Details

sample103.0ms

Algorithm

intervals

Results

50.0ms	261×	body	80	valid
5.0ms	4×	body	1280	valid
5.0ms	6×	body	640	valid
1.0ms	2×	body	320	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (179.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
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)
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite8.7s

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:

20.0ms	(* K (+ m n))
8.5s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
91.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* K (+ m n))
557.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
350.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
99.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.5s

Counts

87 → 87

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	205	1657
1	490	1601
2	1316	1414
3	4431	1395
done	5000	1394

prune683.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

5.0ms	(- l (fabs (- m n)))
89.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series385.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- l (fabs (- m n)))
366.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	104	514
1	216	489
2	424	464
3	947	463
4	2263	455
done	5000	454

prune286.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize66.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
32.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite139.0ms

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:

12.0ms	(cbrt (* K (+ m n)))
16.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
95.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series598.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (* K (+ m n)))
176.0ms	(cbrt (* K (+ m n)))
187.0ms	(cbrt (* K (+ m n)))
66.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify2.5s

Counts

55 → 55

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	86	881
1	186	859
2	355	602
3	714	545
4	1391	521
5	3182	506
done	5001	500

prune428.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize58.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
15.8b	(cbrt (* m K))
30.3b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

13.0ms	(cbrt (* K (+ m n)))
13.0ms	(cbrt (* K (+ m n)))
7.0ms	(cbrt (* m K))
83.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

series568.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (* K (+ m n)))
126.0ms	(cbrt (* K (+ m n)))
95.0ms	(cbrt (* m K))
228.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

simplify2.1s

Counts

53 → 53

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	118	815
1	257	803
2	523	720
3	1106	693
4	2684	666
done	5000	663

prune318.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes236.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.7s	8086×	body	80	valid
135.0ms	124×	body	1280	valid
107.0ms	142×	body	640	valid
43.0ms	106×	body	320	valid
12.0ms	47×	body	160	valid
1.0ms	1×	body	2560	valid