Details

sample63.0ms

Algorithm

intervals

Results

37.0ms	257×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid

simplify50.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
6×	`unpow-prod-down`
5×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `cos-sum` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 44

Calls

3 calls:

9.0ms	(- (/ (* K (+ m n)) 2.0) M)
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series379.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(- (/ (* K (+ m n)) 2.0) M)
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify78.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	274	399
1	743	371
2	3043	367
3	5002	364

prune245.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.4b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite32.0ms

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×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

31.0ms

(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)

simplify44.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	156	164
1	433	159
2	1446	158
3	5001	155

prune101.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite47.0ms

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)))
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
17.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series352.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
85.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify123.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 6 (118.0ms)

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

prune301.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.1b	(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
0.5b	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `cos-sum` `exp-prod`
5×	`add-exp-log` `add-log-exp`
4×	`log-prod` `exp-diff` `log-pow` `add-cbrt-cube`
3×	`cos-diff` `sub-neg` `pow-unpow`
2×	`log-div` `exp-sum` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `rem-log-exp` `pow-exp` `rem-exp-log` `distribute-lft-out--` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
28.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series455.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
83.0ms	(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
53.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify50.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	258	606
1	621	559
2	1855	558
3	5002	555

prune338.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

regimes238.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8090×	body	80	valid
88.0ms	161×	body	640	valid
71.0ms	97×	body	1280	valid
41.0ms	101×	body	320	valid
12.0ms	45×	body	160	valid
5.0ms	5×	body	2560	valid