Details

sample56.0ms

Algorithm

intervals

Results

27.0ms	259×	body	80	valid
4.0ms	7×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	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

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.4b

Counts

2 → 1

localize23.0ms

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	(pow (- (/ (+ m n) 2.0) M) 2.0)
31.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

8.0ms	(* K (+ m n))
20.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series111.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* K (+ m n))
45.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
39.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	465	677
1	1514	631
2	5002	627

prune178.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 1.2b

Counts

90 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

22.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
39.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	307	479
1	865	454
2	3603	442
3	5001	439

prune99.0ms

Filtered

34 candidates to 50 candidates (-47.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Merged error: 1.2b

Counts

54 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* K (+ m n)))
16.3b	(cbrt (* K (+ m n)))
16.3b	(cbrt (* K (+ m n)))
30.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite23.0ms

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)))
4.0ms	(cbrt (* K (+ m n)))
9.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series109.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (* K (+ m n)))
31.0ms	(cbrt (* K (+ m n)))
28.0ms	(cbrt (* K (+ m n)))
22.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (57.0ms)

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

prune147.0ms

Filtered

49 candidates to 55 candidates (-12.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	54	6	60

Merged error: 1.2b

Counts

60 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* K (+ m n)))
30.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
30.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
30.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

4.0ms	(cbrt (* K (+ m n)))
11.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
9.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series94.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (* K (+ m n)))
21.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
21.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))
21.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify65.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	186	854
1	386	760
2	918	754
3	2313	750
4	5001	741

prune179.0ms

Filtered

46 candidates to 53 candidates (-15.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	53	6	59

Merged error: 1.2b

Counts

59 → 6

regimes449.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

861.0ms	8131×	body	80	valid
70.0ms	158×	body	640	valid
64.0ms	107×	body	1280	valid
29.0ms	94×	body	320	valid
11.0ms	53×	body	160	valid
4.0ms	4×	body	2560	valid

Details

sample56.0ms

simplify49.0ms

prune16.0ms

localize23.0ms

rewrite48.0ms

series111.0ms

simplify43.0ms

prune178.0ms

localize15.0ms

rewrite33.0ms

series81.0ms

simplify85.0ms

prune99.0ms

localize30.0ms

rewrite23.0ms

series109.0ms

simplify63.0ms

prune147.0ms

localize35.0ms

rewrite35.0ms

series94.0ms

simplify65.0ms

prune179.0ms

regimes449.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling