Details

sample103.0ms

Algorithm

intervals

Results

52.0ms	263×	body	80	valid
6.0ms	6×	body	1280	valid
5.0ms	6×	body	640	valid
1.0ms	1×	body	320	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (140.0ms)

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: 16.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-log-exp`
12×	`add-sqr-sqrt`
7×	`diff-log` `distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`sub-neg` `associate-r`
3×	`associate-l`
2×	`cos-sum` `flip3--` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `flip--` `associate--r+` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

33.0ms	(* K (+ m n))
1.4s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
26.0ms	(- (/ (* K (+ m n)) 2.0) M)
42.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series433.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* K (+ m n))
231.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
80.0ms	(- (/ (* K (+ m n)) 2.0) M)
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify701.0ms

Counts

83 → 83

Iterations

Useful iterations: done (699.0ms)

Iter	Nodes	Cost
0	160	1258
1	385	1215
2	1405	1103
done	5002	1101

prune479.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize37.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

57.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.4s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series689.0ms

Counts

2 → 6

Calls

2 calls:

405.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
284.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify1.6s

Counts

50 → 50

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	122	937
1	312	879
2	833	826
3	3166	809
done	5000	801

prune249.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.5b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cos-sum` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

27.0ms	(- (/ (* K (+ m n)) 2.0) M)
7.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
10.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
34.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series484.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (/ (* K (+ m n)) 2.0) M)
121.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
191.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
82.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	103	1445
1	258	1249
2	1142	1092
done	5000	1086

prune541.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
34.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
375.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series708.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (+ m n))
196.0ms	(cbrt (+ m n))
167.0ms	(cbrt (+ m n))
182.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify992.0ms

Counts

64 → 64

Iterations

Useful iterations: done (988.0ms)

Iter	Nodes	Cost
0	91	868
1	189	835
2	519	653
3	1838	602
done	5000	596

prune523.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

regimes328.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8123×	body	80	valid
108.0ms	124×	body	1280	valid
90.0ms	145×	body	640	valid
53.0ms	115×	body	320	valid
15.0ms	48×	body	160	valid
2.0ms	1×	body	2560	valid