Details

sample126.0ms

Algorithm

intervals

Results

77.0ms	257×	body	80	valid
7.0ms	4×	body	1280	valid
6.0ms	7×	body	320	valid
4.0ms	3×	body	640	valid
3.0ms	5×	body	160	valid

simplify937.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2910
4	776
3	248
2	100
1	51
0	21

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
40.4b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `add-cbrt-cube` `diff-log`
4×	`associate-r` `insert-posit16`
3×	`pow-unpow` `sub-neg` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `neg-log` `associate-*r/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

28.0ms	(* K (+ m n))
64.0ms	(pow (- (/ (+ m n) 2) M) 2)
785.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
40.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series450.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* K (+ m n))
114.0ms	(pow (- (/ (+ m n) 2) M) 2)
227.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
80.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.4s

Counts

94 → 94

Iterations

Iter	Nodes
3	3297
2	1046
1	410
0	175

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize54.0ms

Local error

Found 3 expressions with local error:

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

rewrite739.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-log-exp`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down`
5×	`add-cube-cbrt` `difference-of-squares`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16`
2×	`distribute-rgt-neg-in` `times-frac` `flip3--` `neg-log` `flip--` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `unpow2` `associate--r-` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

37.0ms	(- (/ (+ m n) 2) M)
34.0ms	(pow (- (/ (+ m n) 2) M) 2)
668.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

series434.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(- (/ (+ m n) 2) M)
129.0ms	(pow (- (/ (+ m n) 2) M) 2)
277.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

simplify918.0ms

Counts

72 → 72

Iterations

Iter	Nodes
3	2477
2	771
1	312
0	129

prune865.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2) M)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(- (- (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (- l (fabs (- m n))))
20.5b	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
16×	`add-log-exp`
13×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`flip3--` `swap-sqr` `add-cube-cbrt` `flip--`
7×	`diff-log`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`sub-neg` `times-frac`
4×	`frac-times` `insert-posit16`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in` `neg-log` `associate-l/` `associate-r/` `associate--r+`
1×	`associate--l-` `pow2` `neg-sub0` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `associate--r-` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

43.0ms	(- (/ (+ m n) 2) M)
178.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
22.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (- l (fabs (- m n))))
1.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ (+ m n) 2) M)
92.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
231.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (- l (fabs (- m n))))
126.0ms	(posit16->real (real->posit16 (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

simplify2.1s

Counts

111 → 111

Iterations

Iter	Nodes
3	5701
2	1312
1	397
0	156

prune2.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

localize84.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt K)
0.5b	(cbrt K)
0.5b	(* (cbrt K) (cbrt K))
40.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`cos-sum` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
15.0ms	(* (cbrt K) (cbrt K))
81.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt K)
299.0ms	(cbrt K)
324.0ms	(* (cbrt K) (cbrt K))
148.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))

simplify3.3s

Counts

88 → 88

Iterations

Iter	Nodes
4	7034
3	1540
2	520
1	203
0	99

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.6b

regimes873.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.5s	8131×	body	80	valid
171.0ms	113×	body	1280	valid
144.0ms	157×	body	640	valid
117.0ms	130×	body	320	valid
36.0ms	82×	body	160	valid
9.0ms	5×	body	2560	valid