Details

sample85.0ms

Algorithm

intervals

Results

40.0ms	255×	body	80	valid
5.0ms	7×	body	1280	valid
5.0ms	9×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	2×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (109.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	210	29
4	640	28
5	3078	28
done	5000	28

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.0b

localize27.0ms

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))
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite8.8s

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:

8.6s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
110.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(* K (+ m n))
72.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

633.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
441.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
49.0ms	(* K (+ m n))
112.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	205	1657
1	541	1615
2	2023	1433
done	5002	1427

prune611.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite80.0ms

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:

79.0ms

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

series479.0ms

Counts

1 → 3

Calls

1 calls:

478.0ms

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

simplify892.0ms

Counts

23 → 23

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	74	337
1	191	318
2	445	305
3	1197	304
done	5000	296

prune147.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
35.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite114.0ms

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)
111.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(cbrt K)
295.0ms	(cbrt K)
289.0ms	(cbrt K)
194.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.8s

Counts

55 → 55

Iterations

Useful iterations: 3 (293.0ms)

Iter	Nodes	Cost
0	60	516
1	116	498
2	307	386
3	1255	335
done	5000	335

prune424.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.9b

localize38.0ms

Local error

Found 4 expressions with local error:

17.7b	(cbrt (* K (+ m n)))
17.7b	(cbrt (* K (+ m n)))
17.7b	(cbrt (* K (+ m n)))
35.4b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite114.0ms

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:

9.0ms	(cbrt (* K (+ m n)))
11.0ms	(cbrt (* K (+ m n)))
8.0ms	(cbrt (* K (+ m n)))
84.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series608.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt (* K (+ m n)))
186.0ms	(cbrt (* K (+ m n)))
146.0ms	(cbrt (* K (+ m n)))
95.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify1.6s

Counts

55 → 55

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	86	881
1	186	859
2	361	602
3	795	545
4	3441	521
done	5001	515

prune448.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

regimes377.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
2	22	18
done	22	18

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8039×	body	80	valid
97.0ms	111×	body	1280	valid
89.0ms	159×	body	640	valid
51.0ms	67×	body	160	valid
44.0ms	100×	body	320	valid
5.0ms	5×	body	2560	valid