Details

sample137.0ms

Algorithm

intervals

Results

96.0ms	259×	body	80	valid
10.0ms	6×	body	1280	valid
6.0ms	5×	body	640	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	160	valid

simplify964.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	3045
4	783
3	250
2	102
1	51
0	21

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* (+ m n) K) 2) M)) (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))
0.0b	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
35.2b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

269.0ms	(* (cos (- (/ (* (+ m n) K) 2) M)) (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))
41.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
187.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
40.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series781.0ms

Counts

4 → 12

Calls

4 calls:

365.0ms	(* (cos (- (/ (* (+ m n) K) 2) M)) (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))
229.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
88.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
98.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify3.7s

Counts

111 → 111

Iterations

Iter	Nodes
3	9195
2	1812
1	528
0	199

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 66

Calls

2 calls:

63.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
225.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series408.0ms

Counts

2 → 6

Calls

2 calls:

274.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
134.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
3	5174
2	1210
1	366
0	132

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ (* (+ m n) K) 2)) (cos M))
0.2b	(* (sin (/ (* (+ m n) K) 2)) (sin M))
38.5b	(sin (/ (* (+ m n) K) 2))
38.6b	(cos (/ (* (+ m n) K) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cos-mult` `sin-mult`

Counts

4 → 56

Calls

4 calls:

16.0ms	(* (cos (/ (* (+ m n) K) 2)) (cos M))
25.0ms	(* (sin (/ (* (+ m n) K) 2)) (sin M))
6.0ms	(sin (/ (* (+ m n) K) 2))
7.0ms	(cos (/ (* (+ m n) K) 2))

series265.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cos (/ (* (+ m n) K) 2)) (cos M))
73.0ms	(* (sin (/ (* (+ m n) K) 2)) (sin M))
38.0ms	(sin (/ (* (+ m n) K) 2))
53.0ms	(cos (/ (* (+ m n) K) 2))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
5	2112
4	1379
3	828
2	379
1	170
0	89

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize103.0ms

Local error

Found 4 expressions with local error:

38.5b	(sin (/ (* (+ m n) K) 2))
38.6b	(cos (/ (* (+ m n) K) 2))
38.6b	(cos (/ (* (+ m n) K) 2))
38.6b	(cos (/ (* (+ m n) K) 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

3.0ms	(sin (/ (* (+ m n) K) 2))
9.0ms	(cos (/ (* (+ m n) K) 2))
5.0ms	(cos (/ (* (+ m n) K) 2))
5.0ms	(cos (/ (* (+ m n) K) 2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sin (/ (* (+ m n) K) 2))
44.0ms	(cos (/ (* (+ m n) K) 2))
42.0ms	(cos (/ (* (+ m n) K) 2))
33.0ms	(cos (/ (* (+ m n) K) 2))

simplify1.5s

Counts

44 → 44

Iterations

Iter	Nodes
9	3122
8	1030
7	472
6	272
5	193
4	145
3	120
2	80
1	47
0	32

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

regimes512.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end1.0ms

sample3.7s

Algorithm

intervals

Results

2.9s	8107×	body	80	valid
168.0ms	130×	body	1280	valid
154.0ms	144×	body	640	valid
70.0ms	93×	body	320	valid
21.0ms	44×	body	160	valid
9.0ms	5×	body	2560	valid