Details

sample58.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
4.0ms	9×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (137.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- 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	(* K (+ m n))
33.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite9.7s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

1.4s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
8.3s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
20.0ms	(* K (+ m n))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

267.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
611.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
41.0ms	(* K (+ m n))
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

91 → 91

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	182	1920
1	472	1875
2	2037	1646
done	5000	1632

prune635.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize19.0ms

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))))

rewrite1.7s

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:

66.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.6s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series618.0ms

Counts

2 → 6

Calls

2 calls:

357.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
260.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify1.8s

Counts

50 → 50

Iterations

Useful iterations: done (1.8s)

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

prune304.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.9b

localize38.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (* K (+ m n)))
13.9b	(cbrt (* K (+ m n)))
13.9b	(cbrt (* K (+ m n)))
33.3b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite97.0ms

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)))
7.0ms	(cbrt (* K (+ m n)))
7.0ms	(cbrt (* K (+ m n)))
73.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series547.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (* K (+ m n)))
137.0ms	(cbrt (* K (+ m n)))
150.0ms	(cbrt (* K (+ m n)))
110.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify1.7s

Counts

55 → 55

Iterations

Useful iterations: done (1.7s)

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

prune421.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
13.9b	(cbrt (* K (+ m n)))
13.9b	(cbrt (* K (+ m n)))
33.0b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (cbrt K) (cbrt (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt K)
7.0ms	(cbrt (* K (+ m n)))
7.0ms	(cbrt (* K (+ m n)))
576.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (cbrt K) (cbrt (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series750.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt K)
179.0ms	(cbrt (* K (+ m n)))
138.0ms	(cbrt (* K (+ m n)))
169.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (cbrt K) (cbrt (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify974.0ms

Counts

55 → 55

Iterations

Useful iterations: done (972.0ms)

Iter	Nodes	Cost
0	115	828
1	260	808
2	595	717
3	2043	697
done	5000	685

prune486.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.8b

regimes567.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.9s	8098×	body	80	valid
87.0ms	151×	body	640	valid
82.0ms	100×	body	320	valid
82.0ms	100×	body	1280	valid
21.0ms	59×	body	160	valid
4.0ms	3×	body	2560	valid