Details

sample104.0ms

Algorithm

intervals

Results

54.0ms	265×	body	80	valid
5.0ms	5×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (169.0ms)

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize79.0ms

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	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite994.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

44.0ms	(* K (+ m n))
750.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
120.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
74.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

50.0ms	(* K (+ m n))
353.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
495.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
129.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	177	1173
1	458	1103
2	1470	1026
done	5001	1023

prune967.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 2 expressions with local error:

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

rewrite882.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

756.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
123.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series855.0ms

Counts

2 → 6

Calls

2 calls:

348.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
507.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.0s

Counts

43 → 43

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	110	770
1	288	711
2	764	672
3	3196	671
done	5001	663

prune445.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize104.0ms

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)))
37.5b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite150.0ms

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:

14.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
19.0ms	(cbrt (* K (+ m n)))
100.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series756.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (* K (+ m n)))
210.0ms	(cbrt (* K (+ m n)))
215.0ms	(cbrt (* K (+ m n)))
122.0ms	(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	361	602
3	795	545
4	3441	521
done	5001	515

prune850.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize94.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(pow (* K (+ m n)) 3)
26.0b	(cbrt (pow (* K (+ m n)) 3))
36.9b	(cos (- (/ (cbrt (pow (* K (+ m n)) 3)) 2.0) M))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `cbrt-prod` `add-cube-cbrt` `unpow-prod-down`
7×	`add-cbrt-cube`
6×	`pow-unpow`
4×	`cube-div` `associate-*r/` `add-log-exp`
3×	`pow-pow` `pow-exp` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `cos-sum` `flip3-+` `unpow3` `cube-prod` `flip-+` `rem-cube-cbrt` `difference-of-squares`
1×	`cos-diff` `sub-neg` `times-frac` `pow1/3` `pow-prod-down` `prod-exp` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

123.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(pow (* K (+ m n)) 3)
7.0ms	(cbrt (pow (* K (+ m n)) 3))
111.0ms	(cos (- (/ (cbrt (pow (* K (+ m n)) 3)) 2.0) M))

series754.0ms

Counts

4 → 12

Calls

4 calls:

495.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
85.0ms	(pow (* K (+ m n)) 3)
55.0ms	(cbrt (pow (* K (+ m n)) 3))
118.0ms	(cos (- (/ (cbrt (pow (* K (+ m n)) 3)) 2.0) M))

simplify1.8s

Counts

85 → 85

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	179	1176
1	484	996
2	1994	915
done	5000	914

prune985.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes637.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	20	19
done	20	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.7s	8091×	body	80	valid
133.0ms	119×	body	1280	valid
131.0ms	165×	body	640	valid
61.0ms	98×	body	320	valid
23.0ms	58×	body	160	valid
4.0ms	2×	body	2560	valid