Details

sample49.0ms

Algorithm

intervals

Results

22.0ms	254×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	7×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (81.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (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))
38.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite5.6s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

5.5s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(* K (+ m n))
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series747.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(* K (+ m n))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.7s

Counts

87 → 87

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	205	1657
1	490	1601
2	1317	1414
3	4420	1395
done	5001	1394

prune370.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.2b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

55.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series260.0ms

Counts

1 → 3

Calls

1 calls:

260.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.6s

Counts

23 → 23

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	74	337
1	157	318
2	312	305
3	731	304
4	1771	296
done	5001	295

prune94.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt K)
0.5b	(cbrt K)
0.5b	(cbrt K)
37.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite89.0ms

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:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
85.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series628.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt K)
174.0ms	(cbrt K)
175.0ms	(cbrt K)
107.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.9s

Counts

55 → 55

Iterations

Useful iterations: 3 (111.0ms)

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

prune268.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ K (/ 2.0 (+ m n)))
0.6b	(pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3)
0.6b	(cbrt (pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3))
38.0b	(cos (- (/ K (/ 2.0 (+ m n))) M))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
85×	`*-un-lft-identity`
61×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`associate-/r*`
12×	`cbrt-prod` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r/`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `div-inv`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/l*`
2×	`cube-mult` `cos-sum` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 144

Calls

4 calls:

17.0ms	(/ K (/ 2.0 (+ m n)))
5.0ms	(pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3)
3.0ms	(cbrt (pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3))
101.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))

series303.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ K (/ 2.0 (+ m n)))
134.0ms	(pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3)
64.0ms	(cbrt (pow (cos (- (/ K (/ 2.0 (+ m n))) M)) 3))
60.0ms	(cos (- (/ K (/ 2.0 (+ m n))) M))

simplify879.0ms

Counts

156 → 156

Iterations

Useful iterations: done (875.0ms)

Iter	Nodes	Cost
0	246	2636
1	520	2336
2	1628	2147
done	5001	2141

prune636.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.1b

regimes396.0ms

Accuracy

0% (0.3b 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

634.0ms	8107×	body	80	valid
57.0ms	121×	body	1280	valid
47.0ms	145×	body	640	valid
24.0ms	104×	body	320	valid
9.0ms	55×	body	160	valid
2.0ms	3×	body	2560	valid