Details

sample108.0ms

Algorithm

intervals

Results

73.0ms	260×	body	80	valid
4.0ms	3×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	818
3	257
2	102
1	51
0	21

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) K)
0.0b	(/ (* (+ m n) K) 2)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
10×	`associate-l`
9×	`associate-r`
8×	`swap-sqr` `difference-of-squares`
7×	`times-frac`
6×	`flip3--` `associate-*l/` `flip--` `distribute-lft-out--`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `sub-neg` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `cbrt-undiv` `cos-sum` `distribute-lft-in` `flip3-+` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `unswap-sqr` `associate-/l/`
1×	`pow2` `cos-diff` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 106

Calls

4 calls:

22.0ms	(* (+ m n) K)
13.0ms	(/ (* (+ m n) K) 2)
208.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
46.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series290.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (+ m n) K)
40.0ms	(/ (* (+ m n) K) 2)
120.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
92.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify1.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	2003
3	2003
2	1965
1	536
0	199

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
9×	`pow1`
8×	`swap-sqr` `difference-of-squares`
6×	`flip3--` `associate-r` `associate-l` `add-cube-cbrt` `flip--` `distribute-lft-out--`
4×	`distribute-rgt-in` `frac-times` `associate-+r+` `sub-neg` `distribute-lft-in` `times-frac` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`associate-l/` `associate-r/` `insert-posit16`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 65

Calls

2 calls:

72.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
503.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series354.0ms

Counts

2 → 6

Calls

2 calls:

246.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
107.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	2001
3	2001
2	1187
1	349
0	119

prune944.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 45

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
35.0ms	(cos (- (/ (* (+ m n) K) 2) M))
25.0ms	(cos (- (/ (* (+ m n) K) 2) M))
33.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series474.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
88.0ms	(cos (- (/ (* (+ m n) K) 2) M))
68.0ms	(cos (- (/ (* (+ m n) K) 2) M))
94.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify1.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	2000
7	2000
6	1207
5	510
4	276
3	167
2	117
1	83
0	50

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize61.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (* (+ m n) K))
16.6b	(cbrt (* (+ m n) K))
16.6b	(cbrt (* (+ m n) K))
35.8b	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 47

Calls

4 calls:

7.0ms	(cbrt (* (+ m n) K))
7.0ms	(cbrt (* (+ m n) K))
7.0ms	(cbrt (* (+ m n) K))
55.0ms	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

series408.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (* (+ m n) K))
116.0ms	(cbrt (* (+ m n) K))
111.0ms	(cbrt (* (+ m n) K))
76.0ms	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

simplify1.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	2004
4	2004
3	992
2	452
1	223
0	105

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

regimes431.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.4s	8088×	body	80	valid
183.0ms	122×	body	1280	valid
152.0ms	139×	body	640	valid
77.0ms	117×	body	320	valid
27.0ms	52×	body	160	valid
1.0ms	1×	body	2560	valid