Details

sample57.0ms

Algorithm

intervals

Results

33.0ms	253×	body	80	valid
4.0ms	7×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

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: 15.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

9.0ms	(* K (+ m n))
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.0s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
17.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series454.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* K (+ m n))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
118.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify41.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	437	613
1	1474	567
2	5001	562

prune361.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize15.0ms

Local error

Found 3 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)
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

546.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
30.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
995.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series557.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
118.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	356	720
1	1112	675
2	5002	670

prune254.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize16.0ms

Local error

Found 3 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)
0.0b	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite914.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

547.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
332.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series573.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
133.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	408	825
1	1316	789
2	5001	784

prune274.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite731.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
22×	`pow-unpow`
18×	`unpow-prod-down`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
8×	`pow1` `add-exp-log`
6×	`unpow-prod-up` `pow-exp` `difference-of-squares`
4×	`pow-to-exp` `pow-pow` `distribute-rgt-neg-in` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sub-neg` `e-exp-1` `times-frac` `associate--r-` `pow-sub`

Counts

4 → 94

Calls

4 calls:

30.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
332.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
333.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series785.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
132.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
135.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	323	1040
1	997	1008
2	4332	988
3	5001	980

prune447.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

regimes250.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	27	23
2	27	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s	8058×	body	80	valid
85.0ms	143×	body	1280	valid
58.0ms	143×	body	640	valid
33.0ms	112×	body	320	valid
9.0ms	40×	body	160	valid
3.0ms	4×	body	2560	valid