Details

sample98.0ms

Algorithm

intervals

Results

50.0ms	259×	body	80	valid
4.0ms	3×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3247
4	684
3	220
2	95
1	50
0	21

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

178×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
141×	`prod-diff`
123×	`exp-sum`
71×	`add-cube-cbrt`
66×	`unpow-prod-down`
52×	`distribute-rgt-neg-in`
50×	`distribute-lft-neg-in`
47×	`difference-of-squares`
41×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
15×	`add-log-exp`
11×	`sqr-pow`
8×	`exp-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube` `diff-log`
5×	`neg-mul-1` `rem-exp-log`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `div-inv`
2×	`sub-neg` `neg-log` `associate-*r/`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 226

Calls

4 calls:

16.0ms	(* K (+ m n))
89.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
2.3s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
73.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series766.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* K (+ m n))
432.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
208.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
79.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.2s

Counts

238 → 238

Iterations

Iter	Nodes
done	5001
2	3027
1	1073
0	542

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

330×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
249×	`prod-diff`
138×	`unpow-prod-down`
123×	`exp-sum`
115×	`add-cube-cbrt`
114×	`distribute-rgt-neg-in`
110×	`distribute-lft-neg-in`
96×	`difference-of-squares`
83×	`distribute-lft-out--`
24×	`fma-neg` `add-log-exp`
23×	`times-frac` `sqr-pow`
12×	`diff-log`
11×	`neg-mul-1` `associate--r+`
8×	`exp-prod`
5×	`rem-exp-log`
4×	`pow1` `neg-log` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `flip3--` `exp-diff` `pow-exp` `flip--`

Counts

3 → 347

Calls

3 calls:

1.3s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
70.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
2.4s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series873.0ms

Counts

3 → 9

Calls

3 calls:

304.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
370.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
199.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify2.9s

Counts

356 → 356

Iterations

Iter	Nodes
done	5000
2	2743
1	831
0	394

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

331×	`add-sqr-sqrt`
278×	`*-un-lft-identity`
249×	`prod-diff`
141×	`unpow-prod-down`
123×	`unpow-prod-up`
116×	`add-cube-cbrt`
114×	`distribute-rgt-neg-in`
110×	`distribute-lft-neg-in`
96×	`difference-of-squares`
83×	`distribute-lft-out--`
24×	`fma-neg` `sqr-pow`
23×	`times-frac`
13×	`add-log-exp`
11×	`pow-unpow` `neg-mul-1` `associate--r+`
6×	`diff-log`
5×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `pow-exp` `log1p-expm1-u`
2×	`pow-to-exp` `pow-pow` `neg-log` `associate--r-`
1×	`associate--l-` `neg-sub0` `e-exp-1` `flip3--` `flip--` `pow-sub`

Counts

3 → 350

Calls

3 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
898.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
46.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series921.0ms

Counts

3 → 9

Calls

3 calls:

266.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
252.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
403.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.7s

Counts

359 → 359

Iterations

Iter	Nodes
done	5000
2	4555
1	1276
0	411

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
123×	`unpow-prod-up`
120×	`prod-diff`
81×	`unpow-prod-down`
61×	`add-cube-cbrt`
52×	`distribute-rgt-neg-in`
51×	`difference-of-squares`
50×	`distribute-lft-neg-in`
43×	`distribute-lft-out--`
17×	`pow-unpow`
14×	`sqr-pow`
13×	`times-frac`
8×	`pow1` `add-exp-log`
5×	`neg-mul-1` `pow-exp`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`e-exp-1` `sub-neg` `associate--r-` `pow-sub`

Counts

4 → 215

Calls

4 calls:

838.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
62.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
67.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
72.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

204.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
401.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
459.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
404.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.7s

Counts

227 → 227

Iterations

Iter	Nodes
done	5000
2	3577
1	1114
0	352

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

regimes681.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	33
2	33
1	31
0	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8076×	body	80	valid
154.0ms	118×	body	1280	valid
128.0ms	112×	body	320	valid
98.0ms	141×	body	640	valid
21.0ms	62×	body	160	valid
3.0ms	2×	body	2560	valid