Details

sample80.0ms

Algorithm

intervals

Results

39.0ms	258×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3247
4	684
3	220
2	95
1	50
0	21

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.0b	(- (/ (* K (+ m n)) 2.0) M)
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite147.0ms

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` `fma-neg` `add-exp-log` `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` `pow-pow` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

68.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(* K (+ m n))
18.0ms	(- (/ (* K (+ m n)) 2.0) M)
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series559.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.0ms	(* K (+ m n))
81.0ms	(- (/ (* K (+ m n)) 2.0) M)
82.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify809.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
2	1768
1	663
0	304

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize52.0ms

Local error

Found 1 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 22

Calls

1 calls:

72.0ms

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

series360.0ms

Counts

1 → 3

Calls

1 calls:

360.0ms

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

simplify707.0ms

Counts

25 → 25

Iterations

Iter	Nodes
done	5000
3	1246
2	455
1	194
0	76

prune275.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize62.0ms

Local error

Found 4 expressions with local error:

15.7b	(cbrt (/ (* K (+ m n)) 2.0))
15.7b	(cbrt (/ (* K (+ m n)) 2.0))
15.7b	(cbrt (/ (* K (+ m n)) 2.0))
33.5b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`cos-sum` `fma-udef`

Counts

4 → 64

Calls

4 calls:

5.0ms	(cbrt (/ (* K (+ m n)) 2.0))
5.0ms	(cbrt (/ (* K (+ m n)) 2.0))
9.0ms	(cbrt (/ (* K (+ m n)) 2.0))
4.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

series1.5s

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (/ (* K (+ m n)) 2.0))
238.0ms	(cbrt (/ (* K (+ m n)) 2.0))
230.0ms	(cbrt (/ (* K (+ m n)) 2.0))
801.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

simplify915.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	1610
2	514
1	242
0	116

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* (+ m n) K) 2.0) M)
0.3b	(expm1 (log1p (cos (- (/ (* (+ m n) K) 2.0) M))))
0.5b	(log1p (cos (- (/ (* (+ m n) K) 2.0) M)))
33.5b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

42×	`prod-diff`
34×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
23×	`cos-sum`
21×	`times-frac`
7×	`fma-neg` `div-inv`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`sub-neg`
1×	`cos-diff` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `log1p-expm1` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 99

Calls

4 calls:

29.0ms	(- (/ (* (+ m n) K) 2.0) M)
0.0ms	(expm1 (log1p (cos (- (/ (* (+ m n) K) 2.0) M))))
1.0ms	(log1p (cos (- (/ (* (+ m n) K) 2.0) M)))
39.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series616.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (/ (* (+ m n) K) 2.0) M)
143.0ms	(expm1 (log1p (cos (- (/ (* (+ m n) K) 2.0) M))))
325.0ms	(log1p (cos (- (/ (* (+ m n) K) 2.0) M)))
77.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify1.8s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
3	3973
2	1048
1	438
0	240

prune842.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

regimes706.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.1s	8096×	body	80	valid
167.0ms	124×	body	1280	valid
114.0ms	164×	body	640	valid
46.0ms	101×	body	320	valid
19.0ms	55×	body	160	valid
1.0ms	1×	body	2560	valid