Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	266×	body	80	valid
5.0ms	3×	body	1280	valid
4.0ms	12×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize21.0ms

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)
31.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.0s

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:

18.0ms	(* K (+ m n))
936.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series551.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* K (+ m n))
192.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
66.0ms	(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	5002	620

prune346.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- l (fabs (- 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)

rewrite994.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

5.0ms	(- l (fabs (- m n)))
932.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series458.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(- l (fabs (- m n)))
184.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	317	557
1	875	532
2	3493	523
3	5002	520

prune218.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
31.1b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite88.0ms

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:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
84.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series655.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt K)
178.0ms	(cbrt K)
177.0ms	(cbrt K)
110.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify94.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (8.0ms)

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

prune308.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt K))
0.6b	(cbrt (cbrt K))
0.6b	(cbrt (cbrt K))
31.2b	(cos (- (/ (* (* (* (* (cbrt (cbrt K)) (cbrt (cbrt K))) (cbrt (cbrt K))) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite726.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`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 → 52

Calls

4 calls:

1.0ms	(cbrt (cbrt K))
2.0ms	(cbrt (cbrt K))
1.0ms	(cbrt (cbrt K))
720.0ms	(cos (- (/ (* (* (* (* (cbrt (cbrt K)) (cbrt (cbrt K))) (cbrt (cbrt K))) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series841.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (cbrt K))
240.0ms	(cbrt (cbrt K))
245.0ms	(cbrt (cbrt K))
111.0ms	(cos (- (/ (* (* (* (* (cbrt (cbrt K)) (cbrt (cbrt K))) (cbrt (cbrt K))) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify61.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	129	526
1	274	476
2	751	470
3	2244	470
4	5001	470

prune390.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

regimes291.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

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

604.0ms	8115×	body	80	valid
51.0ms	113×	body	1280	valid
51.0ms	165×	body	640	valid
24.0ms	106×	body	320	valid
9.0ms	57×	body	160	valid
4.0ms	5×	body	2560	valid