Details

sample8.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.683594%

Guaranteed chance to sample good point: 29.20354%

Results

27.0ms	251×	body	80	valid
2.0ms	4×	body	1280	invalid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	640	valid
1.0ms	5×	body	80	invalid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	invalid

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

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 15.7b

Counts

2 → 1

localize21.0ms

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)
36.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite52.0ms

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:

25.0ms	(/ (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))

series259.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (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))
38.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	527	1267
1	1894	1177
2	5001	1177

prune224.0ms

Filtered

74 candidates to 99 candidates (-33.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	5	100

Merged error: 1.1b

Counts

100 → 5

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

10.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	170	174
1	470	169
2	1593	165
3	5002	157

prune65.0ms

Filtered

17 candidates to 23 candidates (-35.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Merged error: 1.1b

Counts

28 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (* K (+ m n)))
16.5b	(cbrt (* K (+ m n)))
16.5b	(cbrt (* K (+ m n)))
36.1b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series104.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (* K (+ m n)))
27.0ms	(cbrt (* K (+ m n)))
27.0ms	(cbrt (* K (+ m n)))
22.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify64.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	186	514
1	386	464
2	918	446
3	2313	434
4	5001	407

prune153.0ms

Filtered

49 candidates to 55 candidates (-12.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	53	7	60

Merged error: 1.0b

Counts

60 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (* K (+ m n)))
16.5b	(cbrt (* K (+ m n)))
16.5b	(cbrt (* K (+ m n)))
36.1b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series104.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (* K (+ m n)))
30.0ms	(cbrt (* K (+ m n)))
27.0ms	(cbrt (* K (+ m n)))
20.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify65.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	186	514
1	386	464
2	918	446
3	2313	434
4	5001	407

prune136.0ms

Filtered

50 candidates to 55 candidates (-10.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	55	7	62

Merged error: 1.0b

Counts

62 → 7

regimes484.0ms

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	20	10
1	20	10

end0.0ms

sample9.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.683594%

Guaranteed chance to sample good point: 29.20354%

Results

888.0ms	7829×	body	80	valid
53.0ms	90×	body	1280	invalid
39.0ms	77×	body	640	invalid
33.0ms	72×	body	640	valid
25.0ms	39×	body	1280	valid
23.0ms	215×	body	80	invalid
22.0ms	69×	body	320	invalid
13.0ms	38×	body	320	valid
8.0ms	37×	body	160	invalid
5.0ms	22×	body	160	valid

Details

sample8.1s

simplify49.0ms

prune16.0ms

localize21.0ms

rewrite52.0ms

series259.0ms

simplify55.0ms

prune224.0ms

localize13.0ms

rewrite10.0ms

series41.0ms

simplify46.0ms

prune65.0ms

localize25.0ms

rewrite24.0ms

series104.0ms

simplify64.0ms

prune153.0ms

localize32.0ms

rewrite24.0ms

series104.0ms

simplify65.0ms

prune136.0ms

regimes484.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.9s

Profiling