Details

sample62.0ms

Algorithm

intervals

Results

38.0ms	253×	body	80	valid
4.0ms	7×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

Algorithm

egg-herbie

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-sqr-sqrt`
180×	`*-un-lft-identity`
171×	`prod-diff`
94×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
52×	`difference-of-squares`
44×	`distribute-lft-out--`
34×	`times-frac`
31×	`fma-neg`
23×	`cos-sum`
16×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`diff-log` `div-inv`
6×	`neg-mul-1`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

4 → 278

Calls

4 calls:

11.0ms	(- (/ (* K (+ m n)) 2.0) M)
660.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series563.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ (* K (+ m n)) 2.0) M)
186.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify103.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	948	6447
1	2575	4632
2	5002	4553

prune949.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize15.0ms

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)

rewrite724.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

678.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series461.0ms

Counts

2 → 6

Calls

2 calls:

176.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
284.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	608	5050
1	1693	3609
2	5001	3001

prune366.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize31.0ms

Local error

Found 4 expressions with local error:

18.0b	(cbrt (/ (* K (+ m n)) 2.0))
18.0b	(cbrt (/ (* K (+ m n)) 2.0))
18.0b	(cbrt (/ (* K (+ m n)) 2.0))
38.6b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series987.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (/ (* K (+ m n)) 2.0))
165.0ms	(cbrt (/ (* K (+ m n)) 2.0))
163.0ms	(cbrt (/ (* K (+ m n)) 2.0))
493.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

simplify51.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	242	746
1	545	685
2	1523	661
3	5001	655

prune515.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

18.0b	(cbrt (/ (* K (+ m n)) 2.0))
18.0b	(cbrt (/ (* K (+ m n)) 2.0))
18.0b	(cbrt (/ (* K (+ m n)) 2.0))
38.6b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series980.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (/ (* K (+ m n)) 2.0))
159.0ms	(cbrt (/ (* K (+ m n)) 2.0))
160.0ms	(cbrt (/ (* K (+ m n)) 2.0))
499.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	242	746
1	545	685
2	1523	661
3	5001	655

prune518.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes317.0ms

Accuracy

0% (0.3b 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	8077×	body	80	valid
87.0ms	179×	body	640	valid
74.0ms	118×	body	1280	valid
41.0ms	118×	body	320	valid
11.0ms	46×	body	160	valid
2.0ms	2×	body	2560	valid