Details

sample76.0ms

Algorithm

intervals

Results

44.0ms	255×	body	80	valid
4.0ms	6×	body	640	valid
3.0ms	3×	body	1280	valid
2.0ms	4×	body	320	valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (134.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	197	29
4	465	28
5	1141	28
6	4709	28
done	5000	28

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `unpow-prod-down`
6×	`add-cbrt-cube`
5×	`difference-of-squares`
4×	`associate-r` `distribute-lft-out--`
3×	`sub-neg` `pow-unpow` `diff-log` `associate-l`
2×	`cos-sum` `associate-*r/` `associate--l+` `sqr-pow`
1×	`associate--l-` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

259.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
26.0ms	(* K (+ m n))
96.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
49.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series804.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
58.0ms	(* K (+ m n))
408.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.9s

Counts

86 → 86

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	187	1305
1	418	1230
2	996	1151
3	2982	1145
done	5000	1137

prune495.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

345.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
83.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series678.0ms

Counts

2 → 6

Calls

2 calls:

285.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
392.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.2s

Counts

47 → 47

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	120	902
1	261	848
2	556	809
3	1585	803
done	5001	791

prune266.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

2.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
150.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series994.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt K)
305.0ms	(cbrt K)
289.0ms	(cbrt K)
142.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify2.9s

Counts

55 → 55

Iterations

Useful iterations: 3 (205.0ms)

Iter	Nodes	Cost
0	60	516
1	112	498
2	249	386
3	596	335
4	2147	335
done	5000	335

prune417.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ K (/ 2.0 (+ m n))) M)))
33.8b	(cos (- (/ K (/ 2.0 (+ m n))) M))
33.8b	(cos (- (/ K (/ 2.0 (+ m n))) M))
33.8b	(cos (- (/ K (/ 2.0 (+ m n))) M))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

4.0ms	(cbrt (cos (- (/ K (/ 2.0 (+ m n))) M)))
154.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))
141.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))
184.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))

series516.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt (cos (- (/ K (/ 2.0 (+ m n))) M)))
111.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))
88.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))
85.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	48	853
1	80	828
2	124	730
3	192	727
4	288	727
5	534	727
6	1484	727
done	5000	687

prune431.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.0b

regimes336.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	19
1	20	17
done	20	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	8072×	body	80	valid
531.0ms	123×	body	1280	valid
149.0ms	167×	body	640	valid
97.0ms	100×	body	320	valid
14.0ms	42×	body	160	valid
8.0ms	6×	body	2560	valid