Details

sample63.0ms

Algorithm

intervals

Results

36.0ms	258×	body	80	valid
7.0ms	7×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify52.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite623.0ms

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:

9.0ms	(* K (+ m n))
562.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series522.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* K (+ m n))
183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5002	620

prune353.0ms

Pruning

8 alts after pruning (8 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)

rewrite593.0ms

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:

558.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series443.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (74.0ms)

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

prune184.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
45.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series632.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt K)
178.0ms	(cbrt K)
175.0ms	(cbrt K)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify96.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite141.0ms

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 K)
47.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
45.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
48.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series490.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt K)
102.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
102.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	615
1	265	549
2	681	547
3	3070	547
4	5001	547

prune342.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes282.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b 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

sample1.6s

Algorithm

intervals

Results

1.1s	8081×	body	80	valid
103.0ms	177×	body	640	valid
84.0ms	112×	body	1280	valid
45.0ms	108×	body	320	valid
14.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid