Details

sample41.0ms

Algorithm

intervals

Results

20.0ms	260×	body	80	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite637.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

574.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
13.0ms	(* K (+ m n))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series537.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
25.0ms	(* K (+ m n))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5001	620

prune362.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

574.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series452.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5001	432

prune172.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

1.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
17.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series311.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify132.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 6 (123.0ms)

Iter	Nodes	Cost
0	83	464
1	123	418
2	183	416
3	334	416
4	1040	416
5	3218	416
6	5001	397

prune313.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize34.0ms

Local error

Found 4 expressions with local error:

34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cos-sum`
4×	`pow1` `add-exp-log` `cos-diff` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

16.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
17.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series221.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify117.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	66	448
1	100	404
2	140	404
3	178	404
4	236	404
5	363	404
6	913	404
7	2562	404
8	5001	404

prune351.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

regimes144.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

635.0ms	8103×	body	80	valid
53.0ms	106×	body	1280	valid
53.0ms	158×	body	640	valid
25.0ms	104×	body	320	valid
7.0ms	46×	body	160	valid
3.0ms	4×	body	2560	valid