Details

sample106.0ms

Algorithm

intervals

Results

59.0ms	260×	body	80	valid
7.0ms	6×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1365
4	501
3	198
2	91
1	50
0	21

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (* (/ K 2.0) (+ n m)) M)) (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))))
0.0b	(* (/ K 2.0) (+ n m))
0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)
39.2b	(cos (- (* (/ K 2.0) (+ n m)) M))

rewrite4.4s

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt` `associate-l`
11×	`add-exp-log` `times-frac` `associate-r` `add-cbrt-cube`
9×	`pow1`
6×	`unpow-prod-down`
4×	`cos-sum` `exp-sum` `associate--l+` `add-log-exp`
3×	`sub-neg` `pow-unpow` `associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `cos-diff` `pow-to-exp` `pow-pow` `exp-diff` `div-exp` `associate-*l/` `pow-exp` `div-inv` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

4.1s	(* (cos (- (* (/ K 2.0) (+ n m)) M)) (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))))
57.0ms	(* (/ K 2.0) (+ n m))
123.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
93.0ms	(cos (- (* (/ K 2.0) (+ n m)) M))

series1.6s

Counts

4 → 12

Calls

4 calls:

845.0ms	(* (cos (- (* (/ K 2.0) (+ n m)) M)) (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))))
86.0ms	(* (/ K 2.0) (+ n m))
534.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
121.0ms	(cos (- (* (/ K 2.0) (+ n m)) M))

simplify2.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	2106
1	734
0	257

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))
0.0b	(- (/ (+ n m) 2.0) M)
0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)

rewrite582.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`unpow-prod-down` `difference-of-squares`
5×	`add-cube-cbrt` `distribute-lft-out--`
4×	`pow1` `add-exp-log` `diff-log`
3×	`sub-neg` `pow-unpow` `add-cbrt-cube`
2×	`flip3--` `times-frac` `associate--l+` `flip--` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow-pow` `pow-exp`

Counts

3 → 56

Calls

3 calls:

349.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))
105.0ms	(- (/ (+ n m) 2.0) M)
126.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)

series896.0ms

Counts

3 → 9

Calls

3 calls:

341.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))
51.0ms	(- (/ (+ n m) 2.0) M)
503.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)

simplify3.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	2224
2	793
1	346
0	141

prune702.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize122.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ n m))
0.5b	(cbrt (+ n m))
0.5b	(cbrt (+ n m))
39.0b	(cos (- (* (* (/ K 2.0) (* (cbrt (+ n m)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt (+ n m))
7.0ms	(cbrt (+ n m))
8.0ms	(cbrt (+ n m))
1.1s	(cos (- (* (* (/ K 2.0) (* (cbrt (+ n m)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

series984.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (+ n m))
284.0ms	(cbrt (+ n m))
236.0ms	(cbrt (+ n m))
205.0ms	(cos (- (* (* (/ K 2.0) (* (cbrt (+ n m)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

simplify3.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	2455
3	954
2	422
1	189
0	91

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize145.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ n m))
0.5b	(cbrt (+ n m))
0.6b	(cbrt (- n))
35.1b	(cos (- (* (* (/ K 2.0) (* (* (cbrt (- n)) (cbrt -1)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
13×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow1/3`
2×	`cos-sum` `flip3-+` `flip-+` `distribute-lft-out`
1×	`cos-diff` `neg-mul-1` `sub-neg`

Counts

4 → 56

Calls

4 calls:

8.0ms	(cbrt (+ n m))
8.0ms	(cbrt (+ n m))
2.0ms	(cbrt (- n))
1.8s	(cos (- (* (* (/ K 2.0) (* (* (cbrt (- n)) (cbrt -1)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

series1.6s

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt (+ n m))
235.0ms	(cbrt (+ n m))
418.0ms	(cbrt (- n))
646.0ms	(cos (- (* (* (/ K 2.0) (* (* (cbrt (- n)) (cbrt -1)) (cbrt (+ n m)))) (cbrt (+ n m))) M))

simplify3.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5002
3	2550
2	794
1	316
0	149

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes957.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.6s	8083×	body	80	valid
220.0ms	139×	body	1280	valid
139.0ms	145×	body	640	valid
60.0ms	103×	body	320	valid
21.0ms	54×	body	160	valid
4.0ms	2×	body	2560	valid