Details

sample120.0ms

Algorithm

intervals

Results

67.0ms	263×	body	80	valid
6.0ms	5×	body	1280	valid
5.0ms	6×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	4997
5	1382
4	501
3	198
2	91
1	50
0	21

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (* (+ m n) (/ K 2.0)) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.1b	(cos (- (* (+ m n) (/ K 2.0)) M))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

7.0ms	(- (fabs (- m n)) l)
12.0ms	(- (* (+ m n) (/ K 2.0)) M)
48.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
46.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series618.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (fabs (- m n)) l)
81.0ms	(- (* (+ m n) (/ K 2.0)) M)
398.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
111.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5004
3	2277
2	792
1	363
0	158

prune610.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

5.0ms	(- (fabs (- m n)) l)
52.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series440.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- (fabs (- m n)) l)
405.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.3s

Counts

40 → 40

Iterations

Iter	Nodes
done	5004
4	3230
3	1147
2	497
1	243
0	104

prune347.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize94.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
41.8b	(cos (* (* (cbrt (- (* (+ m n) (/ K 2.0)) M)) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`

Counts

4 → 46

Calls

4 calls:

23.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
19.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
18.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
325.0ms	(cos (* (* (cbrt (- (* (+ m n) (/ K 2.0)) M)) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

series1.1s

Counts

4 → 12

Calls

4 calls:

337.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
334.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
317.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
78.0ms	(cos (* (* (cbrt (- (* (+ m n) (/ K 2.0)) M)) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5024
3	1987
2	559
1	214
0	94

prune811.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize198.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
12.2b	(cbrt (- (* (+ m n) (/ K 2.0)) M))
42.0b	(cos (* (* (* (* (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`

Counts

4 → 46

Calls

4 calls:

18.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
20.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
18.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
1.4s	(cos (* (* (* (* (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

series1.2s

Counts

4 → 12

Calls

4 calls:

359.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
375.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
368.0ms	(cbrt (- (* (+ m n) (/ K 2.0)) M))
121.0ms	(cos (* (* (* (* (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))

simplify1.7s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
3	2073
2	579
1	223
0	97

prune822.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes583.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.0s	8113×	body	80	valid
152.0ms	139×	body	1280	valid
85.0ms	139×	body	640	valid
56.0ms	103×	body	320	valid
22.0ms	56×	body	160	valid
3.0ms	2×	body	2560	valid