Details

sample61.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

33.0ms	263×	body	80	valid
3.0ms	7×	body	640	valid
2.0ms	4×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

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

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 15.9b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`add-log-exp`
13×	`add-sqr-sqrt`
12×	`diff-log` `distribute-lft-out--`
8×	`exp-prod`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`sub-neg` `distribute-rgt-neg-in` `associate-r` `neg-log`
3×	`associate-l` `exp-sum`
2×	`cos-sum` `associate-*r/` `associate--r+` `associate--r-` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `distribute-lft-in` `flip3-+` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* K (+ m n))
20.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
24.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series123.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* K (+ m n))
39.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
57.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	393	762
1	1362	694
2	5002	690

prune186.0ms

Filtered

61 candidates to 93 candidates (-52.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	5	95

Merged error: 1.2b

Counts

95 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite56.0ms

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:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
21.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series137.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
43.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
54.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	386	730
1	1179	685
2	5002	677

prune160.0ms

Filtered

51 candidates to 77 candidates (-51.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Merged error: 1.2b

Counts

82 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
37×	`add-log-exp`
24×	`exp-prod`
18×	`diff-log` `distribute-lft-out--`
15×	`rem-exp-log`
14×	`add-sqr-sqrt`
12×	`exp-sum`
8×	`add-cube-cbrt`
6×	`cbrt-prod` `distribute-rgt-neg-in` `neg-log`
4×	`pow1` `add-exp-log` `sub-neg` `exp-diff` `add-cbrt-cube` `associate--r-`
3×	`difference-of-squares`
1×	`cbrt-div` `pow1/3`

Counts

4 → 87

Calls

4 calls:

20.0ms	(cbrt (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
21.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
23.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
21.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
54.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
55.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
57.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	225	1058
1	625	975
2	2674	964
3	5001	954

prune334.0ms

Filtered

71 candidates to 99 candidates (-39.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Merged error: 1.2b

Counts

105 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
33.7b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
18.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series120.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (+ m n))
33.0ms	(cbrt (+ m n))
30.0ms	(cbrt (+ m n))
28.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify161.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	207	539
1	429	499
2	1164	478
3	4632	454
4	5001	454

prune135.0ms

Filtered

53 candidates to 64 candidates (-20.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	63	7	70

Merged error: 1.1b

Counts

70 → 7

regimes503.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	35
1	27	35
2	27	35

end0.0ms

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

918.0ms	8091×	body	80	valid
82.0ms	128×	body	1280	valid
67.0ms	141×	body	640	valid
36.0ms	97×	body	320	valid
11.0ms	51×	body	160	valid
4.0ms	4×	body	2560	valid

Details

sample61.0ms

simplify48.0ms

prune17.0ms

localize24.0ms

rewrite60.0ms

series123.0ms

simplify43.0ms

prune186.0ms

localize15.0ms

rewrite56.0ms

series137.0ms

simplify40.0ms

prune160.0ms

localize20.0ms

rewrite88.0ms

series261.0ms

simplify71.0ms

prune334.0ms

localize28.0ms

rewrite27.0ms

series120.0ms

simplify161.0ms

prune135.0ms

regimes503.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

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