Details

sample73.0ms

Algorithm

intervals

Results

45.0ms	261×	body	80	valid
3.0ms	3×	body	1280	valid
3.0ms	5×	body	320	valid
3.0ms	4×	body	640	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	3132
4	821
3	260
2	102
1	51
0	21

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* K (/ (+ m n) 2)) M)
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(* K (/ (+ m n) 2))
34.6b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `prod-diff` `add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `flip3--` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 84

Calls

4 calls:

25.0ms	(- (* K (/ (+ m n) 2)) M)
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
33.0ms	(* K (/ (+ m n) 2))
45.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series456.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (* K (/ (+ m n) 2)) M)
198.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
55.0ms	(* K (/ (+ m n) 2))
117.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
3	3267
2	1054
1	405
0	188

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize49.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

1.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series203.0ms

Counts

1 → 3

Calls

1 calls:

203.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify3.2s

Counts

14 → 14

Iterations

Iter	Nodes
5	6545
4	1190
3	343
2	130
1	64
0	33

prune307.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.4b

localize57.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
18.8b	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef` `remove-posit16`

Counts

2 → 22

Calls

2 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
1.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

series387.0ms

Counts

2 → 6

Calls

2 calls:

178.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
209.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

simplify2.7s

Counts

28 → 28

Iterations

Iter	Nodes
5	6290
4	1213
3	358
2	143
1	77
0	44

prune830.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
0.4b	(/ K (sqrt 2))
0.5b	(/ (+ m n) (sqrt 2))
34.4b	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
65×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`prod-diff`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 191

Calls

4 calls:

363.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
5.0ms	(/ K (sqrt 2))
15.0ms	(/ (+ m n) (sqrt 2))
41.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

series869.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
99.0ms	(/ K (sqrt 2))
104.0ms	(/ (+ m n) (sqrt 2))
447.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

simplify5.1s

Counts

203 → 203

Iterations

Iter	Nodes
3	8839
2	1975
1	622
0	256

prune4.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

regimes571.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.6s	8108×	body	80	valid
156.0ms	106×	body	1280	valid
136.0ms	142×	body	640	valid
107.0ms	112×	body	320	valid
21.0ms	49×	body	160	valid
4.0ms	2×	body	2560	valid