Details

sample43.0ms

Algorithm

intervals

Results

22.0ms	263×	body	80	valid
2.0ms	7×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid

simplify831.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	92	29
3	195	29
4	438	28
5	1389	28
done	5001	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize23.0ms

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	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite3.5s

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:

3.4s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
9.0ms	(* K (+ m n))
35.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series717.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
31.0ms	(* K (+ m n))
274.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify545.0ms

Counts

87 → 87

Iterations

Useful iterations: done (541.0ms)

Iter	Nodes	Cost
0	205	1657
1	489	1601
2	1447	1414
done	5000	1397

prune383.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(exp (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

9.0ms	(* K (+ m n))
1.3s	(exp (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series532.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* K (+ m n))
177.0ms	(exp (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
272.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: 3 (829.0ms)

Iter	Nodes	Cost
0	188	1125
1	429	1075
2	1204	979
3	4650	966
done	5000	966

prune389.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.8b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite53.0ms

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:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
50.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series648.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt K)
179.0ms	(cbrt K)
184.0ms	(cbrt K)
100.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.5s

Counts

55 → 55

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	60	516
1	113	498
2	235	386
3	580	335
4	2221	335
done	5000	335

prune314.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (* K (+ m n)))
15.6b	(cbrt (* K (+ m n)))
15.6b	(cbrt (* K (+ m n)))
32.8b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
28.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series372.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* K (+ m n)))
105.0ms	(cbrt (* K (+ m n)))
104.0ms	(cbrt (* K (+ m n)))
57.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify2.3s

Counts

55 → 55

Iterations

Useful iterations: 5 (734.0ms)

Iter	Nodes	Cost
0	86	881
1	185	859
2	340	602
3	651	545
4	1420	521
5	3700	506
done	5000	506

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes180.0ms

Accuracy

0% (0.1b remaining)

Error of 1.1b against oracle of 1.0b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	29	37
done	29	37

end0.0ms

sample1.0s

Algorithm

intervals

Results

602.0ms	8116×	body	80	valid
52.0ms	108×	body	1280	valid
45.0ms	141×	body	640	valid
21.0ms	92×	body	320	valid
8.0ms	50×	body	160	valid
2.0ms	3×	body	2560	valid