Details

sample90.0ms

Algorithm

intervals

Results

32.0ms	259×	body	80	valid
2.0ms	4×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3032
4	640
3	210
2	93
1	50
0	21

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize92.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (/ K 2.0) (+ m n)) M)
0.0b	(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.6b	(cos (- (* (/ K 2.0) (+ m n)) M))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

21.0ms	(- (* (/ K 2.0) (+ m n)) M)
3.0s	(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
76.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
47.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

series718.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (/ K 2.0) (+ m n)) M)
189.0ms	(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
347.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
78.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1350
1	450
0	195

prune646.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.6s	(- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l)
147.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
3.1s	(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
57.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

298.0ms	(- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l)
175.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
234.0ms	(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
338.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1172
1	429
0	170

prune622.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize152.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
42.8b	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

rewrite357.0ms

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:

11.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
18.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
22.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
304.0ms	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

series1.1s

Counts

4 → 12

Calls

4 calls:

335.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
390.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
343.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
78.0ms	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

simplify1.9s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
3	2854
2	600
1	212
0	91

prune753.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize198.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
11.5b	(cbrt (- (* (/ K 2.0) (+ m n)) M))
42.6b	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (* (cbrt (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M)))) (cbrt (cbrt (- (* (/ K 2.0) (+ m n)) M))))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

rewrite2.3s

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:

17.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
21.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
16.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
2.2s	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (* (cbrt (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M)))) (cbrt (cbrt (- (* (/ K 2.0) (+ m n)) M))))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

series1.2s

Counts

4 → 12

Calls

4 calls:

334.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
354.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
397.0ms	(cbrt (- (* (/ K 2.0) (+ m n)) M))
97.0ms	(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (* (cbrt (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M)))) (cbrt (cbrt (- (* (/ K 2.0) (+ m n)) M))))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	2876
2	621
1	220
0	94

prune860.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes659.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
2	21
1	20
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.0s	8067×	body	80	valid
137.0ms	99×	body	1280	valid
130.0ms	137×	body	640	valid
67.0ms	70×	body	160	valid
57.0ms	117×	body	320	valid
3.0ms	2×	body	2560	valid