Details

sample93.0ms

Algorithm

intervals

Results

51.0ms	259×	body	80	valid
3.0ms	3×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	2×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	3184
4	821
3	262
2	104
1	51
0	21

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize62.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
30.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
3×	`div-inv`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-diff` `sub-neg` `fma-udef`

Counts

2 → 45

Calls

2 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
48.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series256.0ms

Counts

2 → 6

Calls

2 calls:

178.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
78.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify3.6s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
4	3945
3	1382
2	570
1	353
0	205

prune555.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize40.0ms

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)

series159.0ms

Counts

1 → 3

Calls

1 calls:

159.0ms

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

simplify1.4s

Counts

14 → 14

Iterations

Iter	Nodes
done	5003
4	1451
3	405
2	142
1	64
0	33

prune166.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize84.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
9×	`div-inv`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 116

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
27.0ms	(cos (- (/ (* (+ m n) K) 2) M))
38.0ms	(cos (- (/ (* (+ m n) K) 2) M))
54.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series490.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
98.0ms	(cos (- (/ (* (+ m n) K) 2) M))
96.0ms	(cos (- (/ (* (+ m n) K) 2) M))
73.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
4	1929
3	901
2	462
1	317
0	192

prune876.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize67.0ms

Local error

Found 4 expressions with local error:

30.6b	(cos (- (/ (* (+ m n) K) 2) M))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))
30.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

92×	`cos-sum`
84×	`prod-diff`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
36×	`times-frac`
12×	`div-inv`
4×	`cos-diff` `expm1-log1p-u` `pow1` `sub-neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 136

Calls

4 calls:

23.0ms	(cos (- (/ (* (+ m n) K) 2) M))
25.0ms	(cos (- (/ (* (+ m n) K) 2) M))
23.0ms	(cos (- (/ (* (+ m n) K) 2) M))
23.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series263.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(cos (- (/ (* (+ m n) K) 2) M))
64.0ms	(cos (- (/ (* (+ m n) K) 2) M))
66.0ms	(cos (- (/ (* (+ m n) K) 2) M))
67.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify3.8s

Counts

148 → 148

Iterations

Iter	Nodes
done	5018
5	4312
4	1693
3	861
2	434
1	298
0	178

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes609.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.1b and baseline of 1.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	8090×	body	80	valid
156.0ms	147×	body	640	valid
98.0ms	113×	body	1280	valid
45.0ms	102×	body	320	valid
17.0ms	53×	body	160	valid
5.0ms	4×	body	2560	valid