Details

sample45.0ms

Algorithm

intervals

Results

25.0ms	261×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify47.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 17.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

18.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
13.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series363.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
175.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify41.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	370	612
1	1331	556
2	5001	548

prune280.0ms

Filtered

79 candidates to 55 candidates (69.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 1.2b

Counts

80 → 5

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity` `add-log-exp`
5×	`exp-prod`
4×	`sum-log` `distribute-lft-out`
3×	`add-sqr-sqrt` `add-cube-cbrt` `rem-exp-log`
2×	`pow1` `add-exp-log` `associate-+r-` `associate-+r+` `diff-log` `add-cbrt-cube` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3-+` `exp-diff` `exp-sum` `flip-+`

Counts

2 → 34

Calls

2 calls:

18.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series289.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
177.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify80.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	213	414
1	691	379
2	3418	370
3	5002	364

prune120.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	40	5	45

Merged error: 1.2b

Counts

45 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite29.0ms

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:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series307.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify130.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 6 (124.0ms)

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

prune273.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	52	6	58

Merged error: 1.2b

Counts

58 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.1b	(pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3)
15.5b	(cbrt (pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
16×	`cbrt-prod`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
10×	`unpow-prod-down` `cube-prod`
9×	`distribute-lft-out`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `associate-r` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+`
2×	`cube-mult` `cbrt-div` `cos-sum` `unpow3` `associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* K (+ m n))
18.0ms	(pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3)
18.0ms	(cbrt (pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series5.0s

Counts

4 → 12

Calls

4 calls:

25.0ms	(* K (+ m n))
4.8s	(pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3)
181.0ms	(cbrt (pow (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))) 3))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify59.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	444	1040
1	1764	957
2	5002	951

prune310.0ms

Filtered

101 candidates to 58 candidates (57.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	101	6	107

Merged error: 1.2b

Counts

107 → 6

regimes228.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

816.0ms	8136×	body	80	valid
70.0ms	121×	body	1280	valid
58.0ms	140×	body	640	valid
31.0ms	103×	body	320	valid
11.0ms	52×	body	160	valid
3.0ms	3×	body	2560	valid