Details

sample50.0ms

Algorithm

intervals

Results

23.0ms	267×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	3×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (86.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	207	29
4	499	28
5	1209	28
6	4807	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(/ (* K (+ m n)) 2.0)
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

193×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
72×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
49×	`difference-of-squares`
42×	`distribute-lft-out--`
24×	`times-frac` `fma-neg`
23×	`cos-sum`
14×	`add-log-exp`
12×	`sqr-pow`
11×	`add-exp-log` `add-cbrt-cube` `associate--r+`
6×	`pow1` `neg-mul-1` `diff-log`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `log1p-expm1-u` `div-inv`
3×	`sub-neg` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `neg-log` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `flip--` `distribute-lft-out` `associate-/l` `associate--r-` `unswap-sqr`

Counts

4 → 262

Calls

4 calls:

1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
18.0ms	(* K (+ m n))
13.0ms	(/ (* K (+ m n)) 2.0)
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series328.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
27.0ms	(* K (+ m n))
43.0ms	(/ (* K (+ m n)) 2.0)
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

274 → 274

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	474	11220
1	978	8803
2	2198	7196
done	5000	6078

prune701.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

53.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series462.0ms

Counts

2 → 6

Calls

2 calls:

269.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
193.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify809.0ms

Counts

207 → 207

Iterations

Useful iterations: done (800.0ms)

Iter	Nodes	Cost
0	274	9396
1	597	7377
2	1262	6047
done	5000	4898

prune398.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
34.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
33.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series346.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.2s

Counts

124 → 124

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	190	5299
1	300	4088
2	413	3412
3	711	2959
4	1159	2527
5	1837	1537
6	3519	1510
done	5001	1470

prune395.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(log1p (cbrt (cos (- (/ (* K (+ m n)) 2.0) M))))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `sub-neg`
1×	`log1p-udef` `log1p-expm1`

Counts

4 → 110

Calls

4 calls:

0.0ms	(log1p (cbrt (cos (- (/ (* K (+ m n)) 2.0) M))))
34.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
33.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series468.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(log1p (cbrt (cos (- (/ (* K (+ m n)) 2.0) M))))
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.0s

Counts

122 → 122

Iterations

Useful iterations: 6 (1.7s)

Iter	Nodes	Cost
0	194	5258
1	306	4042
2	419	3364
3	716	2914
4	1105	2482
5	1676	1492
6	2753	1465
done	5000	1465

prune363.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes237.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample1.2s

Algorithm

intervals

Results

619.0ms	8087×	body	80	valid
61.0ms	133×	body	1280	valid
48.0ms	151×	body	640	valid
25.0ms	108×	body	320	valid
9.0ms	58×	body	160	valid
3.0ms	4×	body	2560	valid