ (exp (- im)) (exp im))
90.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (exp (- im)) (exp im))
90.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify4.8s

Counts

41 → 41

Iterations

Useful iterations: 3 (2.4s)

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

prune122.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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)

rewrite508.0ms

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:

437.0ms	(* (* 0.5 (cos re)) (/ (+ (exp (* im -3)) (exp (* 3 im))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
4.0ms	(exp (* 3 im))
4.0ms	(exp (* im -3))
57.0ms	(+ (exp (+ im im)) -1)

series302.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (* 0.5 (cos re)) (/ (+ (exp (* im -3)) (exp (* 3 im))) (+ (exp (* im -2)) (+ (exp (+ im im)) -1))))
12.0ms	(exp (* 3 im))
12.0ms	(exp (* im -3))
34.0ms	(+ (exp (+ im im)) -1)

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: done (1.6s)

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

prune435.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* im -3))
0.1b	(pow (- (exp (* 2 im)) 1) 3)
0.1b	(cbrt (pow (- (exp (* 2 im)) 1) 3))
5.9b	(- (exp (* 2 im)) 1)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
20×	`cbrt-prod`
14×	`unpow-prod-down` `cube-prod`
10×	`add-cube-cbrt` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `difference-of-sqr-1` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

8.0ms	(exp (* im -3))
45.0ms	(pow (- (exp (* 2 im)) 1) 3)
29.0ms	(cbrt (pow (- (exp (* 2 im)) 1) 3))
16.0ms	(- (exp (* 2 im)) 1)

series150.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp (* im -3))
71.0ms	(pow (- (exp (* 2 im)) 1) 3)
34.0ms	(cbrt (pow (- (exp (* 2 im)) 1) 3))
31.0ms	(- (exp (* 2 im)) 1)

simplify4.5s

Counts

102 → 102

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	123	1384
1	275	1115
2	744	1017
3	4347	939
done	5000	939

prune498.0ms

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)

rewrite691.0ms

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:

8.0ms	(exp (* im -3))
61.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im)))))
552.0ms	(* (* (* 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))))
59.0ms	(+ (exp (+ im im)) -1)

series347.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (* im -3))
120.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (* im -3)) (exp (* 3 im)))))
182.0ms	(* (* (* 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))))
39.0ms	(+ (exp (+ im im)) -1)

simplify2.0s

Counts

130 → 130

Iterations

Useful iterations: done (2.0s)

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

prune557.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
done	13	11

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.9s	2965×	body	1280	valid
1.3s	2465×	body	640	valid
907.0ms	8553×	body	80	valid
641.0ms	1244×	body	320	valid
85.0ms	587×	body	160	valid