Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	259×	body	80	valid
2.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	92	29
3	195	29
4	428	28
5	1228	28
6	4591	28
done	5000	28

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
6×	`unpow-prod-down`
5×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `cos-sum` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 44

Calls

3 calls:

9.0ms	(- (/ (* K (+ m n)) 2.0) M)
36.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
16.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series379.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (/ (* K (+ m n)) 2.0) M)
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.7s

Counts

53 → 53

Iterations

Useful iterations: 4 (752.0ms)

Iter	Nodes	Cost
0	130	801
1	273	757
2	563	706
3	1409	699
4	4771	691
done	5000	691

prune230.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

36.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series267.0ms

Counts

1 → 3

Calls

1 calls:

267.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify958.0ms

Counts

23 → 23

Iterations

Useful iterations: 4 (309.0ms)

Iter	Nodes	Cost
0	74	337
1	157	318
2	305	305
3	678	304
4	1668	296
done	5001	296

prune90.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.3b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.3b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
44.7b	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`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--` `difference-of-squares`

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
7.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
7.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
29.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series786.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
239.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
244.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
55.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify1.9s

Counts

64 → 64

Iterations

Useful iterations: 4 (865.0ms)

Iter	Nodes	Cost
0	97	1446
1	213	1414
2	492	1086
3	1361	1020
4	4954	978
done	5000	978

prune355.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.5b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`cbrt-prod` `add-cube-cbrt` `unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `cos-sum` `pow-pow` `unpow3` `pow-exp` `difference-of-squares`
1×	`cos-diff` `sub-neg` `times-frac` `pow1/3` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 74

Calls

4 calls:

37.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
2.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
2.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series507.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
126.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.3s

Counts

86 → 86

Iterations

Useful iterations: 3 (299.0ms)

Iter	Nodes	Cost
0	143	1527
1	294	1307
2	643	1175
3	2472	1174
done	5001	1174

prune341.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

regimes219.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
done	21	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

616.0ms	8091×	body	80	valid
53.0ms	160×	body	640	valid
52.0ms	103×	body	1280	valid
28.0ms	120×	body	320	valid
9.0ms	56×	body	160	valid
4.0ms	2×	body	2560	valid