Details

sample42.0ms

Algorithm

intervals

Results

20.0ms	262×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15
done	5001	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `prod-diff`
36×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`pow1` `add-exp-log` `fma-neg` `div-inv`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

52.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(- (/ (* K (+ m n)) 2.0) M)
18.0ms	(* K (+ m n))
34.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series423.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(- (/ (* K (+ m n)) 2.0) M)
30.0ms	(* K (+ m n))
61.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	612	1660
1	1907	1270
2	5003	1268
done	5003	1268

prune509.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

54.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series273.0ms

Counts

1 → 3

Calls

1 calls:

273.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify43.0ms

Counts

25 → 25

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	159	174
1	445	168
2	1492	167
3	5001	162
done	5001	162

prune112.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(fma 0.5 (fma K n (* m K)) (- M))
0.5b	(fma K n (* m K))
34.6b	(cos (fma 0.5 (fma K n (* m K)) (- M)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `fma-udef`
2×	`difference-of-squares`
1×	`pow-to-exp` `cos-sum` `pow-pow` `times-frac` `pow-exp` `distribute-lft-out--` `sqr-pow`

Counts

4 → 52

Calls

4 calls:

56.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0ms	(fma 0.5 (fma K n (* m K)) (- M))
0.0ms	(fma K n (* m K))
2.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

417.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
58.0ms	(fma 0.5 (fma K n (* m K)) (- M))
42.0ms	(fma K n (* m K))
63.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))

simplify64.0ms

Counts

64 → 64

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	241	387
1	657	356
2	2436	355
3	5001	350
done	5001	350

prune322.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (fma 0.5 (fma K n (* m K)) (- M))))
34.6b	(cos (fma 0.5 (fma K n (* m K)) (- M)))
34.6b	(cos (fma 0.5 (fma K n (* m K)) (- M)))
34.6b	(cos (fma 0.5 (fma K n (* m K)) (- M)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-sum` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (cos (fma 0.5 (fma K n (* m K)) (- M))))
2.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))
2.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))
3.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (cos (fma 0.5 (fma K n (* m K)) (- M))))
65.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))
62.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))
66.0ms	(cos (fma 0.5 (fma K n (* m K)) (- M)))

simplify258.0ms

Counts

55 → 55

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	68	423
1	120	356
2	241	354
3	754	354
4	4878	354
5	5001	354
done	5001	354

prune358.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes202.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10
done	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

610.0ms	8077×	body	80	valid
53.0ms	155×	body	640	valid
48.0ms	103×	body	1280	valid
20.0ms	85×	body	320	valid
9.0ms	55×	body	160	valid