Details

sample115.0ms

Algorithm

intervals

Results

62.0ms	249×	body	80	valid
10.0ms	9×	body	1280	valid
5.0ms	6×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (166.0ms)

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
23×	`cos-sum`
22×	`times-frac`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`pow1` `add-exp-log`
6×	`neg-mul-1` `diff-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `associate-l` `div-inv`
2×	`associate-*r/` `neg-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

1.7s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
116.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(* K (+ m n))
71.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series836.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
413.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
49.0ms	(* K (+ m n))
88.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.6s

Counts

271 → 271

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	478	11285
1	965	8855
2	2002	7290
done	5001	6172

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

localize17.0ms

Local error

Found 2 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)

rewrite1.9s

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:

1.8s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
115.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series661.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
410.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.2s

Counts

207 → 207

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	274	9396
1	597	7377
2	1263	6047
done	5000	4898

prune757.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

localize65.0ms

Local error

Found 4 expressions with local error:

12.9b	(cbrt (/ (* K (+ m n)) 2.0))
12.9b	(cbrt (/ (* K (+ m n)) 2.0))
33.4b	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
34.1b	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

156×	`prod-diff`
102×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
98×	`cbrt-prod`
80×	`cos-sum` `sin-sum`
60×	`unpow-prod-down` `cube-prod`
42×	`times-frac`
14×	`div-inv`
6×	`cube-mult` `unpow3` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`cos-diff` `sin-diff`

Counts

4 → 216

Calls

4 calls:

16.0ms	(cbrt (/ (* K (+ m n)) 2.0))
14.0ms	(cbrt (/ (* K (+ m n)) 2.0))
122.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
164.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series920.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (/ (* K (+ m n)) 2.0))
271.0ms	(cbrt (/ (* K (+ m n)) 2.0))
190.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
177.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify3.3s

Counts

228 → 228

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	493	14384
1	793	8056
2	1186	6156
3	2611	5792
done	5000	5152

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

localize98.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (* K n))
12.9b	(cbrt (/ (* K (+ m n)) 2.0))
22.6b	(cos (- (pow (* (cbrt 0.5) (cbrt (* K n))) 3) M))
33.4b	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

102×	`prod-diff`
80×	`sin-sum`
64×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`cbrt-prod`
33×	`unpow-prod-down` `cube-prod`
26×	`cos-sum`
21×	`times-frac`
7×	`div-inv`
6×	`cube-mult` `unpow3` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow1/3`
1×	`cos-diff` `cbrt-div` `sin-diff`

Counts

4 → 155

Calls

4 calls:

5.0ms	(cbrt (* K n))
7.0ms	(cbrt (/ (* K (+ m n)) 2.0))
95.0ms	(cos (- (pow (* (cbrt 0.5) (cbrt (* K n))) 3) M))
166.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series658.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (* K n))
250.0ms	(cbrt (/ (* K (+ m n)) 2.0))
108.0ms	(cos (- (pow (* (cbrt 0.5) (cbrt (* K n))) 3) M))
184.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify3.6s

Counts

167 → 167

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	537	9487
1	878	5172
2	1395	4001
3	3241	3767
done	5000	3342

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.7b

regimes965.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	8070×	body	80	valid
596.0ms	123×	body	1280	valid
98.0ms	102×	body	320	valid
94.0ms	133×	body	640	valid
21.0ms	65×	body	160	valid
7.0ms	5×	body	2560	valid