Details

sample47.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
2.0ms	5×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	160	valid

simplify48.0ms

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: 17.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down`
4×	`cos-sum` `associate-r` `exp-sum` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `associate-l` `associate-/l*`
2×	`sub-neg` `div-sub` `associate-*r/` `difference-of-squares`
1×	`cbrt-undiv` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `frac-2neg` `distribute-lft-in` `flip3-+` `exp-diff` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

26.0ms	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series702.0ms

Counts

4 → 12

Calls

4 calls:

376.0ms	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
24.0ms	(* K (+ m n))
248.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	500	1257
1	1828	1167
2	5001	1167

prune356.0ms

Filtered

99 candidates to 74 candidates (74.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Merged error: 1.6b

Counts

100 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-log-exp`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `associate-+r+` `diff-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `pow-pow` `flip3-+` `times-frac` `pow-exp` `flip--` `flip-+` `sqr-pow`

Counts

3 → 51

Calls

3 calls:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
3.0ms	(- l (fabs (- m n)))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series437.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
17.0ms	(- l (fabs (- m n)))
254.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	294	456
1	798	439
2	3064	434
3	5001	431

prune172.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Merged error: 1.6b

Counts

66 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite26.0ms

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))
16.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series479.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ m n))
126.0ms	(cbrt (+ m n))
132.0ms	(cbrt (+ m n))
98.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify176.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (165.0ms)

Iter	Nodes	Cost
0	186	485
1	416	445
2	1213	439
3	4532	439
4	5001	433

prune308.0ms

Filtered

64 candidates to 52 candidates (81.3%)

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: 1.6b

Counts

70 → 7

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `cbrt-div` `cos-sum` `pow1/3` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `pow-exp` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3))
5.0ms	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
29.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series479.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ m n))
97.0ms	(cbrt (pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3))
160.0ms	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
96.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify164.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	1180
1	803	1102
2	4265	1094
3	5001	1094

prune281.0ms

Filtered

80 candidates to 50 candidates (62.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	80	7	87

Merged error: 1.6b

Counts

87 → 7

regimes285.0ms

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	20	10
1	20	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

799.0ms	8071×	body	80	valid
76.0ms	173×	body	640	valid
72.0ms	122×	body	1280	valid
40.0ms	125×	body	320	valid
13.0ms	64×	body	160	valid
4.0ms	4×	body	2560	valid

Details

sample47.0ms

simplify48.0ms

prune9.0ms

localize26.0ms

rewrite54.0ms

series702.0ms

simplify53.0ms

prune356.0ms

localize14.0ms

rewrite31.0ms

series437.0ms

simplify81.0ms

prune172.0ms

localize29.0ms

rewrite26.0ms

series479.0ms

simplify176.0ms

prune308.0ms

localize42.0ms

rewrite44.0ms

series479.0ms

simplify164.0ms

prune281.0ms

regimes285.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling