Details

sample45.0ms

Algorithm

intervals

Results

20.0ms	262×	body	80	valid
2.0ms	6×	body	640	valid
1.0ms	3×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15
done	5001	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
31.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.9s

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×	`diff-log` `add-cbrt-cube`
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` `associate-*r/` `neg-log`
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:

19.0ms	(* K (+ m n))
1.8s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
56.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series488.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* K (+ m n))
130.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify97.0ms

Counts

238 → 238

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	1015	6007
1	2788	4853
2	5002	3691
done	5002	3691

prune557.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite3.0s

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` `add-exp-log` `neg-log`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `exp-diff` `pow-exp` `flip--`

Counts

3 → 347

Calls

3 calls:

1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.8s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
57.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series603.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
132.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
278.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify107.0ms

Counts

356 → 356

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	783	9869
1	2227	7499
2	5001	5146
done	5001	5146

prune490.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
37.0b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.0b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.0b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod`
81×	`add-sqr-sqrt`
54×	`unpow-prod-down`
42×	`*-un-lft-identity`
22×	`add-cube-cbrt`
16×	`unswap-sqr`
15×	`swap-sqr` `sqr-pow`
14×	`difference-of-squares`
13×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `distribute-lft-out--`
7×	`times-frac`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 137

Calls

4 calls:

383.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
47.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
48.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
315.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
323.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
314.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify81.0ms

Counts

149 → 149

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	331	1916
1	995	1833
2	3474	1717
3	5001	1690
done	5001	1690

prune687.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
31.8b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod`
9×	`times-frac`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 81

Calls

4 calls:

5.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
267.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series513.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (+ m n))
131.0ms	(cbrt (+ m n))
135.0ms	(cbrt (+ m n))
108.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify87.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	427	1747
1	906	1467
2	3154	1458
3	5001	1308
done	5001	1308

prune422.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

regimes148.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.1b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	23
1	29	23
2	29	23
done	29	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

635.0ms	8136×	body	80	valid
68.0ms	124×	body	1280	valid
56.0ms	166×	body	640	valid
21.0ms	89×	body	320	valid
8.0ms	46×	body	160	valid
2.0ms	3×	body	2560	valid